2.1 Three channels for spatial spillovers

Why do drivers that affect land conversion and land conservation have spatial spillovers? Using relevant economic theories and intuition, we discuss the three channels leading to observed spatial spillovers: (1) individual decisions and behaviors, (2) the efforts of governments and other organizations to seek constrained (local) optimization or sustainability, and (3) intrinsic ecological-geographic links.

In a review article, Pfaff and Robalino (Reference Pfaff and Robalino2017) summarize five channels for spillovers from conservation programs: input reallocation, market prices, learning, nonpecuniary motivations and ecological-physical links. Our channel discussion is different from their work in two ways. First, they investigate spillovers from conservation programs (i.e., unintended consequences of conservation programs). We focus on the impact of spatial spillovers on land conversion (i.e., spillovers as a determinant of land conversion). Second, their scope of spillovers is broader than ours. We focus on spatial spillovers only and their definition of spillovers beyond ‘spatial’. For example, when explaining their second channel (i.e., market prices), they argue that a conservation program can affect the supply and demand of agricultural and forest goods, which can shift the demand for input factors such as labor and capital. Shifts in supply and demand can potentially affect the market equilibrium prices of these commodities and production factors, which can further cause a series of spillovers like out-migration due to decreased demand for labor and wage rate. On the other hand, our channel discussion is solely based on the ‘spatial’ aspect and emphasizes the importance of relative proximity (e.g., local versus global) in quantifying the spillover effects.

In the following discussion, we take the impact of personal income increase on natural land conservation as an example to illustrate the three channels we proposed. The first, channel #1, is spillovers related to individual decisions and behaviors. When an individual's income increases, the income effect may increase the person's demand for various consumer goods, including housing and infrastructure. This may have a negative impact on land conservation. The demand for housing and infrastructure will increase land conversion from natural to development uses; this increase will often happen in the area (e.g., the city or neighborhood) where the individual resides. At the same time, the income effect will increase the demand and willingness to pay (WTP) for leisure and environmental goods (e.g., better air quality and more open space) (e.g., Irwin, Reference Irwin2002). Thus, income growth may increase land conservation demand for amenity and recreational uses such as hunting and sightseeing. Locations protected for such recreational services are not necessarily the same as the individual's residential location. Generally speaking, the recreational activities’ geographic areas will not be too far away from the person's living environment; the sites are likely to be within a reasonable travel distance. Such a location mismatch between individual decisions/behaviors (e.g., the increased demand and WTP for land conservation) and the land conservation outcome is one channel of spatial spillovers.

The above example shows an individual's WTP for use values associated with environmental goods. In addition to use values, the environment and ecosystems also have nonuse values to human beings. Freeman (Reference Freeman2003, chapter 5) discussed and summarized four reasons for people's positive WTP for nonuse values: indirect use values, bequest values, altruistic attitude toward other people's use of a resource, and ethical or altruistic concerns for non-human species. Hanley and Perrings (Reference Hanley and Perrings2019) provide a recent review of the economic value of biodiversity, focusing on the valuation of nonmarket environmental goods and ecological system services. In our land conservation case, if a person is concerned about land protection, his WTP for nonuse value will also increase as his income increases. Note that land conservation not only reflects people's interest in land protection. Natural land is also the habitat for many rare species and is closely related to essential ecosystem services. Therefore, land conservation also reflects a broader interest in protecting the environment and ecosystems and supporting sustainable development. For nonuse values, because people do not need to consume the relevant resources, it is normal that the spatial locations between the protected land and the (locations of) individuals who pay for the protection do not match. In theory, the extent of spillovers, from a geographical perspective, from nonuse values is greater than those from use values. People's WTP may be used more efficiently in distant places through the government and other organizational efforts, as will be discussed below.

In addition to the consumer/demand perspective, we may also explain the impact of income on land conversion from the perspective of individual producers. For example, when income is low, farmers may choose to put undeveloped marginal land into production to increase income or consumption. As income increases, the conversion of such marginal land may decrease, which helps natural land conservation in nearby areas. Ferraro and Simorangkir's (Reference Ferraro and Simorangkir2020) research on the impact of cash transfer on deforestation provides evidence in this regard.

The second channel of the observed spillover, channel #2, is the conservation strategies and efforts of the government and other organizations. As personal income increases, the government's tax revenue also increases. The government's ability and intention to protect natural resources and supply more public open space have also increased. Research on sustainability has increasingly recognized that ecosystems and the environment play an irreplaceable role in sustainable development (Wang et al., Reference Wang, Wang, Shi and Wei2019; Chen et al., Reference Chen, Zhou and Yu2020; Wu et al., Reference Wu, Ren, Yan and Hao2020; Quintero-Angel et al., Reference Quintero-Angel, Coles and Duque-Nivia2021). Accordingly, governments worldwide have made tremendous efforts in protecting the environment and ecosystems. Such conservation efforts usually do not match the geographical distribution of income or other socio-economic indices. The governments’ targets are often to protect those locations with high ecological value, low economic costs (or high economic benefits) and high social acceptance (Brown et al., Reference Brown, McAlpine, Rhodes, Lunney, Goldingay, Fielding, Hetherington, Hopkins, Manning, Wood, Brace, Vass and Swankie2019). In conservation science, location selection is a widely studied topic. The early focus of the literature is on identifying locations with the highest ecological value. More recent literature emphasizes the importance of multi-dimensional criteria related to public acceptance and people's responses (Brown et al., Reference Brown, McAlpine, Rhodes, Lunney, Goldingay, Fielding, Hetherington, Hopkins, Manning, Wood, Brace, Vass and Swankie2019; Albers et al., Reference Albers, Preonas, Capitán, Robinson and Madrigal-Ballestero2020). The optimal conservation design and the collective efforts can explain part of the spatial spillovers that researchers observe from real data.

The third channel for spatial spillovers, channel #3, is the ecological-physical links as discussed in Pfaff and Robalino (Reference Pfaff and Robalino2017). Such spillovers are inherent within ecological or physical processes. The authors give examples of species diversity and oil extraction to illustrate spillovers through such a channel. They explain that ecological spillovers can occur due to factors such as species migration and reproduction behaviors. For example, when species richness increases in one (e.g., if conservation programs successfully target an area), the biodiversity in nontargeted areas can also benefit. Ecosystem interactions can propagate the effects of conservation programs to neighboring regions. Purely physical processes can also have spillovers. Underground extraction of oil is subject to the laws of pressure. Extraction in one location shifts marginal costs of extraction and thus shifts extraction elsewhere.

Unlike the previous two channels, this type of spillover does not require human involvement and can be seen as feedback caused by natural laws. Pfaff and Robalino (Reference Pfaff and Robalino2017) emphasize that this channel does not involve human behavior. In our discussion of spillovers caused by the ecological-physical connections, we allow human behavior/participation as long as natural laws are the dominant reasons. In the land conservation case, take the spillover effect of soil quality on agricultural land use as an example. The soil quality of adjacent land is highly correlated. Severe soil degradation on one farm can also affect the fertility of neighboring farms. This may reduce productivity in a larger area, affecting land-use decisions accordingly (for example, planting different crops or shifting land from agriculture to other uses). Consider another example of land fragmentation – a research topic that has attracted much attention in ecology, biology, and conservation science. The values and quality of land are interrelated. Suppose a small piece of land on a large natural land area is converted to other uses, such as industrial use. Then, the value (for example, measured as biodiversity) of the surrounding natural land can also decline. Sometimes, such land fragmentation can lead to fragmentation of biodiversity and critical habitats, which can be severe to ecological conservation (Fahrig, Reference Fahrig2003). We refer interested readers to Albers et al. (Reference Albers, Lee and Sims2018) for a recent review on habitat fragmentation. Due to such ecological-physical characteristics, many factors affecting focal land use, such as soil quality, will naturally affect surrounding land use and land-use change.

2.2 Local versus global spatial spillovers

From the above discussion of the three channels, especially the ecological-physical links, it is not difficult to see that spatial spillovers are likely to be stronger in closer regions than in distant ones. The locality nature of spatial spillovers is also indicated by Tobler's First Law of Geography, which says ‘everything is related to everything else, but near things are more related than distant things’ (Tobler, Reference Tobler1970). Looking back at our channel #1, although an individual's WTP for use value is not restricted to the community in which he lives, it is usually limited to a reasonable distance range depending on the uses (e.g., hunting vs. scenic view). Even with nonuse values, existing survey studies (e.g., see Wang and Swallow, Reference Wang and Swallow2016; Brown et al., Reference Brown, McAlpine, Rhodes, Lunney, Goldingay, Fielding, Hetherington, Hopkins, Manning, Wood, Brace, Vass and Swankie2019) have shown that people are more willing to pay for conservation closer to their living environment. In addition, local taxation is more dedicated to providing local public goods and services (Williams III, Reference Williams2012). Therefore, governments and other organizations often prioritize or only consider finding the best solution in a specific geographic region. In other words, the local optimum replaces the global optimum.Footnote ¹ Therefore, quantifying local spillovers separately from global ones is important and provides an in-depth understanding of the spatial spillover effects. We provide a diagram for illustration of local versus global spillovers in section 4.2 when discussing the measurement of spatial spillovers.

4.1 Model specification

This paper quantifies the spillovers from drivers of natural land conversion by using a spatial econometric method. Commonly used spatial regression models are the spatial autoregressive model (SAR), spatial error model (SEM), spatial lag of X model (SLX) and spatial Durbin model (SDM). This study employs an SDM, which is often believed to be superior among various options, due to its favorable attributes for potential econometric issues such as the omitted variable bias (LeSage and Pace, Reference LeSage and Pace2009). The choice of SDM is based on relevant statistical tests that will be further explained in section 5.1 when we present the estimation results. The SDM model can be expressed as:

(1)\begin{equation}y = \alpha {\iota _n} + \rho Wy + X\beta + WX\theta + \gamma Z + \varepsilon ,\end{equation}

where y is an $n \times 1$ vector of the dependent variable, and X is an $n \times k$ matrix carrying key explanatory variables. The term $\varepsilon$ stands for a vector of i.i.d. disturbances, ${\iota _n}$ is an $n \times 1$ vector of ones with the associated scalar parameter $\alpha$, and Z is a vector of other controls. Parameters $\rho$, $\beta$, $\theta$ and $\gamma$ are coefficients to be estimated, and W is an $n \times n$ weights matrix representing the spatial relationship between observations. Specifically, ${W_{ij}} > 0$ if j is a defined a neighbor to i, and ${W_{ij}} = 0$ otherwise. Section A2 of the online appendix, ‘Additional information on model specification’, provides more details about the model specification and explanation in the current land conversion context.

4.2 Measurement of spatial spillovers

To serve the purpose of this study, global and local spillovers are measured by employing different post-estimation calculations for the SDM. Global spillovers are obtained from the decomposition of total marginal effects, as suggested by Lesage and Pace (Reference LeSage and Pace2009). To illustrate the point, we first rewrite the SDM into its data generating process,

(2)\begin{equation}y = {({{I_n} - \rho W} )^{ - 1}}({X\beta + WX\theta + \gamma Z + {\iota_n}\alpha + \varepsilon } ).\end{equation}

Equation (2) can also be further rearranged to:

(3)\begin{equation}\begin{aligned} y & = \sum_{r = 1}^k {S_r}(W ){x_r} + V(W )({\gamma Z + {\iota_n}\alpha } )+ V(W )\varepsilon \\ {S_r}(W )& = V(W )({{I_n}{\beta_r} + W{\theta_r}} )\\ V(W )& = {{({{I_n} - \rho W} )}^{ - 1}} = {I_n} + \rho W + {\rho ^2}{W^2} + {\rho ^3}{W^3} + \ldots \end{aligned}\end{equation}

where ${S_r}(W)$ is an $n \times n$ matrix carrying all possible marginal effects from a unit change of a key variable r such as income. ${S_r}(W)$ can also be illustrated as:

(4)\begin{align} \left( {\begin{matrix} {{y_1}}\\ {{y_2}}\\ \vdots \\ {{y_n}} \end{matrix}} \right) & = \sum_{r = 1}^k \left( {\begin{matrix} {{S_r}{{(W )}_{11}}}& {{S_r}{{(W )}_{12}}}& \ldots & {{S_r}{{(W )}_{1n}}}\\ {{S_r}{{(W )}_{21}}}& {{S_r}{{(W )}_{22}}}& \ldots & {{S_r}{{(W )}_{2n}}}\\ \vdots & \vdots & \ddots & \ddots \\ {{S_r}{{(W )}_{n1}}}& {{S_r}{{(W )}_{n2}}}& \ldots & {{S_r}{{(W )}_{nn}}} \end{matrix}} \right)\left( {\begin{matrix} {{x_{1r}}}\\ {{x_{2r}}}\\ \vdots \\ {{x_{nr}}} \end{matrix}} \right)\notag\\ & \quad + V(W ){\iota _n}\alpha + V(W )\varepsilon .\end{align}

The i, jth element ${S_r}{(W)_{ij}}$ is the partial derivative of ${y_i}$ to ${x_{jr}}$, measuring the marginal effects on the dependent variable in location i from a change of the explanatory variable r in location j. Applied to this study, for example, if r denotes income, ${S_r}{(W)_{ij}}$ stands for location i's change of natural land area converted to the developed land due to a unit increase of income in location j. We define the average total effects (ATE), average direct effects (ADE), and average indirect or spillover effects (AIE) based on LeSage and Pace (Reference LeSage and Pace2009: 34–39).

The AIE obtained here are the average global spillover effects, which come from the fact that changes in one region impact all regions’ outcomes because the spillovers will pass to other higher neighbors (i.e., from neighbors to the neighbors of neighbors) through the spatial multiplier ${({I_n} - \rho W)^{ - 1}}$. The AIE of income can be interpreted as the aggregated change of natural land area converted for development uses on a representative focal area, arising from a unit change of income in all locations except itself (i.e., global spillover effects).

To ease the description, we provide a simplified diagram with small samples to illustrate local spillover effects and global spillover effects. In figure 1, ${A_0}$ represents the focal area of interest. ${A_1}$ to ${A_6}$ are local/immediate neighbors of ${A_0}$ if we define neighbors using a Queen's contiguity definition.Footnote ² Any location other than itself can be defined as a global neighbor. Suppose we use the regression method to conduct an impact analysis. For the dependent variable y in the focal area ${A_0}$ with respect to a certain explanatory variable x, the direct/own effects can be represented as $\partial {y_0}/\partial {x_0}$, the total/global spillover effect is $\sum\nolimits_{j = 1}^{18} {\partial {y_0}/\partial {x_j}}$, the local spillover effect is $\sum\nolimits_{j = 1}^6 {\partial {y_0}/\partial {x_j}}$Footnote ³ and the total effects can be written as $(\partial {y_0}/\partial {x_0}) + \sum\nolimits_{j = 1}^{18} {\partial {y_0}/\partial {x_j}}$, or $\sum\nolimits_{j = 0}^{18} {\partial {y_0}/\partial {x_j}}$.

Figure 1. Simplified diagram for illustration of the spillover effects.

Distinguishing the local and global spillover effects provides more detailed information from the resource governance perspective. For example, for local collaboration purposes, policymakers at nearby geographic units are likely to be more interested in quantifying local spillovers, which will directly affect their jurisdiction levels. Meanwhile, the central government at the federal level is probably more interested in knowing the total spillovers across the entire country or region due to local action in a specific area. Recent studies (e.g., see Shobe, Reference Shobe2020) discussed some emerging issues in resource governance when there are spillovers among vertical and horizontal jurisdictions.

Obtaining local spillovers in the estimation based on a general SDM is straightforward. Without considering the passing paths through W and its higher orders such as ${W^2}$ and ${W^3}$, the local spillover effects on the dependent variable can be calculated as $\rho W{I_n}{\beta _r} + {I_n}W{\theta _r}$ from equation (3). Therefore, the average local spillover effects for the variable r can be expressed as $(1/n)\sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^n {(\rho W{I_n}{\beta _r} + {I_n}W{\theta _r})} }$. Given that W is row-standardized and all diagonal elements are zero, this term can be simplified as the estimated coefficient $\rho {\beta _r} + {\theta _r}$. Again, if r denotes income, the area of natural land converted to development land on location i will change by $\rho {\beta _r} + {\theta _r}$ if its immediate neighbors see a unit change in income (i.e., local spillover effects).

4.3 Data and description

The 2000 and 2016 land-use/land-cover data (30-meter resolution raster images) are obtained from Agriculture and Agri-Food Canada. Four types of land are grouped and classified as the natural land in this study: Shrubland, Wetland, Grassland, and Forest. Therefore, the dependent variable is represented by the total area of the natural land in 2000 that has been converted to the developed land in 2016. As for explanatory variables, the road density is calculated using road network data from the AltaLIS Ltd. The land suitability information is provided by the Alberta Agriculture and Rural Development. According to the Canadian Land Suitability Rating System, larger rating scores represent lower suitability for agricultural uses. Since Alberta does not have Class 1 land due to the harsh climate, Class 2 or 3 land is the most suitable for agriculture. The 2016 population data are collected from the 2016 Canadian Census Program, while the 2000 population information use 2001 Census data as a proxy. Road network data are obtained from the CanMap Content Suite purchased by the University of Alberta.

For the empirical investigation, a grid of 5-km diameter hexagons is overlaid on each metropolitan area to divide the study area into the hexagonal regions of the same size. The choice of 5 km is a compromise between the observational unit of the dependent variable and the key independent variables. The dependent variable land conversion is observed at a high-resolution 30 m × 30 m ($= 900\,{\textrm{m}^\textrm{2}}$) level. However, key explanatory variables (i.e., median income and population) are only observed at the Census dissemination area (DA) level, which is the smallest standard geographic unit in the Canadian Census Program. The average DA sizes are 7.4 and 11.0 km² in EMR and CRP, respectively. However, DAs in some rural areas are quite large. Therefore, we chose to use a 5-km hexagon (about 16.2 km²) to balance the heterogenous DA sizes in rural and urban areas. In a similar setting, Stone and Wu (Reference Stone, Wu, Duke and Wu2014) choose to use a grid of 2-mile (i.e., 3.2 km) diameter circles for their empirical analysis. Their independent variables are at the census block level, smaller than our DA unit, so our diameter selection is also bigger than theirs.

The final dataset includes 872 observations for the EMR and 1,197 for the CRP. To conduct the spatial regression analysis, all variables are adapted to the hexagonal level. Table 1 presents the summary statistics of the variables. Figure 2 displays the distribution of natural land converted to development uses for the study area. The results show that for the EMR, the natural land loss is mainly distributed on the east and west outside of the city of Edmonton; while for the CRP, most loss occurs in the northwest of Calgary city. Also, the CRP has more units with over 200 ha natural land loss to development than the EMR.

Table 1. Summary statistics of the variables

Figure 2. Natural land converted for development uses in EMR and CRP (2000–2016).