Spatial variations in broadband and air passenger service provision in the United States

Abstract

With the resurgence of regions as key nodes in the global economy, there is a growing interest in better defining their competitive advantages, particularly those accrued through infrastructure provision. Two important components of this competitive landscape are information and communication technologies (ICTs) and commercial air passenger service. While the development of these two networks is frequently cited as being a critical factor in regional economic competitiveness, few empirical studies address the statistical relationship(s) between these infrastructures or the complexities associated with their spatial distribution. The purpose of this paper is to determine if an association exists between the provision of broadband telecommunication service and air passenger service in the United States. In addition, basic spatial statistical approaches are utilized to identify a suite of important social and economic determinants that play a central role in spurring infrastructure provision.

Appendices

Appendix 1: Specification of local spatial statistics

The following notation is used to specify the local spatial statistics utilized in this paper (Anselin et al. 2002):

$$ \begin{gathered} z_{k} \, = {\frac{{\left[ {x_{k} - \bar{x}_{k} } \right]}}{{\sigma_{k} }}}{\text{ or a standardized random variable with a mean equal to zero and a standard}} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{deviation equal to 1}}. \hfill \\ \end{gathered} $$

$$ \begin{gathered} z_{k} \, = {\frac{{\left[ {x_{l} - \bar{x}_{l} } \right]}}{{\sigma_{l} }}}{\text{ or a standardized random variable with a mean equal to zero and a standard}} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{deviation equal to 1}}. \hfill \\ \end{gathered} $$

W is typically a Euclidean (straight-line) row standardized spatial weights matrix with binary values of 0 or 1. However, W can also be specified using a simple spatial adjacency metric, such as queen’s contiguity. n is the number of observations.

The global Moran’s I statistic is specified as follows:

$$I={\frac{{n\sum\limits_{k} {\sum\limits_{l} {Wz_{k} z_{l} } } }}{{W\sum\limits_{k} {z_{k}^{2} } }}}$$

(1)

The local Moran’s I is specified as:

$$I_{k}=z_{k} \sum\limits_{l} {Wz_{l}}$$

(2)

The bivariate global Moran’s I specified as follows:

$$I_{kl}={\frac{{z_{k}^{\prime } Wz_{l} }}{{z_{k}^{\prime } z_{k} }}}$$

(3)

Finally, the local version of the bivariate Moran’s I is:

$$I_{kl}^{i}=z_{k}^{i} \sum\limits_{j} {w_{ij} z_{l}^{j}}$$

(4)

Given specifications above, it is also important to note that since the spatial weights are row-standardized it is not necessary to account for the usual scaling factors, since $S_{0}=\sum\nolimits_{i} {\sum\nolimits_{j} {w_{ij} = n}}$ and thus $\left( {{n \mathord{\left/ {\vphantom {n {S_{0} }}} \right. \kern-\nulldelimiterspace} {S_{0} }}} \right)\left( {{{z_{k}^{\prime } Wz_{l} } \mathord{\left/ {\vphantom {{z_{k}^{\prime } Wz_{l} } {z_{k}^{\prime } zk}}} \right. \kern-\nulldelimiterspace} {z_{k}^{\prime } zk}}} \right) = {{z_{k}^{\prime } Wz_{l} } \mathord{\left/ {\vphantom {{z_{k}^{\prime } Wz_{l} } {z_{k}^{\prime } z_{k} }}} \right. \kern-\nulldelimiterspace} {z_{k}^{\prime } z_{k}}}$.

Appendix 2: Specification of regression models

The OLS model and the spatial lag model can be derived from the following general expression (Anselin 1988):

$$ y = \rho W_{1} y + X \beta + \varepsilon $$

(5)

where

$$ \varepsilon = \lambda W_{2} \varepsilon + \mu $$

and

$$ \mu \sim N({0,\Upomega}),$$

$$ \Upomega_{ii} = h_{i} \left( {z\alpha } \right) \quad h_{i} >0$$

β is a k × l vector of parameters, X is a n × k matrix of exogenous variables, ρ coefficient of spatially lagged dependent variable y, λ coefficient in an error term with a spatial autoregressive structure, μ is a normally distributed error term with a diagonal covariance matrix, Ω, z are the diagonal elements of the covariance matrix which are a function of p +1 exogenous variables, including the constant term, W ₁ and W ₂ are n × n row standardized weights matrices.

In the event of homoskedasticity (α = 0) and no spatial dependence in values of the dependent variable (ρ = 0) or in the error term (λ = 0) Eq. 1 simplifies to a standard linear regression model which may be estimated with ordinary least squares (Anselin 1988):

$$ y = X \beta + \varepsilon $$

(6)

If spatial autocorrelation is present in values of the dependent variable but the errors in the variance- covariance matrix are homoskedastic (α = 0) and there is no additional spatial autocorrelation in the error term (λ = 0), Eq. 1 becomes a spatial lag model:

$$ y = \rho W_{1} y + X \beta + \mu,$$

(7)

where

$$\mu \sim N({0,\Upomega})$$

(8)

The value of p in this model provides an estimate of the amount of spatial dependence in the dependent variable values.