2.1 Environmental economic valuation method: hedonic pricing

Environmental economic valuation aims to find a monetary measure of the earnings/losses of welfare that a person gets from the provision of an environmental good or change in the provision of that good. It is a fundamental tool for the proper definition of environmental policy instruments (Kolstad, Reference Kolstad2011; Zambrano-Monserrate, Reference Zambrano-Monserrate2020; Zambrano-Monserrate and Ruano, Reference Zambrano-Monserrate and Ruano2020). Environmental economic valuation methods are classified into two categories: (1) the stated preference method or the direct method, which exploits the survey technique of asking people about the value they give to environmental goods and nonmarketable services and about the changes in the environmental goods provided; and (2) the revealed preference method or the indirect method, which studies the ‘substitute markets,’ measures the value of nonmarketable goods and environmental services through analysis of the price fluctuations in the market for related economic goods (Zambrano-Monserrate, Reference Zambrano-Monserrate2016; Gregg and Wheeler, Reference Gregg and Wheeler2018).

The hedonic price method (HPM) is an indirect economic valuation method that has been applied in different areas, one of them being the housing market. Residences are multi-attribute; nevertheless, most of their attributes – for example, the environmental ones – are not commercially separated, meaning they do not have an explicit price (do not have a market). In spite of this, they have value, the reason why people are willing to pay for them. HPM tries to identify these attributes and differentiate the quantitative importance of each one of them. In other words, the method assigns an implicit price to each attribute of the good. This implicit price represents an individual/family's marginal willingness to pay for an additional unit of the given attribute (Rosen, Reference Rosen1974).

In the housing market, HPM generally uses regression analysis to estimate the effects of the attributes on the housing price. An attribute that has received special attention is location, since it is common for the residence price to be strongly related to the prices of contiguous residences and weakly related to the prices of distant homes. This could show that there are spatial effects that must be considered in the analysis. These spatial effects are spatial autocorrelation and spatial heterogeneity. Due to such effects, traditional estimations by ordinary least squares (OLS) generate non-consistent estimators. To solve this problem, several academics have developed econometric models that consider these spatial effects (Huang et al., Reference Huang, Chen, Xu and Zhou2017).

2.2 Econometric specification

To determine the effect of the estuaries on the residences' values, a base model is estimated through the OLS method. This can be represented as:

(1)\begin{equation} {\rm ln}( P ) = \beta Destuary + X\xi + \varepsilon ,\end{equation}

where ${\rm ln}( P )$ is the natural logarithm of the housing rental price; X represents several control variables; $Destuary$ is the interest variable and represents the distance between a residence and the closest estuary; and $\varepsilon$ is the stochastic disturbance term with a distribution $\varepsilon \sim ( {0, \;{\sigma^{2}}{I_{n}}} )$.

As previously mentioned, the models estimated by OLS do not consider the possible spatial effects, which are usually in the hedonic rental price model. There are three spatial regression models: the spatial lag model (SLM), the spatial error model (SEM) and the spatial Durbin model (SDM) (Elhorst, Reference Elhorst2010). According to LeSage and Pace (Reference LeSage and Pace2009) and supported by Li and Wu (Reference Li and Wu2017), the SDM is superior to the first two models since it can capture both the spatial correlation of the explained variable (global effects) and the spatial spillover effects of the explanatory variables (local effects). Furthermore, the SDM incorporates new explanatory variables that could have been omitted, thus correcting the bias of the omitted variable. However, because of this interaction, the model may exhibit an endogenous problem. To solve this problem, LeSage and Pace (Reference LeSage and Pace2009) advise applying the maximum likelihood (ML) method, hence providing the necessary theoretical framework to estimate the spatial lag values of the dependent and independent variables, including the direct and indirect effects as well.

In our model, the SDM can be presented as:

(2)\begin{equation} \ln ( P ) = \lambda Wln( P ) + \beta Destuary + {\rm \Gamma }WDestuary + X\xi + {\rm \Upsilon }WX + \varepsilon ,\end{equation}

where $\lambda$ is an autoregressive spatial parameter and W is the spatial autocorrelation matrix $N \times N$ in which the weighing element, ${w_{ij}},$ is specified as:

(3)\begin{equation} {w_{ij}} = \begin{cases} 1 & {{\rm if}\;i{\rm \;and\;}j\;{\rm are\;nearest\;neighbors}}\\ 0 & {{\rm if\;they\;are\;not}} \end{cases}, \end{equation}

where $i \ne j$. ${\rm \Gamma }$ and ${\rm \Upsilon }$ are added to capture the local spatial effect of the variable Destuary and of other exogenous variables, respectively. As previously mentioned, the SDM has the advantage of capturing global $( \lambda )$ and local effects $( {{\rm \Gamma }, \;{\rm \Upsilon }} )$ at the same time. The other elements of equation (2) were previously defined.

On a different note, it is important to mention that under a non-spatial regression model (equation (1)), the total effect on the dependent variable will be equal to the estimation of the ${\beta _k}$ coefficient, ceteris paribus, no matter the location. However, in the case of the spatial effects model (equation (2)), the total effect depends on the neighbor units of each location and the magnitude of the coefficients along with the spatial variables. The total effect can be deconstructed into a direct and an indirect effect. The direct effect is the impact of the change of the explanatory variable on the dependent variable in each residence. This effect will tend to be similar to the one obtained by a non-spatial regression model if the spatial elements are close to zero. The indirect effect is due to the spatial dynamic generated by the presence of the spatial parameter and which affects all the model's units (Drukker et al., Reference Drukker, Prucha and Raciborski2013).

2.3 Construction of the spatial weights matrix and spatial autocorrelation tests

Prior to the analysis of any test of spatial contrast, it is necessary to construct the spatial weights matrix. In order to correctly construct it, the nature of the externality to be modeled should be considered, in this case, the estuaries. If the model to be estimated follows an exponential decay process (ergodic process), the spatial autocorrelation matrix can be structured through a nonparametric approach to this process.

Due to the structure of the data (points rather than polygons), the applied criteria were of k nearest neighbors.Footnote ¹ Following Mei et al. (Reference Mei, Hite and Sohngen2017), the test and error method was used to calculate the importance of the spatial parameter and thus determine the nearest neighbor specification. As such, the five nearest neighbors were chosen for the analysis.Footnote ² Finally, the matrix created was binary and standardized by row. Once the spatial weights matrix was built, a spatial autocorrelation diagnostic was done through the test of the Lagrange Multiplier (simple and robust). This test contrasts the SLM and SEM models.

2.4 Construction of influence zones (buffers)

The construction of areas of influence is a useful technique when studying the spatial effect of environmental externalities. They allow us to analyze this effect graphically and numerically, producing a detailed view of the externality. There are two basic methods to build areas of influence: Euclidean and Geodesic. Euclidean influence zones are the most common type of influence zone and work well when analyzing distances around entities in a projected coordinate system that are concentrated in a relatively small area (such as a Universal Transverse Mercator (UTM) zone) (ArcMap, 2018).

2.5 Data collection

Despite the fact that the statistics in Ecuador on a national level have improved, the transaction data with regard to the housing market are very limited and are restricted. On the one hand, the housing companies refuse to hand out data on the executed transactions due to confidentiality issues. On the other hand, public information on the housing market is very limited (data is incomplete and is not geo-referenced). Therefore, primary, geo-referenced information was collected on the residential rental market of the city of Machala.

A conglomerate sampling was implemented since it is the most recommended when there are ‘natural’ clusters as is the case with people or families that rent houses. Machala is divided into census areas, which are comprised of an average of 10 sectors. Likewise, each sector represents a conglomerate of blocks. Of all the census areas, only the most representative ones were considered. Then the sectors were also selected. In the sectors chosen, a block was picked, and surveys were carried out in up to four blocks surrounding the given block.

The study population was families (individuals) who lived in Machala, who rented houses, apartments or rooms. Sampling was used in order for the surveyed homes that were chosen to geographically represent all the areas in the city. A qualified and experienced pollster was in charge of data collection. Four groups of interviewers were formed, with two members each. The questionnaire had an average duration of approximately 10 min, and the interviews were done face-to-face at the homes. Data were collected over a two-week period, on weekends and workdays, from 23 July 23 to 5 August 2018. Four hundred surveys were carried out in total, with a sampling error of ± 5 per cent with a 95 per cent confidence level.

2.6 Variables

Despite the fact that several hedonic studies use the housing rental market price as the independent variable, other authors such as Donovan and Butry (Reference Donovan and Butry2011) and Choumert et al. (Reference Choumert, Stage and Uwera2014) have determined the housing rental price as the dependent variable. This was done due to the dynamism of the rental market, which perfectly reflects the changes in the environment, particularly in the characteristics of the study subject, such as the pollution of the estuaries. Thus monthly payments of rental values in US$ was taken as the dependent variable (table 1). Additionally, control variables were considered as groups divided into three categories: structural, surrounding and environmental, where the main exogenous variable was the distance of the houses from the closest estuary.

Table 1.

Description of variables considered in this study

^a Noise measurements were made at different times. However, only data for 9:00 p.m. was chosen, since it is one of the times with the greatest variation in noise in the city. The detail of noise measurement can be found in Zambrano-Monserrate and Ruano (Reference Zambrano-Monserrate and Ruano2019).