Using Nighttime Lights Data as a Proxy in Social Scientific Research

Abstract

This chapter presents a formal statistical approach to estimate the amount of information that can be provided by proxy variables to improve current estimation of variables in social scientific research. The chapter introduces two useful geocoded datasets, satellite-based nighttime lights and Geographically-based Economic Data (GEcon), and demonstrates how the proposed statistical approach can be used to estimate information provided by lights data as a proxy for economic statistics. An application of lights data to urbanization measures also shows that proxy-based subnational estimates of urbanization in poor countries can improve results in testing theoretical relationships between urbanization and poverty rates. The chapter concludes that both the proposed methodology and nighttime lights data holds great potential for social scientific research where data availability and quality of data at smaller scales have proven a hindrance in past research.

Appendices

Appendices

1.1 Appendix 15.1

The formula for corrected coefficient using classical errors-in-variable correction:

$$ \tilde{\beta}=\left(\frac{\sigma_{y*}^2+{\sigma}_{\varepsilon}^2}{\sigma_{y*}^2}\right)\tilde{\beta} $$

$\tilde{\beta}$ is the estimated coefficient from the regression model; σ ² _ε is the a priori estimate of error variance of true value of Y, y *, and σ ² _y * is variance of y *.

1.2 Appendix 15.2

The mean squared error (MSE) of ${\widehat{x}}_i$, V(θ), is a function of the weight, θ:

$$ \begin{array}{c}\hfill V\left(\theta \right)=E{\left[\left(1-\theta \right)y+\theta \widehat{z}-y*\right]}^2\hfill \\ {}\hfill \kern8.5em =E{\left[\left(1-\theta \right)\;\left(y*+\varepsilon \right)+\frac{\theta }{\beta}\left(\beta y*+u\right)-y*\right]}^2\hfill \\ {}\hfill =E{\left[\left(1-\theta \right)\varepsilon +\frac{\theta }{\beta }u\right]}^2\hfill \\ {}\hfill ={\left(1-\theta \right)}^2{\sigma}_{\varepsilon}^2+\frac{\theta^2}{\beta^2}{\sigma}_u^2\hfill \end{array} $$

Minimizing V(θ) with respect to θ yields the optimal weight, θ*, as a function of three parameters, σ ² _ε , σ ² _u , and β:

$$ {V}^{\prime}\left(\theta *\right)=0=-2\left(1-\theta *\right){\sigma}_{\varepsilon}^2+\frac{2\theta *}{\beta^2}{\sigma}_u^2 $$

Or Eq. (15.6):

$$ \theta *=\frac{\beta^2{\sigma}_{\varepsilon}^2}{\beta^2{\sigma}_{\varepsilon}^2+{\sigma}_u^2} $$

(15.6)