## Abstract

We use a spatial autoregressive model with directional effects to assess the impact of airport noise on housing values in Memphis, Tennessee, home of the busiest cargo airport in the United States. Our model is combined with a spatial dataset that contains information on noise levels, property characteristics, and neighborhood characteristics for 9,606 properties sold between 2011 and 2016. Results of our research suggest that the Memphis International Airport is perceived as a disamenity, with areas of the city affected to different degrees, with a potential average external cost of $4,795 per decibel of noise per household. *(JEL C31, D62)*

In Southlake, [Texas,] an entirely new model for building an affluent community has been put into practice. Wealthy individuals and companies began coming in for the logistical connectivity proximity to the airport offered, which caused a socio-economic snowball effect where the influx of money raised the profiles of schools and other public amenities, which in turn attracted more wealthy individuals and companies. The result was one of the most wealthy places in the country right outside the gates of a major airport—a direct about-face from how this story usually goes.

—Shepard (2016)

## 1. Introduction

Conventional wisdom considers a major airport to be a real estate nightmare, much like a landfill or chemical plant, with the surrounding households perpetually complaining about the roar of the aircraft overhead (Shepard 2016). As a result, the traditional American model has been to locate these hubs on the outskirts of cities. This tradition is supported by academic research dating back at least to Nelson (1979), who provides empirical evidence of significant property depreciation due to airport noise suffered by households located within two to three miles of an airport. More recently, following the growing practice of cities in Asia and the Middle East, major airports in the United States are being viewed as magnets for residents and businesses, given how critical they are to modern business infrastructure (Shepard 2016, 3).^{1} In fact, Kasarda and Lindsay (2011) argue that close proximity to major airports will be critical for companies in the twenty-first-century global economy. Their assertion is supported by a recent report by Stilwell and Hansman (2013) indicating that 50% of Fortune 500 companies in the United States are now located within 10 miles of a hub airport (Shepard 2016).

Traditional models and recent trends are at odds regarding the benefits of airport proximity, and academic research has yet to thoroughly explore the competing considerations. To address this void in the literature, this study examines the impact of airport noise on housing prices in Memphis, Tennessee, in order to discern whether airport proximity is an amenity, consistent with recent trends, or a disamenity, as in the traditional model. The Memphis case is compelling given that it is the headquarters of three Fortune 500 companies: FedEx Corporation, International Paper, and AutoZone. The first of these, FedEx, is a global shipping company employing more than 400,000 people worldwide.^{2} It is also the largest private employer in Memphis, with 30,000 local employees. The remaining two companies, International Paper and AutoZone, together employ about 4,500 workers.^{3} Clearly, easy access to the Memphis International Airport—the busiest cargo airport in the United States—is important to a sizable portion of Memphis residents.

Empirical results presented in this study are unique in that they come from a spatial autoregressive model with directional effects that are estimated using a spatial dataset containing information on noise levels, property characteristics, and neighborhood characteristics for 9,606 properties sold between 2011 and 2016 in Memphis. In addition, we construct a proxy for aircraft noise based on the interaction of the city sound pressure level and property distance from the airport that is assumed to follow the Weber-Fechner law of perceived stimuli (i.e., a logarithmic inverse law based on acoustic physics). We note that in certain areas close to the airport other noise in the environment may confound or mitigate the impact of aircraft noise. We find that aircraft noise is capitalized in residential property values with an average external cost that is approximately $4,795 per decibel of noise per household.

## 2. Prior Literature: A Brief Review

Several studies in the medical literature find evidence of harm associated with noise. For example, noise exposure has been associated with increased risk of hearing impairment and poor school performance (Passchier-Vermeer and Passchier 2000). In addition, there is evidence of aircraft noise being associated with hypertension (Rosenlund et al. 2001) and cardiovascular disease (Correia et al. 2013). In light of these findings, the U.S. Congress passed the Airport Noise and Capacity Act of 1990 as an amendment to the previous Aviation Safety and Noise Abatement Act of 1979, which provides $3.35 billion each fiscal year (from to 2012 through 2017) in grants to be used, in part, to soundproof residential properties affected by aircraft noise.^{4}

In addition, there is a considerable literature in urban and environmental economics that aims to determine whether and to what extent air traffic noise impacts the value of residential properties. An early study by Gautrin (1975) uses a modified Möhring model to evaluate the impact of air traffic noise from London’s Heathrow Airport on land rent. That study finds approximately a 5% depreciation per property in areas adjacent to the airport when compared to similar properties located in quiet areas. In the United States, Nelson’s (1979) pioneering research uses a more robust empirical approach based on hedonic analyses for different distance radii from the closest airport for six selected locations. Nelson (1979) finds a potential property depreciation of 0.48% per forecast decibel of noise exposure within two to three miles of the airport. A meta-analysis by Nelson (2004), based on 33 studies using hedonic models to measure the noise discount on properties in North America, leads to the conclusion that differences in findings about the impact of noise on property values are due mainly to the country of origin of the study (United States vs. Canada) and the model specification (linear vs. logarithmic functional form). The author finds that studies using logarithmic models conducted in Canada estimate a higher noise depreciation index in comparison to studies conducted in the United States.

More recently, McMillen (2004) estimates a hedonic model of property values to estimate the impact of the Chicago O’Hare Airport expansion. The model includes a binary variable that captures aircraft noise exposure. McMillan (2004) argues that because modern aircraft engines are quieter, airport expansion could increase property values in densely populated areas near the airport. Dekkers and Straaten (2009) reach the opposite conclusion for the case of Amsterdam’s Schiphol Airport. They add a spatial component to their hedonic model and find a total social benefit of €574 million per decibel reduction in aircraft noise pollution. These opposing findings support Nelson’s claim that geographic location and model specification affect the conclusions reached in empirical work, implying that future investigations use multiple approaches including GIS analyses, contingent valuation, and hedonic models allowing for spatial correlation (Nelson 2004, 21).

In particular, the omission of spatial processes may lead to biased results (Anselin 1988; LeSage and Pace 2009). The importance of spatial effects is highlighted in the work by Cohen and Coughlin (2008). These authors find a spatial spillover effect that amplifies the negative impact of aircraft noise pollution on the value of properties in proximity to the Hartsfield-Jackson International Airport in Atlanta (i.e., a 20.8% decrease in property values) due to spatially autocorrelated property prices. However, these authors also find an inelastic appreciation relationship between property value and distance to the airport, concluding that the airport, per se, could be perceived as an amenity by home buyers in the area.

Our study adds to empirical work in this area by focusing on the case of the Memphis International Airport in Tennessee that was, for many years, the busiest cargo airport in the world due in large part to the airport’s association with FedEx. FedEx is a global courier service provider headquartered in Memphis.^{5} Although the Memphis International Airport is no longer the world’s busiest cargo airport, it remains the busiest cargo airport in the United States.^{6} We examine the impact of proximity to the Memphis International Airport on property values.

There are several novel features of our study. First, we measure the impact on property values of increased proximity to the airport and airport noise (according to the inverse law of acoustic physics as perceived by consumers, based on the Weber-Fechner paradigm). Second, we estimate the extent to which other environmental noise of an anthropogenic nature could mask the airport noise. And third, we include directional effects in our spatial hedonic model to account for winds that may force planes to fly over some neighborhoods of the city and mitigate or amplify the aircraft noise. We believe that the inclusion of the directional effects is especially useful in helping policy makers identify areas needing interventions.

## 3. Empirical Model

Our empirical work is based on a traditional hedonic regression model we employ to estimate the capitalization of aircraft noise in property values. The theoretical background of the hedonic model is given by Rosen (1974) and Sheppard (1999). The theory of acoustic physics suggests that the sound pressure level of a sound wave (1 N/m^{2} = 1 pascal) is inversely related to the distance of the receptor from the sound source, *r*, such that *Pa* ~ 1/*r* (Rayleigh 1878). In addition, according to the Weber-Fechner law of psychophysics, physical stimuli, like sound waves, are logarithmically perceived by humans, in other words, perceived(*Pa*) ~ ln(1/*r*) (Fechner 1966). In an attempt to proxy airport noise, we use the distance of each housing unit from the FedEx hub, assuming that if the noise is capitalized in the property’s price, then the housing value declines with the airport proximity following the same inverse law of acoustics and psychophysics. Thus, we assume that the property value is affected by property and neighborhood attributes and also by environmental characteristics including background sound noise, population density, the logarithm of the inverse distance to the FedEx hub, and the property location with respect to the airport.

Our model is given by
[1]
where *y* is the sales price of property *i*; **x**_{i} is a row vector of housing and neighborhood attributes; *μ _{i}* is a level of background sound noise/non-point-source sound pollution, that is, city sound (in millipascals) associated with each property;

*r*is the distance of property

_{i}*i*from the airport;

*δ*is the population density per neighborhood;

*φ*(longitude) and

*λ*(latitude) are the geographic coordinates of each property in a reference system centered at the airport; and

*ε*is one element from a vector of spherical disturbances.

_{i}We include background noise for three reasons: (1) to reduce the bias from omitting information on sound noise from sources other than the airport, (2) to assess the property discount per unit increase of noise at different property locations from the airport (through the interaction of *μ* and ln(*r*^{–1})), and (3) to measure the home buyers’ propensity for noise avoidance. In fact, we believe that *μ* and *δ* are positively associated, and their interaction can be used to test the hypothesis that citizens who live in less densely populated areas farther away from the airport are less accustomed to sound noise and therefore more sensitive to the additional unit increase in the level of sound pressure. Therefore, we have
[2]
where we expect *γ*_{1} < 0 and, *γ*_{4} and *γ*_{5} > 0, with , *δ _{i}* and

*r*∈ ℝ

_{i}^{+}. In addition to its intuitive appeal, this relationship is supported by the results of a Dutch survey in which noise-sensitive people seek to live in less populated, more natural areas (Booi and van den Berg 2012; Goossen, Langers, and de Vries 2001).

Given that it is well known that sound travels with the wind (Ingård 1953), we believe that aircraft noise could either be propagated to longer distances (with the wind) or attenuated to shorter distances (against the wind). In addition, the wind may alter flight paths over the city. These are good reasons for including directional effects in the model. In order to do so, we convert the geographic coordinates of each property from Cartesian to polar, using a reference system centered at the airport location. This transformation allows us to include directional heterogeneities in distance profiles in our model, the omission of which could be a source of bias (see Cameron 2006). After including the directional effects, the hedonic price equation becomes
[3]
where *ϑ* is the direction of property *i* expressed in radians (counterclockwise from due east). If airport proximity is a determinant of the demand for housing in Memphis, then partially differentiating [3] with respect to the distance to the airport yields
[4]
where the change in housing price with respect to the distance from the airport depends on background noise and, nonlinearly, on distance and direction of the property from the airport. For example, moving from east to south (counterclockwise), for those properties that are located the same distance to the airport, the airport proximity effect will depend on the background noise at each location and the direction as follows: east, ; north, ; west, ; south, .

## 4. Data and Econometric Approach

Our sample consists of information on 9,606 individual property sales that occurred between 2011 and 2016, which we obtained from the Shelby County Assessor of Properties. Housing prices are deflated using the U.S. Bureau of Labor Statistics Housing Consumer Price Index (with 2016 as the base year). These data are merged with other census-tract-level demographic data obtained from the U.S. Census Bureau. This information is used to construct population density per census tract, percentage of African American households per census tract, percentage of Hispanic households per census tract, unemployment rate per census tract, median household income per census tract, and average commuting time per household per census tract.

To account for curvature of the earth, distances are calculated using the haversine formula, as outlined by Affuso, Cummings, and Le (2018). The proximity tools of the Esri ArcGIS software package^{7} were used to compute the distances of each housing unit from the closest major road (which includes interstate, U.S., and state highways), the Mississippi River, and four major open space areas (Shelby Farms Park, Memphis Botanic Garden, Overton Park, and T. O. Fuller State Park). The azimuth of property *i* (*ϑ _{i}* expressed in radians) is calculated using the arctangent function with two arguments [(LAT

_{i}– LAT

_{airport}) and (LON

_{i}– LON

_{airport})]. To capture city sound, we use the sound pressure level of a typical summer day.

^{8}A georeferenced soundscape map containing this sound pressure level for the continental United States has been developed by Mennitt et al. (2013), who constructed a geospatial sound model based on the machine learning algorithm of Breiman (2001).

^{9}

Figure 1 illustrates the soundscape of Shelby County, Tennessee. The noisiest areas are in proximity to Memphis International Airport, the major roads, and the densely populated areas (which are indicated in Figure 2).

Next, Table 1 reports the descriptions and summary statistics for the variables used in the hedonic model. Our model also includes year and zip code dummy variables to capture unobserved dynamic economic processes that could affect the housing price and other unobserved neighborhood heterogeneities at a higher scale as done by Caudill, Affuso, and Yang (2015). Consistent with the literature, we express the dependent variable (property value) in logarithmic form in order to assess the home buyers’ sensitivity to sound noise and airport proximity. We use the Akaike information criterion (AIC) to assess several model specifications and choose the one with the minimum loss of information (i.e., the lowest AIC value). This resulted in a model including the age of the property (AGE) in quadratic form and the following regressors in logarithmic form: SFLA (square footage of living area), ACRES (lot size in acres), MEDHHINC (median income of household per census tract), and POPDENSITY (population density per census tract expressed in inhabitants per square mile). Along the same lines, given the nonlinearity of the decibel scale, the background noise of the city has been converted into millipascals.^{10}

Based on Tobler’s first law of geography, housing data are assumed to be spatially interdependent. Hence, we investigated this assumption using Moran’s *I* test^{11} and the robust Lagrangian multiplier statistic, as outlined by Anselin et al. (1996), on the following econometric model:
[5]
where **y** is a vector of property prices in logarithmic form. Additionally, *ρ* is a scalar coefficient of spatial correlation, **W** is a row-standardized spatial contiguity matrix in sparse form based on the three closest neighbors, as presented by Caudill, Affuso, and Yang (2015), **X** is a data matrix, **β** is a vector of 71 parameters, **I** is an identity matrix, *λ* is a scalar coefficient of spatial correlation in the residuals, and **u** is a vector of spherical disturbances.^{12}

As expected, the results of Moran’s *I* test indicated rejection of the null hypothesis of no spatial correlation.^{13} In addition, the robust Lagrangian multiplier statistic indicated rejection of the spatial error model (*ρ* = 0 and *λ* ≠ 0) in favor of the spatial autoregressive model (*ρ* ≠ 0 and *λ* = 0).^{14} Therefore, we estimated the values of *ρ*, **β**, and the standard error, *σ*, using a nonlinear unconstrained numerical optimization procedure to maximize the following log-likelihood function:
[6]
where *N* = 9,606 is the sample size, and **u** = (**I** – *ρ***W**)**y** –**Xβ** and ln|**I** – *ρ***W**| are the terms of the log-Jacobian transformation of **u** into **y**.

Failing to account for spatial dependence causes severe statistical and economic consequences. For example, ordinary least squares estimators are biased in the presence of spatial correlation of the dependent variable. In addition, accounting for this correlation using a spatial autoregressive hedonic model allows one to disentangle the direct and indirect effects of disamenities on housing prices (see LeSage and Pace 2009).

To illustrate the indirect effect, assume there are two neighbors, *i* and *j*, with household *j* being potentially protected by soundproof materials that would mitigate the impact of sound pollution. The property value *j* would still be affected by airport noise (indirectly) because there exists a spatial spillover effect due to the value of property *i* (affected by aircraft noise) that could potentially impact the value of property *j* (i.e., ∂ln(*Price*)_{i} / *∂r _{j}* ≠ 0 with

*i*≠

*j*). LeSage and Pace (2009) derive formulae for decomposing these effects: the average direct effect is

*N*

^{–1}Tr[(

**I**–

*ρ*

**W**)

^{–1}

**I**

*β*], the average indirect effect is

_{k}*N*

^{–1}{

**1′**

_{N}[(

**I**–

*ρ*

**W**)

^{–1}

**I**

*β*]

_{k}**1**

_{N}– Tr[(

**I**–

*ρ*

**W**)

^{–1}

**I**

*β*]}, and the average total effect impact is

_{k}*N*

^{–1}

**1′**

_{N}[(

**I**–

*ρ*

**W)**

^{–1}

**I**

*β*]

_{k}**1**

_{N}for each predictor

*β*with

_{k}*k*= 1, 2, … , 71 and

*N*= 9,606.

A pitfall of spatial regressive models is their inability to fully disentangle the spatial correlation between the dependent variable and the error term, which may lead to endogeneity that could be severe if the data generating process (hence **W**^{15}) is unknown (Gibbons and Overman 2012). Von Graevenitz and Panduro (2015) suggest using a spatial generalized additive model (GAM) to mitigate the detrimental impact of omitting spatial processes. A spatial GAM is essentially a linear regression that includes nonparametric smoothing functions of the geographic coordinates of each property unit that enter the model as penalized regression splines. Following Von Graevenitz and Panduro (2015), we estimate the GAM model using the *mgcv* library developed by Wood (2006) (available in the R statistical package) using 40 basis functions for the spline based on a rule of thumb provided by Ruppert (2002).^{16}

## 5. Results and Discussion

We estimate four spatial autoregressive hedonic models: (1) an unrestricted model (Model I), (2) a restricted model without the airport effect and its interaction with the city soundscape (Model II), (3) a restricted model without directional effects (Model III), and, finally, (4) a restricted model without population density and its interaction with city soundscape (Model IV).

In Table 2 we report maximum likelihood estimates for the four spatial autoregressive models, along with ordinary least squares estimates (which omit the spatial processes) and maximum likelihood estimates from the GAM model for comparison. In terms of the AIC, ordinary least squares is the worst performer, as expected (largest AIC = 14,272), followed by the GAM (AIC = 14,066). The parameter estimates and relative *z*-statistics of the spatial GAM and Model I are of similar magnitude except for the coefficients of the directional effects. As the directional effects are the geographic coordinates *ϕ* and *λ* of each property in a polar reference system centered at the airport (see equation [1]), they are very likely correlated with the spatial GAM smoothing functions (s(LON) and s(LAT)), thus inducing multicollinearity. To investigate this issue we perform a diagnostic analysis of the concurvity measures of the GAM (dependence among parameter and smoothing functions, i.e., **β** ~ s(LON) ~ s(LAT)), and we find that the three estimated concurvity measures span between 0.976 and 0.999, suggesting almost perfect collinearity. In addition, the computation of the relative likelihood^{17} between the two models suggests that the spatial GAM is 4.15 × 10^{–18} times as likely as Model I to minimize the information loss. Given these findings, we focus our analysis on the spatial autoregressive models; but before turning to the individual results, we compare the restricted spatial autoregressive models to the unrestricted version, Model I.

Model II imposes four zero restrictions on Model I; variable omissions include the logarithmic inverse distance (log(*r*^{–1})), its interaction term with the city background noise (*μ*⋅log(*r*^{–1})), and the geographic location of each property with respect to the FedEx hub. These restrictions were imposed to test the research question of the current study according to the null hypothesis, *H*_{0}: home buyers in Memphis are not sensitive to aircraft and airport noise. The likelihood ratio test rejects the four imposed restrictions (Λ = 31.5) with 99% confidence. Hence, home buyers are sensitive to aircraft noise, and Model I (which includes the interaction city noise/distance to airport) is preferred to Model II.

In Model III we impose restrictions on directional effects being simultaneously equal to zero (*H*_{0}: the relationship between aircraft noise and property price depends only on the distance to the airport regardless of the property’s location). This hypothesis is rejected with 95% confidence, because the log-likelihood ratio statistic (Λ = 7.67) exceeds the appropriate critical value.

Finally, Model IV imposes two zero restrictions on Model I, which are the coefficients of population density (log(POPDENSITY)) and its interaction with city sound (*μ*·log(POPDENSITY)). These restrictions imply that home buyers are either not sensitive to sound pollution or they are all equally sensitive to sound pollution. The likelihood ratio test indicates that the null hypothesis that the coefficients of population density and its interaction with city sound are both zero can be rejected (Λ = 18.01) with 99% confidence. Hence, Model I is preferred to Model III and Model IV. Based on these test results we focus our discussion of the results on Model I.

In terms of the individual effects, the parameter estimates of housing and neighborhood characteristics have the expected signs and are generally statistically significant at the 95% and 99% confidence levels. As expected, total square feet (SFLA), the number of fixtures (FIXTOT), and lot size (ACRES) all contribute positively and significantly to the price of a given property. Similarly, the presence of central heating (CENTRALHEAT*), a fireplace (FP*), and a brick construction (BRICK*) also contribute, ceteris paribus, to significantly higher property prices, as expected. Additionally, electric heating (ELECTRICFUEL*) is associated with significantly higher property prices. On the other hand, the number of floors (STORIES) and townhouses (TOWNHOUSE) are, as expected, all negatively and significantly related to the price of a particular property, ceteris paribus, and there is a significant U-shaped relationship between the value of the house and its age. Our results also indicate that the condition of a house is economically significant. In fact, a house in poor condition is discounted approximately 23.31% compared to a house in average condition, while a house in good condition is appreciated only by 13.75% compared to a similar house in average condition.^{18}

In addition, a 10% increase in the median income of the household in a census tract corresponds to a 1.23% appreciation in the property’s value. As expected, the Memphis housing market experienced the subprime mortgage crisis and the economic recession of 2008–2013. In 2012 a property lost 4.85% of its real value compared to the previous year. The last year of the economic recession (2013) a property gained, on average, 0.361% compared to the previous year; in 2014 and 2015, the property appreciated by approximately 7.88% and 0.66% compared to the previous year. In 2016, the average price of a property declined by 12.07% compared to 2015 (i.e., 8.02% compared to the base year 2011). These results are statistically significant at the 90%, 95%, and 99% confidence level. As expected we find a negative and significant relationship between property value and commuting time. In fact, at the average household commuting time of 22 minutes and 37 seconds, a home buyer is willing to pay an additional 0.6% in property value for a 1-minute decrease in travel time. In monetary terms, the marginal opportunity cost of commuting (in 2016 dollars) for a household in Shelby county is, on average, $1,035 per minute per household per day over the entire six year period between 2011 and 2016.

We now turn our attention to the issue of housing location and the noise externality. First, we note that access to main roads (i.e., dist2road) is neither economically significant nor statistically different from zero. However, open space proximity is perceived as an externality with a property appreciation of 1.1% per 1 km increase in distance (95% confidence). As expected, a negative and significant (1%*α*-level) relationship exists between property value and proximity to the central business district (i.e., downtown Memphis). In fact, a household would be willing to pay a premium of 14% of the average property value to live 1 km closer to downtown Memphis. On the contrary, the Mississippi riverfront is perceived as a disamenity. The latter result is consistent with the fact that downtown Memphis is on the river and desirable, but some other locales on the riverfront lack the security and amenities of the downtown area and instead come with increased flood risk.

The analysis of city sound sensitivity of home buyers involves using information from the parameter estimates of the sound pressure level (L50(*μ*)), the logarithmic inverse distance to the airport (log(*r*^{–1})), population density (log(POPDENSITY)), and their respective interactions. The sign of L50(*μ*) is negative, as expected, and statistically significant, as is the parameter estimate of the interaction between *μ* and the acoustic inverse distance. However, the parameter estimates of log(*r*^{–1}), log(POPDENSITY), and the interaction of the latter with *μ* are not statistically different from zero. Although rejecting the restrictions imposed in Model II and Model IV suggests that these parameters are jointly statistically significant and should be included in the model, we perform an additional likelihood ratio test for the joint significance of city sound (*μ*), airport proximity (log(*r*^{–1})), population density (log(POPDENSITY)), interactions of the latter two variables with city sound and directional effects (i.e., imposing seven restrictions). The likelihood ratio statistic for this test is Λ = 76.1, which is greater than the critical *χ*^{2}_{7df} of 18.48 for the 99% confidence level. Therefore, rejecting this restriction implies that a model including the acoustic, demographic, and geographic measures and their interactions with the sound pressure level, L50(*μ*), is preferred.

Next, we use the result of [2] above, multiplied by 100, to calculate the city sound semielasticity of property value. We evaluate the impact of a 1 mPa increase in the sound of the city on the percentage change in property value at different values of distance from the airport and different quantiles of the population density. We also convert the semielasticity into a decibel scale^{19} and compute the standard errors of the semielasticity using the delta method. We do not report direct and indirect spatial effects of the estimated elasticities given that we determined that the first represents 81.55% of the total impact and the latter only 18.45%. Therefore, we focus our analysis on the total impact. According to the calculated semielasticities reported in Table 3, a property located at an average distance of 18.21 km from the airport in an area that is, on average, densely populated (1,125 inhabitants/km^{2}), will lose 2.36% of its value per 1dB increase in the city noise. Consistent with our expectations, we find that home buyers who live in more isolated areas are more sensitive to sound pollution. In fact, at the minimum value of the population density variable (i.e., 26 inhabitants/km^{2}), home buyers would be willing to pay 3.23% more for a 1 dB noise reduction. At the other end of the spectrum, in densely populated areas (i.e., 4,560 inhabitants/km^{2}), property owners become less sensitive to noise pollution and are willing to pay only 2.03% for a 1 dB noise reduction. This relationship is depicted in the graph in Appendix Figure A1.

The most important result of our study, in line with our research question, is that home buyers located in proximity to the airport are willing to pay an additional premium for the same decibel reduction. In fact, properties located 2.5 km from the airport in an area with average population density are discounted by 7.26% for each 1 dB increase in the noise level. It should be pointed out that the semielasticity derived from [2] is point based and depends on each property’s location as well as on the population density at that location. Therefore, a better picture of the airport noise externality is provided by the thematic map, which is based on the geographic distribution of the semielasticity reported in Figure 3.

Consistent with previous research, we find that an increase in sound noise is perceived as an external cost that is capitalized in the value of the property across the entire observed sample. The average potential external cost of aircraft noise in Memphis between 2011 and 2016 is as high as $4,795 per mPa/household.^{20}

After assessing the potential external cost of aircraft noise conditional on distance to the airport and population density, we turn our attention to the impact of airport proximity on house values in an attempt to assess the home buyers’ perception of the airport itself as the major source of externality. We calculate the airport proximity elasticity of property value through logarithmic differentiation of the estimated model according to the following formula:
[7]
to obtain the direct impact of a 1% increase in the distance to the airport on the percentage change in value of property *i* (LeSage and Pace 2009, 36). It should be restated that, given the nonlinear psychophysical relationship between property value and distance to the airport, this point-based elasticity depends on the distance itself, the direction of the property from the airport, and the level of background noise at each property location. Therefore, we use [7] to estimate the airport sensitivity of each home buyer in the sample and display the geographic behavior of the elasticity in the map given in Appendix Figure A2.

Homeowners located west of the airport perceive the airport as a disamenity. Particularly, those in the northwestern quadrant. Moving eastward, the negative perception declines and becomes positive for those properties located over 20 km east of the airport. In Table 4 we report the elasticity of airport proximity (average total impact) evaluated at 2.5 km, 5 km, 10 km, and 18.21 km (i.e., the sample average) distance from the Memphis airport and at the minimum (1.53 mPa), average (6.61 mPa), and maximum (13.36 mPa) sound pressure level of the city background noise. However, to the southeast and south, the elasticity is available only for properties in proximity to the airport, because in these directions there are no properties beyond 5.74 km from the airport; similarly, to the west and southwest, toward the Mississippi River, there are no properties beyond 13.59 km.

As expected, the negative perception of the airport increases as the sound pressure level increases. In fact, the airport proximity elasticities are statistically equal to zero at the minimum value of the city sound pressure level for those properties located in the immediate airport proximity (2.5 km).

In general, homeowners located within 5 km southeast or east of the airport perceive the airport less negatively than those located to the northwest or west. Appendix Figure A3 summarizes the directional effects of home buyers’ sensitivity to airport proximity evaluated at 5 km distance from the airport at the average and maximum city sound pressure levels.

With the distance fixed at 5 km, at the average sound pressure level of city sound (6.61 mPa), the airport proximity elasticity becomes a univariate sinusoidal function with local maximum at *ϑ*^{max} = 2.753 rad (≈719/250*π*—slightly west of the northwest line), local minimum at *ϑ*^{min} = –0.389 rad (≈469/250*π*—slightly east of the southeast line), and two inflection points in the interval [0, 2*π*], at *ϑ*° = 1.181 rad (≈47/125*π*—slightly north of the northeast line) and *ϑ*° = –1.961 rad (≈172/125*π*—slightly east of the southwest line). Consequently, the directional elasticity is convex on [0, 47/125*π*] and [172/125*π*, 2*π*] and concave on [47/125*π*, 172/125*π*]. In behavioral terms, moving counterclockwise from due east, home buyers’ sensitivity to the airport first increases at an increasing rate toward the northeast, afterward increases at a decreasing rate to reach its maximum, afterward starts decreasing at a decreasing rate as we move toward the south/southwest. Beyond this point, the price sensitivity continues decreasing at an increasing rate, with minimum sensitivity reached between south and southeast of the airport. After this point, the airport sensitivity starts to increase again at a decreasing rate as one moves toward the east.

In further support of our rationale to include directional effects in the study of airport externalities, Appendix Figure A4 depicts the wind rose of Memphis based on data from the Western Regional Climate Center^{21} collected between January 1, 2011, and December 31, 2016. The figure shows a clear pattern of predominant winds blowing from the south. Predominant wind directions justify the orientation of the runaways of the airport that go from slightly east of the south line to slightly west of the north line. Takeoff and landing operations usually occur into the wind to facilitate lift to become airborne. Takeoff operations (with engine in full power) are usually noisier than landing, which could explain why in proximity to the airport (2.5 km ~ 5 km), the price of properties located northwest of the airport is more sensitive to the airport proximity (negatively affected) than those located south/southeast of the airport.

In general, our study supports findings in previous studies that an airport is perceived as a negative externality. However, our study indicates that home buyers’ sensitivity varies across the region due to different propensity to noise avoidance and other environmental factors that could mitigate some of the effects of aircraft noise.

Our study does not account for potential benefits provided by the airport itself in macroeconomic terms. For example, FedEx is the largest private employer in the Memphis metropolitan area, employing 30,000 workers, with 12,000 working at the FedEx Superhub in 2008 (Greater Memphis Chamber of Commerce 2017; Dunavant 2008).

Another limitation of our study is due to our inability to disentangle the noise produced by the takeoffs and landings from other environmental noise. However, our use of several proxies for homeowners’ propensity for noise avoidance and external cost of sound pollution at different locations from the airport should mitigate the bias that arises from being unable to disentangle aircraft noise from other noise.

We believe that the results of our study are useful for two important reasons. First, including directional effects should greatly reduce the bias arising from the modeling approach of previous studies that omitted this information. Second, the directional effects may assist policy makers in identifying geographic areas in proximity to airports that are particularly sensitive to noise avoidance and thus may guide the use of federal funding to protect consumers who are more subject to airport externalities.

## 6. Concluding Comments

Due to the exceedingly large number of FedEx flights in the area, aircraft noise is a fact of life in Memphis, Tennessee. In this study we examine the impact of noise on property values. We use spatial data on sound pressure (city sound) and housing data from Shelby County (Memphis) in Tennessee to estimate a spatial autoregressive model that allows for directional heterogeneity in the impact of noise on residential property prices. Our noise proxy is based on property distance to the airport and its interaction with city sound, according to the Weber-Fechner law of psychophysics. In addition, we include the interaction between population density and city noise to identify areas of the city that are less densely populated, possibly by home buyers who are more sensitive to noise.

We find that Memphis International Airport is perceived by the citizens as a negative externality, with areas of the cities affected to different degrees, and the average social cost of aircraft noise estimated to be approximately $4,795 per mPa of noise per household.

Our study contributes to the debate on whether proximity to an airport provides external benefits or costs. We find that it depends. We believe that the inclusion of the directional heterogeneities in the distance profiles represents an improvement on earlier work by mitigating the omitted directional information bias that is typical of previous studies. Policy makers should find our approach useful in identifying specific geographic areas around major airports that are affected by aircraft noise, which can help guide the use of federal funds provided by the Aviation Safety and Noise Abatement Act of 1979 in order to protect the associated households.

Lastly, given that Memphis International Airport is the country’s largest in terms of cargo shipments, comparison of the results presented in this study to those examining other airports that do not rank among the largest in terms of cargo may be problematic. Thus, future research might focus on airports such as the Ted Stevens Anchorage International Airport in Anchorage, Alaska. This particular facility handles almost 90% of the amount of tonnage that is shipped through Memphis, making it the most comparable airport to that in Memphis. Perhaps a more thorough understanding of the joint effect on residential prices of both convenience and noise associated with a major cargo airport could be gleaned from such a comparison.

## Acknowledgments

The authors thank two anonymous referees of this journal and Jim LeSage for helpful comments on a prior version. We also thank seminar participants at Tulane University and Florida Atlantic University for similarly helpful comments. Any remaining errors are our own.

## Footnotes

↵1 Southlake, Texas, is one of the wealthiest communities in the United States, with more than 70% of households earning more than $100,000 per year, and where the average house price exceeds $780,000 (Shepard 2016). Home to Sabre Holdings, the community of Southlake also sits only about 230 yards from Dallas–Ft. Worth International Airport (Shepard 2016).

↵2 See http://about.van.fedex.com/our-story/company-structure/corporate-fact-sheet/.

↵3 See http://www.memphischamber.com/community/work/employers.

↵4 See https://www.law.cornell.edu/uscode/text/49/48103 and https://www.law.cornell.edu/uscode/text/49/47504.

↵5 According to FedEx’s business model, which is responsible for almost $50 billion in annual revenue, parcels shipped by the courier are centralized in Memphis, where they board planes bound for their destinations.

↵6 See Memphis–Shelby County Airport Authority, 2019, http://www.flymemphis.com/NewsDetails?newsid=3236 (accessed March 7, 2019).

↵8 This is the sound pressure that exceeds the threshold of 50 dB during 50% of the day. It is adjusted to the human ear using a weighting scheme (see https://www.osha.gov/dts/osta/otm/new_noise/appendixb.pdf).

↵9 This map (270 m resolution) and data are publicly available from the National Park Service of the U.S. Department of the Interior (as part of the Integrated Resource Management Applications repository). The U.S. Department of Transportation publicly releases the National Transportation Noise Map based on a 24 hour equivalent noise metric for major roads and airports in the United States. Unfortunately, the geographic area covered by this geospatial dataset for the city of Memphis is limited to the airport proximity. Merging these noise data with our housing dataset involves dropping almost 60% of the housing units sampled (housing units that would fall outside the boundaries of the map). However, we compared the sound pressure levels of the U.S. Department of Transportation dataset with those of the National Park Service, and we found very similar noise values in terms of airport proximity (http://osav-usdot.opendata.arcgis.com/datasets/8defcb1df7ae4c1598aedc2801af7bd2?geometry=-90.862%2C34.702%2C-87.014%2C35.377, accessed July 20, 2018).

↵10 1 mPa = 0.02·10

^{dB/20}↵11

*Z*= (_{I}*I*–*E*(*I*))/*Var*(*I*)^{0.5}~*N*(0, 1), where*I*=**ε′**W**ε/ε′ε**is a measure of spatial correlation.↵12 Based on the values of the robust Lagrangian multiplier tests, RLM

_{ρ}= (**ε′Wy**/*σ*^{2}–**ε′Wε**/*σ*^{2})^{2}/{*σ*^{2}[(**WXβ**)**′M**(**WXβ**) +*nσ*^{2}] –*N*}, and RLM_{λ}= (**ε′Wε**/*σ*^{2}–*N*{*σ*^{2}[(**WXβ**)**′M**(**WXβ**) +*Nσ*^{2}]}^{–1}**ε′Wy**/*σ*^{2})^{2}/*N*(1 –*N*{*σ*^{2}[(**WXβ**)**′M**(**WXβ**) +*Nσ*^{2}]})^{–1}, with*N*= 9,606 being the sample size and**M**=**I – X(X′X)**^{–1}**X**. In practice we select the model with the largest statistics, as recommended by Florax and de Graaff (2004).↵13 More specifically, Moran’s

*I*= 0.104 and Z_{I}= 14.5, with an associated*p*-value < 0.001.↵14 More specifically, RLM

_{ρ}= 132.01*** > RLM_{λ}= 0.636.↵15 In real estate studies, partial information on the spatial process,

**W**, could be based on somewhat realistic assumptions about the behavior of real estate appraisers who assess the value of properties based on previous sales of nearest properties. We conducted a sensitivity analysis by increasing the number of nearest neighbors constructing**W**, and we did not find substantial changes in the estimated effects, as expected from LeSage and Pace (2014).↵16 Basis dimension for smoothing functions (

*k*): min(*N*/4, 40).↵17 The relative likelihood is computed as exp[(AIC(Model GAM) – AIC(Model I))/2].

↵18 The former figure is calculated as Δlog(

*price*)/Δ(*poor condition*) = 100·[exp(–0.262 – 0.5·*Var*(*β*= 0.0065)) – 1]%, while the latter is calculated as Δlog(*price*)/Δ(*good condition*) = 100·[exp(–0.129 – 0.5·*var*(*β*= 0.0011)) – 1]%, according to Kennedy (1981).↵19 A 1 dB increase from the sample average converted into millipascals is calculated as 1/

*N*·∑_{i=1…N}[0.02·10^{(μ(i)+1)/20}_0.02·10^{μ(i)/20}] ≈ 0.807 mPa.↵20 The average welfare change per household per decibel is computed as .

↵21 See https://wrcc.dri.edu/cgi-bin/wea_windrose2.pl (accessed March 27, 2018).