# Introduction

The proliferation of big data obtained from satellites and mobile devices, as well as research demonstrating that satellite and mobile phone records are strongly correlated with household welfare, has sparked great interest in statistical methods that combine big data with survey data.<sup>1</sup> A key motivation for complementing survey data with comprehensive big data is the potential for small area estimation, which can produce more precise and granular estimates of socioeconomic indicators by combining household-level survey data in surveyed enumeration areas with predicted values from all enumeration areas, whether sampled or not. Established methods for small area estimation typically utilize household survey data and contemporaneous household census data, by first estimating a prediction model of welfare in the survey data and then using the estimated model parameters to simulate welfare in the census.<sup>2</sup> Because traditional small area estimation links household survey with census auxiliary data through the estimated model parameters, the set of potential predictor variables is limited to those present in both the survey and the census. Furthermore, when the wording of questions or timing of the data collection differs significantly between the census and the survey, small area estimates using the standard method can suffer from bias. Finally, because this method relies on census data, a new census is required to credibly estimate welfare changes for small areas. Census data are typically dated and collected once per decade at best, which presents a significant hurdle to deriving timely small area poverty estimates.

To overcome these challenges, we link survey data with geospatial and remote-sensing auxiliary data at the _subarea_ level.<sup>3</sup> S _ubarea refers to_ the lowest geographic level at which spatial auxiliary data can be merged with household surveys containing data on welfare and poverty, while _area_ refers to the target level for the small area poverty estimates. In recent household surveys, GPS coordinates of households, enumeration areas, or villages are often available, which allows analysts to link survey data with other auxiliary sources of remote-sensing or geospatial data and improve the precision of poverty estimates.

Although linking surveys with geospatial auxiliary data generates less precise small area estimates than using a census, it offers several important benefits. Geographic linking allows the relationship between the spatial auxiliary indicators and economic welfare to be estimated directly in the prediction model, avoiding the restrictive assumption that predictors must be identically distributed in the survey and auxiliary data. In addition, some spatial auxiliary data are collected continuously and are highly predictive of subarea poverty, and both the quality and availability of geospatial data are improving rapidly. Compared to other forms of “big data” such as mobile phone data, indicators derived from satellite imagery are attractive because of the comparative ease of acquiring data and the absence of selection bias.

Despite the potential value of this approach, only a couple of existing studies have quantified the gain in the precision of small area estimates achieved by supplementing survey data with geospatial data, in the

> 1  Examples of papers that find strong correlations between big data and welfare are Yeh et al (2020), Jean et al, 2016, Steele et al, 2018, Engstrom et al (2017) and Pokhriyal and Jacques (2017), among others. 2 Elbers, Lanjouw, and Lanjouw (2003), Tarozzi and Deaton (2009), and Molina and Rao (2010), among many others.

> 3 Lange, Pape, and Putz (2018).

2