metadata: authors: 0: author: Van Der Weide,Roy
1: author: Blankespoor,Brian
2: author: Elbers,Chris T.M.
3: author: Lanjouw,Peter F.
count: Malawi,Nigeria
docna: 0: docna: How Accurate Is a Poverty Map Based on
            Remote Sensing Data ?  An Application to Malawi
docty: Policy Research Working Paper
abstracts: cdata!: This paper assesses the reliability of
            poverty maps derived from remote-sensing data. Employing
            data for Malawi, it first obtains small area estimates of
            poverty by combining the Malawi household expenditure survey
            from 2010/11 with unit record population census data from
            2008. It then ignores the population census data and obtains
            a second poverty map for Malawi by combining the survey data
            with predictors of poverty derived from remote sensing data.
            This allows for a clean comparison between the two poverty
            maps. The findings are encouraging - although that
            assessment depends somewhat on the evaluation criteria
            employed. The two approaches reveal the same patterns in the
            geography of poverty. However, there are instances where the
            two approaches obtain markedly different estimates of
            poverty. Poverty maps obtained using remote sensing data may
            do well when the decision maker is interested in comparisons
            of poverty between assemblies of areas, yet may be less
            reliable when the focus is on estimates for specific small areas.
display_title: How Accurate Is a Poverty Map Based
            on Remote Sensing Data ? An Application to Malawi
listing_relative_url: /research/2022/09/33897437/accurate-poverty-map-based-remote-sensing-data-application-malawi
topicv3: Human Resources m1326304 1211,Poverty m1326687 695,Data Catalogues m1326864 2385
publishtoextweb_dt: 2022-09-13T00:00:00Z
dois: 10.1596/1813-9450-10171
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 677092
1: author_key: 957135
2: author_key: 606516
3: author_key: 95180
model_extractions: Policy Research Working Paper 10171 How Accurate Is a Poverty Map Based on Remote Sensing Data?

# An Application to Malawi

_Roy van der Weide Brian Blankespoor Chris Elbers Peter Lanjouw_ Development Economics Development Research Group September 2022
Policy Research Working Paper 10171

# **Abstract**

This paper assesses the reliability of poverty maps derived from remote-sensing data. Employing data for Malawi, it first obtains small area estimates of poverty by combining the Malawi household expenditure survey from 2010/11 with unit record population census data from 2008. It then ignores the population census data and obtains a second poverty map for Malawi by combining the survey data with predictors of poverty derived from remote sensing data. This allows for a clean comparison between the two poverty maps. The findings are encouraging—although that assessment depends somewhat on the evaluation criteria employed. The two approaches reveal the same patterns in the geography of poverty. However, there are instances where the two approaches obtain markedly different estimates of poverty. Poverty maps obtained using remote sensing data may do well when the decision maker is interested in comparisons of poverty between assemblies of areas, yet may be less reliable when the focus is on estimates for specific small areas.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at rvanderweide@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# How Accurate Is a Poverty Map Based on Remote Sensing Data? An Application to Malawi<sup>_∗_</sup>

Roy van der Weide<sup>_†_</sup> , Brian Blankespoor,<sup>_‡_</sup> Chris Elbers<sup>_§_</sup> , and Peter Lanjouw<sup>_¶_</sup>

**Keywords:** Poverty, Small Area Estimation, Remote Sensing Data **JEL Classification:** C13, D31, I32, O15, R13, Y91

> _∗_ The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. The authors gratefully acknowledge financial support from the World Bank Knowledge for Change Program.

> _†_ World Bank: rvanderweide@worldbank.org

> _‡_ World Bank: bblankespoor@worldbank.org

> _§_ Vrije Universiteit Amsterdam: c.t.m.elbers@vu.nl

> _¶_ Vrije Universiteit Amsterdam: p.f.lanjouw@vu.nl
# **1 Introduction**

Tracking poverty at the global, regional, and national levels helps international organizations and the development community identify lagging regions and allocate their resources accordingly (see e.g. Ravallion (2018), Ferreira et al. (2015), Bourguignon (2017)). Poverty is commonly measured by the percentage of the population whose income or consumption expenditure falls below a poverty line. The household income and expenditure data used to estimate poverty come from household surveys that are conducted every 1-5 years by the national statistical agencies. Individual countries use these data to monitor poverty at the national and subnational levels.

Elbers et al. (2007) demonstrates the value of estimating poverty at a more disaggregated level. Specifically, they estimate by how much governments could lower the costs of providing resources to the poor if they had access to a poverty map that provides estimates of poverty down to the district or municipality level. Their simulation study using data from Madagascar, Cambodia, and Ecuador suggests that the gains can be substantial. In all three countries, the reduction in poverty that is achieved with a uniform transfer to all households can often be realized with less than half the budget if the transfers could be targeted on the basis of municipality level estimates of poverty. Unfortunately, collecting data on household income and expenditure is costly and time consuming (Kilic et al. 2017; Fujii and van der Weide, 2020). As a result, survey samples tend to be relatively small, permitting only a limited degree of disaggregation, often not beyond large sub-regions.

Estimating poverty at the small area level requires alternative sources of data, ideally a population census, that are able to provide complete coverage of the population. Elbers, Lanjouw, and Lanjouw (2003), hereafter referred to as ELL, pioneered the small area estimation of poverty by combining household survey with population census data. The proposed approach imputes household income or consumption expenditure (multiple times) for each household into the population census, and then aggregates the multiple imputed values to obtain estimates of poverty at the municipality or district level. The population census arguably provides the richest possible data source for this purpose. It contains a comprehensive set of variables that are highly correlated with household income or consumption (although not, usually, income itself). Specifically, a census typically includes information on demographics, education, employment, housing characteristics, asset ownership, and community services (i.e. local amenities) for all households in the population. In the ELL procedure, a household survey is used to infer the relationship between these variables and household income, taking advantage of the fact that many of these variables are available in both the census and household survey.

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Elbers et al. (2008) assess the validity of the approach using data from Brazil and find that small-area estimates based on the ELL procedure are close to direct calculations of sub-national poverty in this setting. ELL has been adopted to obtain small area estimates of poverty and inequality in over 60 countries worldwide.<sup>1</sup> Poverty maps are also increasingly used as a source of data in a variety of empirical applications, see e.g. Araujo et al. (2008), Baird et al. (2013), Bazzi (2017), Crost et al. (2014), Demombynes and Ozler (2005), Elbers et al. (2005), and Maloney and Caicedo (2015).

An important limitation of the ELL approach, however, is precisely its reliance on the population census. For all the strengths of a population census, a notable disadvantage is its limited availability. Population censuses are generally conducted only once every 10 years, and it often takes two years or longer to process the data. These factors combine to imply that ELL-based poverty maps are rarely up-to-date (i.e. are often already outdated at the time of release). Furthermore, even when current population census data exist and are ready for analysis, getting access to such data is often not trivial. As a result, areas that may be most in need of a timely poverty map may lack the data necessary to implement the ELL approach. An alternative approach that can produce a poverty map in the absence of population census data will thus have obvious appeal.

The objective of this study is to evaluate whether an accurate map of poverty can be obtained using predictors derived from publicly available remote sensing data instead of a population census. A requirement in such a case would be that the household expenditure survey is also geo-referenced, i.e. that the enumeration areas (or primary sampling units) can be located on a map. While this would have been a demanding requirement a decade ago, geo-referencing of household surveys is now increasingly becoming standard practice. To preserve the anonymity of sampled households, the geographic coordinates of the primary sampling units in public use datasets are not exact, i.e. some random offsets are applied. Our secondary objective is to investigate whether these random offsets undermine this alternative approach of obtaining a poverty map. The primary sampling unit, such as a village or a neighborhood in a city, will be the unit of observation (rather than the household). Correspondingly, the level of poverty in the primary sampling units will now serve as the dependent variable. Examples of possible predictors of local poverty rates include local Night-Time-Lights (NTL), road network, urban footprint, vegetation, elevation, surface temperature, rainfall.

The use of remote sensing data in the economics literature has expanded dramatically in recent years, as these data have become richer and more accessible, see e.g.

> 1See e.g. Alderman et al. (2002) and and Bedi et al. (2007). Recently, the approach has also been extended to the small area estimation of child malnutrition (Fujii, 2010). For an overview of the literature on small area estimation we refer the reader to Elbers and van der Weide (2014).

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Donaldson and Storeygard (2016). Early applications to the measurement of economic activity and welfare include Henderson et al. (2012), which also established the value of these data as predictors of economic outcomes (see also Pinkovskiy and Sala-I-Martin, 2016). These early studies confirm that national income can be accurately predicted using NTL data.<sup>2</sup> Economists have since expanded the set of predictors extracted from remote sensing data and increased the spatial resolution at which economic welfare including poverty is estimated. Jean et al. (2016) is among the early studies to use a comprehensive set of predictors derived from remote sensing data to estimate poverty at the small area level. The studies vary in the resolution of imagery used, with higher resolution images allowing for a richer set of predictors that can be extracted from them (see e.g. Marx et al., 2019). The increased accessibility of remote sensing data combined with the continued demand for highly disaggregated poverty data has prompted a surge in the production of poverty maps in recent years. In the years following Jean et al. (2016), dozens of remote sensing-based poverty and/or household welfare maps have been produced, see e.g. Blumenstock et al. (2015), Blumenstock (2016), Bosco et al. (2017), Burke et al. (2021), Engstrom et al. (2021), Imran et al. (2014), Pokhriyal and Jacques (2017), Steele et al. (2017), Watmough et al. (2016), Watmough et al. (2019), Zhao et al. (2019), and Lee and Braithwaite (2022).

This highlights the importance of assessing the accuracy of remote-sensing-based poverty maps. One logical entry-point in this regard is an assessment of how closely a poverty map obtained using remote sensing data tracks a poverty map derived from population census data. Such assessments are currently missing from the literature. Existing studies typically validate their small area poverty estimates by comparing them against direct-estimates obtained from the household survey. However, these direct estimates are subject to large sampling error and cover only a small subset of the total number of areas. They thus fail to confront what motivates the use of small area estimation methods to begin with. Engstrom et al. (2021) is a notable exception. That study uses the census-based small area estimates of poverty obtained using the ELL approach as the dependent variable in their model employing predictors derived from remote sensing data as independent variables. This does not allow, however, for a validation of a poverty mapping approach that does not use any population census data (i.e. an approach that combines household survey with remote sensing data).

The validation exercise presented here provides a clean comparison between poverty maps obtained with and without population census data. Employing data for Malawi, we first obtain small area estimates of poverty that combine the Malawi household

> 2More recent examples of empirical studies that use remote-sensing data to track local economic activity include Nhu and Noy (2020), Marx et al. (2019), and Van der Weide et al. (2018), among others.

4
expenditure survey from 2010 with the unit record population census data from 2008 using the ELL approach. This poverty map serves as our benchmark. We then ignore the population census data and obtain a second poverty map for Malawi by combining the household expenditure survey data with predictors of poverty derived from publicly available remote sensing data.

An important motivation for using data from Malawi is that we have access to the exact coordinates of the survey PSUs. This enables us to produce the remote-sensingbased poverty map both using the publicly available geographic coordinates (that have been subjected to random offset to protect the anonymity of households) and exact coordinates (that are not publicly available) to investigate whether the random offsets – might undermine the approach and inspect the correspondence.

Our findings are two-fold. First, assessments of the correspondence between the remote-sensing-based poverty estimates and the census-based poverty estimates depend on how the correspondence is evaluated. The two approaches reveal the same patterns in the geography of poverty in Malawi; it is hard to tell the difference in a side-by-side comparison of the two poverty maps. The statistical correlation between the two different small area estimates of poverty is above 0.9, again confirming their close correspondence. However, there are districts for which the two approaches obtain markedly different estimates of poverty. Accordingly, poverty maps obtained using remote sensing data can be expected to do well when the decision maker is interested in estimates or comparisons of poverty between assemblies of areas. Yet, the decision maker may not be served as well by remote-sensing-based estimates when the focus is on estimates for specific small areas. Second, the random offsets embedded in the geographic coordinates of the public use data do not meaningfully alter the estimated geography of poverty. But they may, however, lead to an under-estimation of the standard errors of the small area poverty estimates (i.e. an over-estimation of precision). The reason for this is that the random offsets partially destroy the spatial correlation structure in the data and error term.

The decision to restrict attention to publicly available remote sensing data is a deliberate one. This ensures that the data are available at no cost in any given country, and so the approach can easily be replicated and readily repeated as new survey data become available. By the same token, our exercise arguably provides a conservative assessment, i.e. a lower bound of success as higher resolution remote sensing data that come at a cost will allow for more precise estimates. It should be noted that with the rapid technological advancements in this field, what is costly today will in all likelihood become low-cost or publicly-available in the near future.

The paper is organized as follows. An overview of the two small area estimation 5
methods is presented in Section 2. In this section we also offer a methodological contribution by deriving standard error estimates for the remote-sensing based poverty map. Section 3 describes the different data used in this study. Our empirical findings are presented in Section 4. Finally, Section 5 concludes.

# **2 Methodologies**

## **2.1 Population census-based small area estimation of poverty**

Elbers et al. (2003; ELL) pioneered the use of unit record population census data combined with household consumption expenditure survey data for the small area estimation of poverty and inequality. ELL assume the following data generating process (DGP): where _y_ is log per capita income or expenditure, _x_ is a vector with independent variables, and where _v_ and _ε_ are zero expectation error terms that are independent of each other with variances denoted by _σv_<sup>2and</sup><sup>_σ_</sup> _ε,ah_<sup>2, respectively.The subscripts indicate household</sup> level _h_ residing in small area _a_ . The predictors _x_ may consist of variables observed at different levels of aggregation, i.e. household level employment status and local area employment rates may both serve as good predictors of household expenditure.

The model permits heteroskedasticity in the household errors _εah_ to allow for instances where the predictability of expenditures varies between demographics (i.e. elder versus young), employment status (i.e. unemployed versus employed), and sectors (i.e. blue collar versus white collar). Specifically, the variance _σε,ah_<sup>2isassumedtobeafunc-</sup> tion of household and area characteristics, denoted by _zah_ . A logistic transformation of the squared error will serve as the dependent variable (as the distribution of the untransformed squared error tends to be heavily skewed): where the vector _zah_ includes the constant term. An estimate of _σε,ah_<sup>2=</sup><sup>_E_[</sup><sup>_ε_2</sup> _ah_<sup>_|zah_]is</sup> obtained by applying the inverse of the logistic transformation (see Elbers et al., 2003). Estimates of the household level variances are re-scaled such that the sample mean matches the estimate of the unconditional variance _σ_<sup>2i.e.</sup><sup>_E_[</sup><sup>_σ_2</sup> _ε_<sup>,</sup> _ε,ah_<sup>] =</sup><sup>_σ_</sup> _ε_<sup>2.</sup>

For households sampled in area _a_ , the residuals _eah_ = _yah − x_<sup>_T_</sup> _ah_<sup>_β_=</sup><sup>_va_+</sup><sup>_εah_are</sup> informative of the latent area error _va_ . Assuming both errors are normally distributed, 6
it follows that conditional on the residuals observed in the survey data, the error _eaj_ is normally distributed with mean and variance given by (see e.g. van der Weide, 2014): where _γa_ = _σv_<sup>2</sup><sup>_/_(</sup><sup>_σ_</sup> _v_<sup>2+</sup><sup>_σ_</sup> _ε_<sup>2</sup><sup>_/ma_),with</sup><sup>_ma_equaltothenumberofsurveyhouseholdssam-</sup> pled into the area _a_ , and where: If there are sampling weights these will be absorbed by (and modify) the weights _αah_ (see van der Weide, 2014). Conditioning on the survey data when drawing the errors is known as Empirical Bayes (EB) prediction (see e.g. Molina and Rao, 2010). Note that EB prediction only concerns the drawing of the area errors, and only those areas that have been sampled into the survey. The gain in precision resulting from conditioning on the survey data for these areas is most notable when the variance _σv_<sup>2and the number</sup> of sampled households _ma_ are relatively large.

The small area estimates of poverty and corresponding standard errors are obtained by means of bootstrapping. Let _R_ denote the number of simulations. The estimator for poverty then takes the form: where _h_ ( _y_ ) is a function that converts the vector _y_ with (log) consumption expenditures for all households into the corresponding poverty rate, and where _y_ ̃<sup>(</sup><sup>_r_)</sup> denotes the _r_ -th simulated vector with elements: ̃ ̃ ̃ ̃ where the model parameters _β_<sup> ̃(</sup><sup>_r_)</sup> _, σ_<sup>(</sup> _v_<sup>_r_)</sup> and _σε_<sup>(</sup><sup>_r_)</sup> and the errors _va_<sup>(</sup><sup>_r_)</sup> and _ε_<sup>(</sup> _ah_<sup>_r_)aredrawn</sup> ̃ ̃ from their estimated distributions. We draw _β_<sup> ̃(</sup><sup>_r_)</sup> _, σ_<sup>(</sup> _v_<sup>_r_)</sup> and _σε_<sup>(</sup><sup>_r_)</sup> by re-estimating the model parameters using the r-th bootstrap version of the survey.<sup>3</sup> The error term _v_ ̃ _a_<sup>(</sup><sup>_r_)+ ̃</sup><sup>_ε_(</sup> _ah_<sup>_r_)is drawn from a normal distribution with mean and variance given by eq. (1)-</sup>

> 3Alternatively, the model parameters can be drawn from their estimated asymptotic distribution.

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(2). Finally, the point estimates and their corresponding standard errors are obtained by computing respectively the average and the standard deviation over _R_ imputed poverty rates. Note that the standard errors of the poverty estimates are driven both by model error and idiosyncratic error. The contribution of the idiosyncratic error (the area- and the household error) will tend to zero as the size of the target population of a small area (in the population census) tends to infinity. Similarly, the contribution of the model error tends to zero when the sample size of the survey (which is used to estimate the model parameters) tends to infinity.

# **2.2 Remote-sensing-based small area estimation of poverty**

Relying on remote sensing data to estimate small area poverty rates alters the dimensions of the model with which we work. The unit of observation will be a geographic unit, think of a small administrative unit such as a village. The dependent variable in this case will be village level poverty rather than household level consumption expenditure. Furthermore, restricting the set of the covariates that can be derived from publicly available remote sensing data could conceivably increase the magnitude as well as the spatial correlation structure of the error term. Adopting a spatial error model will help fit this spatial structure (e.g. Anselin, 2001).

We use a spatial error model (henceforward SEM) that assumes iid normal shocks to local poverty spilling over to other locations depending on distance. It is assumed that village level poverty _q_ can be described (in matrix notation) by: where _X_ is the matrix with geo-covariates (rows indicating villages and columns indicating covariates), _u_ satisfies _u_ = _ρWu_ + _ε_ , where _ε_ is a vector of independent local errors satisfying _ε ∼ N_ (0 _, σ_<sup>2</sup> _I_ ) and _E_ [ _ε|X_ ] = 0, and where _W_ is a spatial weight matrix with elements _wij_ measuring the spatial correspondence between villages _i_ and _j_ (relative to other villages). We define _wij_ = _t_<sup>_−_</sup> _ij_<sup>_τ_</sup> (for _i_ = _j_ ) as a function that is inversely related to travel time _tij_ between _i_ and _j_ with _τ >_ 0. We take _W_ to be symmetric, with _wii_ = 0, and normalize it by its largest eigenvalue, i.e. _W_ = _W_<sup>_∗_</sup> _/λmax_ , where _W_<sup>_∗_</sup> is the un-normalized spatial weight matrix and _λmax_ is the largest eigenvalue of _W_<sup>_∗_</sup> (see e.g. Bell and Bockstael (2000) and Kelejian and Prucha (2010)). Locations that are in close proximity to each other are exposed to the same latent geographical features which induces spatial correlation. These correlations are modeled as the product of _W_ and _ρ_ , where _ρ_ is a scalar, expected to be positive. The spatial covariance structure of

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the error term _u_ = ( _I − ρW_ )<sup>_−_1</sup> _ε_ is seen to satisfy: where _C_ = ( _I − ρW_ )<sup>_−_1</sup> .

Let _m_ = _Xθ_ be the mean of _q_ conditional on _X_ . Let the subscripts _S_ and _O_ indicate whether the village is “in sample” or “out of sample”, respectively. For ease of exposition, let us also sort the villages such that the “in sample” villages are stacked above the “out of sample” villages, which permits for the following notation: The corresponding partition of the variance matrix Σ takes the form: Suppose that we know the model parameters (in practice we will have to work with estimates) such that _mS_ and _mO_ are both observed (note that _X_ is observed for all villages). Let us also assume for now that we observe _qS_ , the outcome variable of interest for a sub-set of locations. (Since the village level poverty rates are derived from a sample of households in any given village, we observe _qS_ with error due to sampling; we will return to this later.) The objective then is to estimate _qO_ given our observations (or estimation) of _mS_ , _mO_ , Σ, as well as _qS_ , so as to obtain a map of poverty that covers the whole country. If the data exhibits spatial correlation (i.e. _ρ_ = 0), then observing _qS_ and _mS_ will carry information that is relevant for the estimation of _qO_ above and beyond the information that is conveyed in _mO_ . It follows from the normality assumptions that the Best Linear Unbiased Predictor (BLUP) of _qO_ solves (Goldberger, 1962): Let us next account for the fact that _qS_ is observed with sampling error. We shall ˆ denote the sampling direct estimate of _qS_ by _qS_ : 9
where _eS_ denotes sampling error. This modifies the BLUP estimate of _qO_ to: where _DS_ is a diagonal matrix with the sampling variances (i.e. variance of _eS_ ) as diagonal elements. Note that when the magnitude of sampling variance is large (i.e. when _q_ ˆ _S_ denotes a noisy observation of _qS_ ), more weight is given to the synthetic estimator _mO_ .

We can similarly use the model to obtain a more precise estimate of _qS_ . It can be verified that the BLUP estimator of _qS_ in this case satisfies: Note that _q_ ̃ _S_ is of the same form as the estimator put forward by Pratesi and Salvati (2008), who consider a different choice of SEM model. As Pratesi and Salvati (2008) restrict their analysis to in-sample prediction, they do not offer an estimator for _qO_ .

**Precision** In practice a prediction of _qO_ is also subject to error induced by the sampling variation of estimators for model parameters. Denote by a ‘check’ ˇ estimators and predictions derived from them. The covariance matrix _H_ of prediction errors of _q_ ˇ _O_ can be decomposed into three terms:

where:

- ˇ

- _• V_ 1 reflects the sampling variation of _mO_ = _XOθ_<sup>ˇ</sup> , resulting from the fact that _θ_ is estimated from the survey data (indicated by _θ_<sup>ˇ</sup> ) and the sampling distribution of _θ_ ˇ carries over to _XOθ_ ˇ

- _V_ 2 represents sampling variation induced by _θ_<sup>ˇ</sup> , as well as the estimators of the variance parameters, on Σ _OS_ (Σ _SS_ + _DS_ )<sup>_−_1</sup> (ˆ _qS − mS_ )

- _V_ 3 reflects the variance component that is due to the residuals _uO_ = _qO − mO_ , to the extent that they are independent of (and therefore cannot be predicted by) ˆ _qS − mS_

Estimators for _V_ 1 _, V_ 2 and _V_ 3 are proposed in Lemma 1 and in Appendix 1.

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**Aggregation** In general, precision will be comparatively low at the level of geographical units, while predicting poverty over larger areas increases precision as idiosyncratic errors are averaged out. Aggregation over groups of units (‘areas’) can be represented by a linear mapping _B_ . The estimator for the area-level poverty rate is seen to equal _Bq_ ˇ _O_ , while its variance-covariance matrix solves:

The standard errors of the area-level poverty estimates reported in Table 5 (in the column headed ‘SEM’) are obtained by evaluating the square root of the diagonal elements of _BHB_<sup>_T_</sup> .

**Lemma 1** _Let q, u, W, X,_ Σ _, ε; ω_ = ( _ρ, θ, σ_<sup>2</sup> _, τ_ ) _and index sets S, O be as defined and discussed above; assume further that observation errors eS are independent of ε and normally distributed with zero mean and given variance matrix DS_ = _EeSe_<sup>_T_</sup> _S_<sup>_._</sup> _Let_ ˇ _ω_ = (ˇ _ρ,_ Σ<sup>ˇ2</sup> _, θ,_<sup>ˇ</sup> ˇ _τ_ ) _be maximum-likelihood estimators of the corresponding parameters with_ ˇ _variance matrix V_ (ˇ _ω_ ) _, and let qO_ = _XOθ_<sup>ˇ</sup> +Σ<sup>ˇ</sup> _OS_ [Σ<sup>ˇ</sup> _SS_ + _DS_ ]<sup>_−_1</sup> (ˆ _qS−XSθ_<sup>ˇ</sup> ) _denote predictions of qO. Denote by SOS the matrix:_

_Then: (i)_ _with:_ _And: (ii) The three terms on the right side are asymptotically independent and their covariance matrices can be consistently estimated by:_

**Proof** Here we provide an outline of the proof. The detailed proof is given in Ap-

11
pendix 1. The first assertion follows from: Asymptotic independence of the first and second term on the right hand side of eq. (3) ˆ follows from the independence of _θ_<sup>ˇ</sup> and _qS − XSθ_<sup>ˇ</sup> and the fact that the information matrix of the model for _q_ ˆ _S_ is block diagonal in _θ_ and ( _ρ, σ_<sup>2</sup> _, τ_ ) respectively. As for independence between the third and the first two terms, note that the estimator _ω_ ˇ is a function of _uS_ + _eS_ and hence is uncorrelated with _rO_ = _uO − E_ ( _uO|uS_ + _eS_ ), which together with the normality assumptions implies independence.

To emphasize that the expectations of the first two terms are taken with respect to the sampling distribution of _ω_ we have used the symbol _Eω_ . The expressions for the asymptotic covariance of the first and third terms of eq. (3) are obvious. Details on the covariance matrices of the three terms and estimators for them are discussed in Appendix 1. □

# **3 Data**

Figure 1 (left panel) shows the map of Malawi, our study area. Malawi is a landlocked country in the South-East of Sub-Saharan Africa, situated between Zambia, Mozambique, and Tanzania, with a large lake alongside its Eastern border. Its territory has an elongated shape that is divided into a Northern, Central, and Southern region, with over 80 percent of the population residing in the Central and Southern regions (see Table 1). The country is still highly rural with just over 15 percent of the population (in 2010) residing in urban areas. The three largest cities span all three regions: Lilongwe (the capital) in the Central region with a population of 674,448 (2008), Blantyre in the Southern region with a population of 661,256 (2008) , and Mzuzu in the Northern region with a population of 133,968 (2008) (Malawi NSO 2008).

Both approaches considered in this paper rely on the 2010-11 Malawi Third Integrated Household Survey (IHS3), which is part of the Living Standards Measurement Study - Integrated Surveys on Agriculture (LSMS-ISA) project (Malawi National Statistical Office (NSO) and World Bank, 2012). The survey contains high-quality data on household consumption expenditure that is used to measure poverty, defined as the percentage of individuals whose total annual household consumption per capita fall below the national poverty line. Household expenditure and the poverty line are expressed in Malawi kwacha using February/March 2010 prices.<sup>4</sup> The poverty line, the sum of the

> 4For details on the price deflator used in the Malawi IHS3, we refer the reader to Malawi National

12
food and non-food poverty lines, equals kwacha 37,001.68.<sup>5</sup> The ELL approach combines the household survey with the Malawi 2008 Population and Housing Census (henceforward referred to as the census). The census provides individual and household level information on household composition, education, employment, dwelling characteristics and asset ownership. These data are used to obtain multiple imputed values for household consumption expenditures for all households in the census, which are then aggregated to obtain estimates of poverty at the small area level. Alternatively, the SEM approach model combines the household survey with remote sensing data, such as night time lights, urban footprints, major roads, population density, vegetation, surface temperature, rainfall. It uses these data to obtain multiple imputed values for village level (i.e. enumeration area) poverty rates which too can be aggregated to the small area level to facilitate a comparison between the two approaches. The following sub-sections provide further details on the respective databases used.

|In 2010|% population|% urban|
|---|---|---|
|Malawi|100|15.2|
|North|13.1|14.3|
|Central|42.6|15.4|
|South|44.3|15.2|

Table 1: Population in 2010

# **3.1 Household expenditure survey**

The Third Integrated Household Survey (IHS3) was conducted between March 2010 and March 2011. Its target universe consists of the households and individuals in all districts, except for the Likoma district. A total of 12,271 households were interviewed (with 668 replacements), see Table 2. The sample is designed to be representative at Statistical Office and World Bank (2012). For a more general discussion on spatial (and temporal) price deflation and real consumption measurement, see e.g. Gibson et al. (2017) and van Veelen and van der Weide (2008).

> 5The food poverty line in the IHS3 is Kwacha 22,956, the monetary cost of 2,400 calories per person per day, where the price of a calorie is estimated from the population in the 5th and 6th deciles of the aggregate distribution for consumption. The non-food poverty line (non-basic food needs) in the IHS3 is kwacha 14,045, and is estimated as the average non-food consumption of the population whose food consumption is close to the food poverty line.

13
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line. While there is a larger concentration of sampled clusters in and around major urban centers, the survey provides a complete coverage of the country including rural and more remote areas. Poverty rates are seen to vary considerably across space. On average however, poverty levels tend to be higher in more remote areas that located further away from the urban centers. Note that this does not imply that poverty is less of a concern in urban centers. In fact, the majority of the poor plausibly reside in urban centers due to the higher concentration of population there, i.e. despite the lower prevalence of poverty.

||2008 census|IHS3|
|---|---|---|
|# regions|3|3|
|# districts|32|31|
|# Wards/TAs|353|279|
|# EAs|12,575|767|
|# Households|2,859,720|12,271|

Table 2: Descriptive statistics of 2008 census and IHS3

# **3.2 Population census**

The enumeration for the 2008 Population and Housing Census for Malawi was carried out between June 8 and 28, 2008. It covers regular households, institutions, and the homeless. For the purpose of this exercise, institutions and the homeless are omitted. The total population was found to be 13,077,160. Table 2 reports the number of households in the census and number of sampled households in the survey at different levels of aggregation. The most disaggregated level at which poverty will be estimated is the Traditional Authority (TA) level, which we may also refer to as the‘small area level.

The administrative boundary data are taken from the National Statistical Office (NSO) of Malawi in order to match the boundaries with the census data at the enumeration area level. Malawi has 12,666 enumeration area boundaries from the 2008 census. The IHS3 household survey has 12,271 observations from 768 enumeration areas.<sup>6</sup>

> 6See the background report for more details on the design, sample and survey results at: http://microdata.worldbank.org/index.php/catalog/2939/download/41224

15
# **3.3 Public remote sensing data**

The analysis uses publicly available global remote sensing data from numerous sources and summarizes predictors derived from them at the administrative level (i.e. TA level) for Malawi. For most of the variables, we take advantage of the geographically comprehensive raster data structure, which uses pixels to form a grid that covers all land areas. From the raster structure we extract geo-referenced information at the administrative level. Using Geographic Information Systems (GIS) and Google Earth Engine, we overlay the administrative boundaries with other geo-referenced gridded data, (e.g. temperature, precipitation, elevation, etc.). When an administrative area consists of multiple pixels (which is typically the case), the pixel observations are collapsed (i.e. aggregated) to obtain summary statistics (e.g. mean and sum) at the administrative area level.<sup>7</sup> This process of extraction provides a nearly exhaustive correspondence. For a select few cases, we make two minor adjustments:

- Administrative areas near boundaries with water or small islands do not always overlay with the raster data. In this case, we first extract data by center point if the results from the polygon extract are missing. Second, we make a small adjustment by filling in the missing cells from the original raster with the average value of data from contiguous neighbors.

- When the polygon representing an administrative area is much smaller than the raster pixel size, we disaggregate the raster data. If the center point of the polygon is located in an area of “no data” (e.g. a lagoon or a lake), then we move the center point to the nearest land pixel. We also calculate the area at the pixel size to ensure consistency between the sum of pixel values and the corresponding land area.<sup>8</sup>

For the remaining data, we use vector data to calculate distances. Table 3 lists the variables considered in this paper that have been derived from publicly available remote sensing datasets. These variables are assembled into various themes related to initial conditions, agriculture, climate, environment, socio-economic conditions, population and remoteness. Specific details on the source and construction of the variables can be found in Appendix 2.

> 7 We use two geometries (center points and polygons) to represent the administrative area. We extract raster data by polygon using the extract function in R. In Google Earth Engine, we use the Reducer function over a region at the administrative level.

> 8An area calculation with the vector data provides more accurate measurements, however it does not always yield consistent area with the pixel calculations, which is necessary to ensure variables with the share are between 0 and 1.

16
|**_Theme_ / Layer**|**Description**|**approximate grid**<br>**size**|**Source**|
|---|---|---|---|
|_Initial conditions_||||
|dist2cap|Distance to capital|N/A|NSO and Global|
||||Insights v6.1|
|dist2border|Distance to border|N/A|NSO|
|dist2major<br>river|Distance to major river<br>(centerline)|N/A|NSO and Nat-<br>ural Earth 3.0<br>1:10 million|
||||(2017)|
|dist2rail|Distance to railway|N/A|NSO and Global<br>Insights v6.1|
|elev30m|Elevation from SRTM|90m and 1km2|Jarvis et al.<br>(2008)|
|srtm<br>~~p~~opmask|Elevation in populated ar-|1km2|Jarvis et al.|
||eas in 2012 from Landscan||(2008); Bright<br>et al. (2013)|
|Slope|Slope (degrees of slope<br>(x100))|30-arc-seconds|Verdin et al.<br>(2007)|
|Ruggedness|Ruggedness Index|3 arc-seconds|Nunn and Puga<br>(2012)|
|rugged<br>~~p~~opmask|Ruggedness Index in popu-<br>lated areas|1km2|Nunn and Puga<br>(2012); Bright<br>et al. (2013)|
|_Agriculture_||||
|ag<br>~~h~~ybrid|Agricultural Hybrid|1km2|Fritz et al.<br>(2015)|
|lgp50<br>~~v~~6990|Length of Growing Period|10km2|FAO-GAEZ ver-<br>sion 3 (Fischer<br>et al. 2012)|
|rain<br>~~c~~rop<br>~~s~~h|Share of area with rainfed|1km2|GFSAD1000|
||crop||V1.0: (Telu-|
||||guntla et al.<br>2014)|

17
|**_Theme_ / Layer**|**Description**|**approximate grid**<br>**size**|**Source**|
|---|---|---|---|
|irrigated<br>~~c~~rop<br>~~s~~h|Share of area with irrigated<br>crop|1km2|GFSAD1000<br>V1.0: (Telu-<br>guntla et al.<br>2014)|
|agr<br>~~o~~ppt<br>~~c~~ost|Global map of gross eco-<br>nomic rents from agricul-<br>tural lands (2000 US dol-<br>lars per hectare per year)|10km2|Naidoo and<br>Iwamura (2007)|
|_Climate_||||
|bio1|Annual Mean Temperature|1km2|Bioclim (Hi-<br>jmans et al.<br>2005)|
|bio4|Temperature Seasonality<br>(standard deviation *100)|1km2|Bioclim (Hi-<br>jmans et al.<br>2005)|
|bio12|Annual Precipitation|1km2|Bioclim (Hi-<br>jmans et al.<br>2005)|
|bio15|Precipitation Seasonality|1km2|Bioclim (Hi-|
||(Coefcient of Variation)||jmans et al.<br>2005)|
|bio16|Precipitation of Wettest|1km2|Bioclim (Hi-|
||Quarter||jmans et al.<br>2005)|
|bio17|Precipitation of Driest<br>Quarter|1km2|Bioclim (Hi-<br>jmans et al.<br>2005)|
|oxmap<br>~~d~~aylst|Day time land surface tem-<br>perature (Celcius)|5km2|MOD11A2 and<br>Weiss et al.<br>(2014)|
|oxmap<br>~~n~~gtlst|Night time land surface<br>temperature (Celcius)|5km2|MOD11A2 and<br>Weiss et al.<br>(2014)|

18
|**_Theme_ / Layer**|**Description**|**approximate grid**<br>**size**|**Source**|
|---|---|---|---|
|Aridity|Aridity Index|1km2|Trabucco and<br>Zomer (2009)|
|Pet|Potential Evapotranspira-|1km2|Trabucco and|
||tion||Zomer (2009)|
|_Environment_||||
|NDVI|Normalized Diference|10km2|Zhu et al.|
||Vegetation Index (NDVI)<br>(1981-2011)||(2013)|
|lndsatndvi<br>~~2~~008|Normalized Diference||LandSat|
||Vegetation Index (NDVI)<br>(2008)|||
|EVI|Enhanced Vegetation Index<br>(EVI)|5km2|MODIS BRDF-<br>corrected<br>imagery<br>(MCD43B4)<br>with gap-flled<br>method by<br>Weiss et al.<br>(2014)|
|Forloss|Forest Loss (2008 – 2000)||Hansen et al.<br>(2013)|
|PM2.5|Particulate Matter 2.5 at<br>35% RH (ug/m3) (no dust<br>or seasalt) (2008)|1km2|van Donkelaar<br>et al. 2015|
|ET<br>~~s~~olrad|Extraterrestrial Solar Radi-<br>ation by month|2.5km2|Zomer et al.<br>2008|
|_Socio-economics_||||
|NTL|Night Time Lights (1996,|1km2|NOAA DMSP-|
||2000, 2010)||OLS|

19
|**_Theme_ / Layer**|**Description**|**approximate grid**|**Source**|
|---|---|---|---|
|||**size**||
|_Population count and_||||
|_density_||||
|lpop12|Landscan (2012)|1km2|Bright et al.<br>(2013)|
|urban<br>~~l~~pop12|Urban population|1km2|Bright et al.<br>(2013); WDI<br>(2017); Authors’<br>calculations|
|ghspop|GHS-Pop (1975, 1990,<br>2000, 2014)|1km2|Freire et al.<br>(2016)|
|ghsbuiltup|GHS-Built up (1975, 1990,<br>2000, 2014)|300m|Freire et al.<br>(2016)|
|_Travel time and ac-_<br>_cessibility_||||
|dist2railway|Distance to railway|N/A|NSO and Global<br>Insights v6.1|
|tt50k2000|Mean Travel time to major<br>cities (circa 2000)|1km2|Uchida and Nel-<br>son (2008)|
|tt50k2010|Mean Travel time to major<br>cities (circa 2010)|1km2|Berg et al. (in<br>prep)|
|ai50k2000|Agglomeration Index (circa<br>2000)|1km2|Uchida and Nel-<br>son (2008)|
|ai50k2010|Agglomeration Index (circa|1km2|Roberts et al.|
||2010)||(2017)|

Table 3: Data source summary 20
# **4 Empirical application to Malawi**

## **4.1 Model selection and estimation of model parameters**

### **4.1.1 ELL approach: Household level data with household expenditure as dependent variable**

We rely on variables that are available in both the survey and the census. The first step of our model selection procedure groups candidate variables by type: (i) demographics, (ii) education, (iii) employment, (iv) dwelling characteristics, (v) asset ownership, and (vi) village level variables. This latter group includes variables that are created by computing mean values of selected variables from the population census at the enumeration-area (EA) levels (think of local employment rates, share of the population with given levels of education and the penetration of phone use) and variables derived from the publicly available remote data (think of night-time-lights, distance to nearest city and river, local climate, and agricultural land quality).

Next, we regress the log of per capita expenditure (combined with region and urban dummies) on each group separately using Ordinary Least Squares (OLS). Independent variables that are not significant at the 5% level are sequentially dropped from the regressions, starting with those that are least significant. Once all groups have been considered we select the group that provides the best fit, combine this with the group that provides the second-best fit, and continue to trim the variables that cease to be significant. This process is continued until every single group has been given a chance to contribute one or more variables to the model. We allow for interactions with the urban-rural dummy to capture selected area heterogeneities (see Tarozzi and Deaton, 2009; Tarozzi, 2011). Finally, LASSO model selection is implemented to verify that all key variables are accounted for. The same procedure is applied to obtain the heteroskedasticity model describing the variance of the errors. The resulting regression models are included in Appendix 3.

Among the different categories of explanatory variables, dwelling characteristics and household asset ownership rank as the strongest predictors of household consumption expenditure per capita, followed by household head education and employment variables. An interesting observation is that local area night-time-lights, agricultural land quality, and climate data (derived from public remote sensing data that serve as predictors in the SEM approach) are found to be significant when included on their own – but once we control for variables available in the population census, these variables lose their significance and are subsequently dropped from the model.

Once the models have been selected, the model parameters are estimated by going 21
through the following steps: (a) estimate the models using OLS and extract the residuals; (b) estimate the unconditional variance parameters _σv_<sup>2and</sup><sup>_σ_</sup> _ε_<sup>2,usingHenderson’s</sup> method III (see Henderson, 1953; and Searle et al., 1992); (c) estimate the conditional variance _σε,ah_<sup>2;andfinally(d)constructthecovariancematrixΩ=</sup><sup>_E_</sup> � _vv_<sup>_T_</sup> + _εε_<sup>_T_</sup> _|x_ � = _σv_<sup>2</sup><sup>_In_+ diag(</sup><sup>_σ_</sup> _ε,ah_<sup>2),andcomputethefeasibleGLSestimatorfor</sup><sup>_β_.</sup>

While the regression coefficients purely capture correlations and not causal effects, it is instructive to verify what predictors stand out and inspect the signs of their effects. As one would expect, higher (lower) quality materials used for roof, floor, and walls as well as a larger (smaller) number of rooms are positively (negatively) correlated with (log) household expenditure. Household assets, particularly, owning a car, fridge, cooker, and tv, all report positive regression coefficients. Furthermore, we observe that per capita household expenditures tend to be higher (lower) for smaller (larger) households, and for households with a more (less) educated household head.

# **4.1.2 SEM approach: Village level data with village poverty rate as dependent variable**

A similar procedure is adopted to build the model for village level poverty using variables derived from public remote sensing data as predictors which are grouped into: (i) population density and land size, (ii) night time lights, (iii) road connectivity and distance to cities, borders and rivers, (iv) climate and environment, and (v) agricultural suitability variables. Among these categories of variables, night time lights, market access (i.e. road connectivity), and local climate and environment report the highest correlations with village poverty with similar in-sample goodness-of-fit levels. The final model has 15 explanatory variables.

We estimate the model by maximum likelihood. The distance decay parameter _τ_ is set to _τ_ = 0 _._ 54, which maximizes the in-sample goodness-of-fit (measured by the correlation between predicted and observed poverty rates). It turns out that, except for _ρ_ , the parameters (as well as their conditional covariance matrix) are not very sensitive to the choice of _τ_ . The estimation results are reported in Table 4, where poverty is measured as a percentage. Details on working out the asympototic variance-covariance matrix of the parameter estimators are given in Appendix 1.

While also here the regression coefficients capture correlations and not causal effects, it will nevertheless be instructive to inspect the signs of the correlations. Lower poverty rates are associated with higher levels of population density, higher values of night time lights and higher shares of cultivated land that can be irrigated through rainfall. In contrast, higher poverty rates are associated with increased remoteness (i.e. larger distances from major cities), higher levels of ruggedness, and higher rates of forest loss.

22
||Poverty (NSO)|
|---|---|
|(Intercept)|-0.45205 **<br>(0.21987)<br>|
|ln<br>~~l~~pop12|-0.03781 ***<br>(0.00734)|
|ln<br>~~r~~ugged|0.02051 **<br>(0.01005)|
|ln<br>~~s~~lope|-0.06148 ***<br>(0.01745)|
|ln<br>~~f~~orloss|0.07558 ***|
||(0.01169)|
|agr<br>opp<br>~~c~~st|0.0085 ***|
||(0.00328)|
|rain<br>~~c~~rop<br>~~s~~h|-0.02675<br>|
||(0.01844)|
|dist2major<br>~~r~~iver|-0.00131 ***<br>(0.00016)|
|ln<br>~~t~~t50k2010|0.02608 **|
||(0.01045)|
|ln<br>~~n~~tl<br>~~2~~010|-0.02033 **|
||(0.00968)|
|ln<br>~~n~~tl<br>~~1~~996|-0.03566 ***|
||(0.01279)|
|bio1|-0.00406 ***|
||(0.00077)|
|bio4|-0.00021 ***|
||(4e-05)<br>|
|pet|0.00147 ***<br>(0.00016)|
|s2|0.02357<br>(0.24747)|
|rho|0.75524 ***<br>(0.00165)|
|Observations|765|
|adj. _R_<sup>2</sup>|0.558|

Table 4: Parameter estimates of SEM model with _τ_ = 0 _._ 54 t-statistics in parentheses: * p _<_ 0.10, ** p _<_ 0.05, *** p _<_ 0.01

# **4.2 Comparing poverty maps**

Before we inspect the estimates of poverty at the small area level, let us first evaluate the estimates at the national and the regional levels. Since the IHS3 survey is designed to be representative at these levels, the survey direct estimates provide a natural benchmark to compare our model-based estimates against. The ELL and SEM estimates are 23
obtained by aggregating the small area estimates to the national and regional level using population weights. The results are shown in Table 5. The model-based estimates from both approaches are seen to line up with the survey-direct estimates. ELL and SEM both identify the North and South as the regions with the highest rates of poverty.<sup>9</sup> While the two approaches disagree slightly on the ordering of these two regions, the observed difference in the poverty estimates lies well within the 95 percent confidence interval.

More striking is the difference in statistical precision between the two approaches. ELL achieves slightly greater statistical precision than the survey-direct estimates (by virtue of combining the survey with unit record population census data), while the standard errors obtained by the SEM approach are notably larger (between two and three times the ELL standard errors). This difference in precision is in large part due to divergence in number of observations used to estimate the model parameters: 12,271 households in the ELL approach versus 767 PSUs in the SEM approach. The variance of the poverty estimates are largely driven by the variance of the model parameter estimates, which in turn scales with the number of observations used in the respective regression model. As the model adopted by ELL is at the household level, it has 16 times more observations to work with compared to the SEM approach.

||survey-direct|ELL||SEM||
|---|---|---|---|---|---|
|Malawi|0.507 (0.009)|0.498|(0.006)|0.492|(0.023)|
|North|0.543 (0.021)|0.562|(0.018)|0.540|(0.022)|
|Central|0.445 (0.015)|0.438|(0.009)|0.434|(0.024)|
|South|0.555 (0.014)|0.537|(0.008)|0.533|(0.026)|

Table 5: Estimates of poverty from the survey, ELL and SEM The small area estimates of poverty for the two approaches are presented in Figure 2, which shows the two poverty maps side by side. A visual inspection of the two maps shows a striking agreement on the spatial distribution of poverty. Both maps suggest low levels of poverty in the urban areas of Mzuzu, Kasungu, Lilongwe, Zomba, and Blantyre, as well as areas of high poverty in the far north and south of the country.

9SEM slightly underestimates poverty in areas of the Northern region with comparatively low rates of poverty.

24
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||Poverty (NSO)|Poverty (Public)|
|---|---|---|
|(Intercept)|-0.45205 **|-0.58123 **|
||(0.21987)|(0.22611)|
|ln<br>~~l~~pop12|-0.03781 ***|-0.02969 ***|
||(0.00734)|(0.00848)|
|ln<br>~~r~~ugged|0.02051 **|0.02977 ***|
||(0.01005)|(0.01076)|
|ln<br>~~s~~lope|-0.06148 ***|-0.05727 ***|
||(0.01745)|(0.01836)|
|ln<br>~~f~~orloss|0.07558 ***|0.04426 ***|
||(0.01169)|(0.01122)|
|agr<br>opp<br>cst|0.0085 ***|0.01517 ***|
||(0.00328)|(0.00357)|
|rain<br>~~c~~rop<br>~~s~~h|-0.02675|-0.02488|
||(0.01844)|(0.02009)|
|dist2major<br>~~r~~iver|-0.00131 ***|-0.00131 ***|
||(0.00016)|(0.00017)|
|ln<br>~~t~~t50k2010|0.02608 **|0.02195 *|
||(0.01045)|(0.01145)|
|ln<br>~~n~~tl<br>~~2~~010|-0.02033 **|-0.01452|
||(0.00968)|(0.01016)|
|ln<br>~~n~~tl<br>~~1~~996|-0.03566 ***|-0.03638 ***|
||(0.01279)|(0.01248)|
|bio1|-0.00406 ***|-0.00401 ***|
||(0.00077)|(0.00079)|
|bio4|-0.00021 ***|-0.00025 ***|
||(4e-05)|(4e-05)|
|pet|0.00147 ***|0.00153 ***|
||(0.00016)|(0.00017)|
|s2|0.02357|0.02622|
||(0.24747)|(0.3463)|
|rho|0.75524 ***|0.6478 ***|
||(0.00165)|(0.00181)|
|Observations|765|738|
|adj. _R_<sup>2</sup>|0.558|0.514|

Table 6: Parameter estimates of SEM model with _τ_ = 0 _._ 54 t-statistics in parentheses: * p _<_ 0.10, ** p _<_ 0.05, *** p _<_ 0.01 difference is small, and (b) as expected, the correlation between the two SEM estimates is high. Figures 8 and 9 confirm the close correspondence by comparing the respective poverty maps.

29
<!-- Start of picture text --> Public NSO<br>9° - ors-<br>@<br>N iN<br>11°S- = 11°S- :<br>? yy [-] Protected Area<br>Ye 8s<br>Poverty<br>all as (0.682,0.973]<br>13°S - /; Li Ki 13°S - b Fil i (0-619.0-682]<br>& g t (0.554,0.619]<br>< a). 3S US (0.504,0.554]<br>Z —. : : (0.445,0.504]<br>Yi éA sy éi N (0.399,0.445]lo0.321,0.399 rvooson<br>: % ] : > ] (0.092,0.172]<br>15°S- - 15°S- . [0,0.092]<br>qf Cw dt % A<br>17°S- 47°S-<br>33.5°E 35.0°E 33.5°E 35.0°E<br><!-- End of picture text -->
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estimation of statistical precision, meaning that the estimated SEs obtained using the private NSO coordinates will arguably provide more accurate estimates of precision.

||BP (NSO)|BP (Public)|OLS (Public)|
|---|---|---|---|
|EA|0.155|0.165|0.186|
|TA|0.039|0.0.038|0.036|
|Region|0.0245|0.0199|0.011|
|National|0.0230|0.0178|0.0075|

Table 8: Mean standard errors (SEs) of poverty estimates from BP (NSO), BP (Public), and OLS for different levels of aggregation.

Provided that the spatial correlation structure is only partially destroyed by scrambling the coordinates, this explanation would predict that SEs obtained with public coordinates would be higher than SEs obtained using OLS which would fully ignore any spatial correlation structure in the errors, yet lower than SEs obtained with the private NSO coordinates (where the spatial correlation structure is fully accounted for). Fully ignoring the spatial correlation structure, as the OLS model does, would lead to a comparatively larger downward bias in SEs at more aggregate levels (as errors are – incorrectly assumed to average out) relative to SEs obtained with the spatial regression models. Both predictions are born out, as can be seen in Table 8 (which also includes estimates of SEs obtained with OLS). Standard statistics measuring the degree of spatial correlation found in the residuals are reported in Table 6, which confirm that the errors from the regression model with public coordinates exhibit a weaker spatial correlation structure.

# **5 Concluding remarks**

This study investigates whether an accurate poverty map could be obtained by combining remote sensing data that are available in the public domain with household consumption survey data. This approach to poverty mapping takes advantage of the fact that geo-referencing survey locations (i.e. Primary Sampling Units; PSUs) have become standard in recent years and that remote-sensing data from which predictors of poverty can be derived have become widely available. It should be noted, however, that 32
the publicly available geo-coordinates of survey locations are generally subjected to a random offset (i.e. are scrambled) in order to protect the anonymity of survey respondents. A second objective of this study therefore is to investigate whether these random offsets undermine the ability of this approach to produce accurate poverty maps.

Assessing the success of this alternative approach to producing a poverty map will depend on how success is measured. When the ability to capture the geography of poverty is used as the metric of success, our analysis suggests that estimating small area poverty using remote sensing data offers a promising alternative to building a poverty map using population census data. In our application to Malawi the two approaches are found to produce maps that show nearly identical geographies of poverty. When the objective is to identify poverty in a specific district or set of districts of the country, however, we find that poverty estimates obtained using remote sensing data can deviate substantially from the benchmark estimates obtained using population census data. In summary, the value of poverty maps built using remote sensing data alone will depend on the needs of the decision makers.

On the empirical question of whether randomly off-setting survey coordinates (to protect anonymity of survey respondents) may undermine the accuracy of a poverty map derived from remote-sensing data, our findings echo the comparison with census-based estimates. The random scrambling of the geographic coordinates does not meaningfully alter the estimated geography of poverty, yet may have meaningful impact on estimates for individual districts and may furthermore lead to an over-estimation of statistical precision. The latter observation arguably stems from the fact that the random offsets partially destroys the spatial correlation structure in the data and error term.

Our validation study confirms that for many practical purposes accurate poverty maps can be obtained in countries where population census data are not available. Given that remote sensing data are globally available and are typically updated on an ongoing basis, this also opens the door to updating poverty maps on a higher frequency – whenever new household survey data become available. On a practical note, since the remote-sensing-based models are estimated at the survey PSU level (rather than household level), with the area-level poverty rate as dependent variable (rather than household income or consumption), experimenting with alternative poverty measures or alternative poverty lines would require returning repeatedly to the basic modeling stages of the analysis. This is not the case in the census-based approach, where the model is estimated at the household level. In this sense the remote-sensing-based approach can become rather burdensome.

It remains to be verified whether the remote-sensing-based approach is equally successful in heavily urbanized settings. Small, though not necessarily low-population, 33
administrative units found in cities may be more difficult to model, particularly when wealthy and poor neighborhoods are in close proximity to each other. Differences across such neighborhoods are conceivably harder to capture using the satellite images that are currently available in the public domain. On a positive note, the technology underlying satellite imagery data is rapidly evolving, and with it the artificial intelligence algorithms that derive usable data from the images (see e.g. Jean et al., 2016; Burke et al., 2021). In conclusion, validating the approach in different locations will be important. Now that we established that the approach works well in a country like Malawi, it remains to be verified whether it is equally successful in countries with different levels of development, different levels of urbanization and different degrees of population density.

34
# **Appendix 1: Variance of the prediction error**

## **Introduction**

Consider a simple data generating mechanism: with the assumptions that _ε_ and _x_ are independent, realizations of the DGP are independent, and _Eε_ = 0 _, Eε_<sup>2</sup> = _σε_<sup>2.Wewanttoestimatetheprecisionofpredicting</sup> ˇ _y_ conditional on _x_ , using parameter values _θ_<sup>ˇ</sup> and _σ_<sup>2</sup> for _θ_ and _σε_<sup>2,consistentlyesti-</sup> mated from an appropriate sample of ( _y, x_ ) observations. If ( _y_ 0 _, x_ 0) is an out-of-sample ˇ observation and _y_ 0 is predicted by _y_ 0 = _f_ ( _x_ 0 _, θ_<sup>ˇ</sup> ) the prediction error is: The prediction error consists of two parts, which we will term _model error f_ ( _x_ 0 _, θ_ ) _− f_ ( _x_ 0 _, θ_<sup>ˇ</sup> ) and _idiosyncratic error ε_ 0. Under the model assumptions (and assuming a typical sampling scheme for the sample of ( _y, x_ ) observations on which the estimator for _θ_ is based) the two error components are independent and a consistent estimator for the mean square prediction error is: where: and where the latter expectation is based on the (asymptotic) distribution of the _θ_<sup>ˇ</sup> estimator (typically using the ‘delta method’ if _f_ is nonlinear).

## **Prediction errors in the SEM model**

Denote by _qS_ and _qO_ the vectors of poverty rates in survey locations and non-survey locations respectively. Predictions of _qO_ are based on out-of-sample application of the SEM model: where we have imperfect observations _q_ ˆ _S_ of _qS_ , due to sampling variation: 35
With this data generating process the best linear unbiased prediction of _q_ is: for both in-sample and out-of-sample locations, and _uS_ = _qS − XSθ_ . Let the idiosyncratic part of prediction error given _X_ and _q_ ˆ _S_ be denoted by _r_ : with variance matrix _Err_<sup>_T_</sup> .

An empirical implementation involves sampling variation of estimators for _θ_ and ˆ hence estimates of the residual _uS_ + _eS_ = _qS − XSθ_ . Let _θ_<sup>ˇ</sup> denote the maximumlikelihood estimator for _θ_ . Then: With normally distributed residuals ( _uS, eS, uO_ ), _E_ ( _u|uS_ + _eS_ ) is linear in _uS_ + _eS_ . Because _q_ ˆ _S − XSθ_<sup>ˇ</sup> and _θ_<sup>ˇ</sup> are asymptotically independent for consistent and asymptotically normal estimators of _θ_ , the sampling variance of _q_ ˇ, given _X_ and _q_ ˆ _S_ can be estimated by:

ˇ ˆ where _Z_<sup>ˇ</sup> denotes the sampling variance of _u_ = _E_ ( _u|uS_ + _eS_ = _qS −XSθ_<sup>ˇ</sup> ). Combining the sources of idiosyncratic and model error, the total covariance matrix _H_ of prediction ˇ error _q − q_ is estimated by:

Below, these three components will be discussed in turn.

# **Estimation**

## **Estimating** _V_ ( _θ, ρ, σ_<sup>ˇ2</sup> _, τ_ )

The SEM model is estimated by maximum likelihood (ML), assuming normally distributed error terms throughout. Under these assumptions, and given the variance parameters _ρ_ and _σu_<sup>2aswellasexogenous</sup><sup>_V_(</sup><sup>_eS_),MLestimationof</sup><sup>_θ_amountstoGLS.</sup> Moreover, asymptotically the full covariance matrix of the full parameter estimator is block diagonal in the components relating to _ρ, σu_<sup>2and</sup><sup>_θ_respectively.Inpracticewe</sup> concentrate the likelihood function on ( _ρ, σu_<sup>2),estimatingthevarianceparametersand</sup> 36
their covariance matrix first. The estimator for _θ_ and its covariance matrix then follows from GLS.

**Estimating** _Z_<sup>ˇ</sup> = _V_ (ˇ _uO_ )

Given the residual process _u_ = _σ_ ( _I − ρW_ )<sup>_−_1</sup> _ε_ , we have: where _C_ = ( _I − ρW_ )<sup>_−_1</sup> . Recall that for _i_ = _j_ , _Wij_ = _Tij_<sup>_−τ_</sup> with _T_ a (scaled) symmetric matrix of distances between locations _i_ and _j_ , and _Wii_ = 0. Partition the variance matrix Σ according to in-sample locations ( _S_ ) and out-of-sample locations ( _O_ ) so that we can write: Also, let Σ _·S_ denote the first ’column’ of this partition: Assuming normally distributed _ε_ and survey error _eS_ , it follows that: where _DS_ is the variance matrix of _eS_ , established separately, based on the survey design, and taken as a given matrix of parameters.<sup>10</sup> The empirical counterpart is: – and is subject to model error the topic of this sub-section.

We approximate the MSE of _u_ ˇ using the Delta method. Let operator _d_ () indicate taking (infinitesimal) deviations from the true parameter values. Then: ˆ To simplify notation, write _A_ = Σ _·S_ [Σ _SS_ + _DS_ ]<sup>_−_1</sup> and _b_ = _qS − XSθ_ , with obvious derived meaning of _A,_<sup>ˇˇ</sup> _b_ . Then, denoting actual deviations from true parameter values

> 10Under the model assumptions _DS_ stems from variation in _XS_ and _σε_ 2<sup>.Alternatively,itcould</sup> therefore be argued that _DS_ is increasing in _σ_<sup>2</sup> . We ignore this complication here.

37
by ∆, we get: In the expression above, symbols without accent indicate ‘true’ values, i.e, constants with respect to the expectation operator. In actual computation they are replaced by estimated values. The two last terms of the equation vanish asymptotically, because ∆( _A_<sup>ˇ</sup> ) and ∆(<sup>ˇ</sup> _b_ ) are asymptotically independent with zero expectation.<sup>11</sup> The second term of equation (4) evaluates to: For the first term of equation (4) we need to work out _d_ ( _A_<sup>ˇ</sup> ). Note that: and that Σ _/σ_<sup>2</sup> does not depend on _σ_<sup>2</sup> . In what follows Σ<sup>_∗_</sup> and _DS_<sup>_∗_will refer to Σ</sup><sup>_/σ_2 and</sup> _DS/σ_<sup>2</sup> . Also, when there is no danger of confusion, we will omit accents from symbols. It follows that: where: _d_ (Σ _·_<sup>_∗_</sup> _S_<sup>)isthe</sup><sup>_·S_sub-matrixof:</sup> Likewise, with _d_ (Σ<sup>_∗_</sup> _SS_<sup>)the</sup><sup>_SS_sub-matrixof</sup><sup>_d_(Σ</sup><sup>_∗_)givenabove.Toevaluatetheseexpressions,it</sup>

> 11Independence follows from (i) the normality assumptions; (ii) linearity of ∆( ˇ _A_ ) in (∆(ˇ _ρ_ ) _,_ ∆ � _σ_ ˇ<sup>2�</sup> ) and linearity of ∆(<sup>ˇ</sup> _b_ ) in ∆( _θ_<sup>ˇ</sup> ); (iii) the information matrix _I_ ( _θ, ρ, σ_<sup>2</sup> _, τ_ ) of the data generating process is block diagonal, _I_ � _θ, ρ, σ_<sup>2</sup> _, τ_ � = diag( _I_ ( _θ_ ) ; _I_ ( _ρ, σ_<sup>2</sup> _, τ_ )). See e.g., Mardia, K. V.; Marshall, R. J. (1984). “Maximum likelihood estimation of models for residual covariance in spatial regression”. Biometrika. 71 (1): 135–46.

38
can be that: so that: Finally, when working out _E_ (∆ _A_ ) _bb_<sup>_T_</sup> ∆ _A_<sup>_T_</sup> , the (co)variance between ∆ _ρ_ and ∆ _σ_<sup>2</sup> is taken from the corresponding components of the covariance matrix of the estimators for the model’s variance parameters.

**Estimating** _E_ [ _rorO_<sup>_T_]</sup>

Finally, using _r_ = _u − E_ ( _u|X,_ ˆ _qS_ ), the idiosyncratic variance _Err_<sup>_T_</sup> is consistently estimated by:

# **Appendix 2: Source of Remote Sensing Variables**

We describe below the data sources and provide an overview of the specific variables that are constructed for the remote-sensing based analysis in this paper.

## **Initial conditions:**

The capital is distinct from other areas due to its centrality of political decisions and public disbursement. We measure the bird-flight (Euclidean) distance from the center 39
point of each administrative area to the coordinates of the capital (from the Global Insights (v 6.1) data), which we call _dist2cap_ . Likewise, we calculate distance from the center point of each administrative area to the border ( _dist2border_ ) using the boundary file provided by the NSO.

In consideration of the initial conditions of administrative areas for regional trade, we construct distance to major rivers ( _dist2major_ _~~r~~ iver_ ) and distance to coast ( _dist2coast_ ). Also here we use the center point of the administrative areas as the points of origin and destination. Major rivers and coastline data are from Natural Earth<sup>12</sup> .

In addition, we consider the terrain with regards to the elevation, slope and ruggedness. The elevation data are from the Shuttle Radar Topography Mission (SRTM) Digital Elevation dataset (version 4) and is measured in meters at 3 arc-seconds and 30 arc-seconds (approximately 1km<sup>2</sup> ) (Jarvis et al. 2008). We summarize mean and max: _elev_ and _elev_ _~~m~~ ax30_ . We derive elevation in populated places using a 1% threshold level, which is approximately 10 people per km2 from the Landscan 2012 dataset (described in the population count and density section). We take advantage of the slope function on Google Earth to process the 3 arc-seconds elevation data into a slope variable: _slope_ .<sup>13</sup> Figure A2.1 (left panel) illustrates the variation of slope, where the Great Rift Valley is seen to run from North to South. The Ruggedness Index we use is developed by Nunn and Puga (2012) which measures the level of ruggedness in hundreds of meters of elevation difference for each grid cell. We summarize the pixel mean ( _rugged_ ) and maximum ( _rugged_ _~~m~~ ax_ ) of this ruggedness index evaluated over the entire administrative areas as well as over populated areas ( _rugged_ _~~p~~ opmask_ and _rugged_ _~~m~~ ax_ _~~p~~ opmask_ ). Populated areas are defined as areas with any population in the Landscan 2012 population model (described in population count and density section below). Figure A2.1 (right panel) shows the spatial variation of the log of _rugged_ .

# **Agriculture:**

Agriculture and arable land can indicate higher economic growthpotential, or conversely, imply a lack of urbanization and infrastructure. Agricultural activities provide evidence of economic activity, which in turn may indicate a presence of water infrastructure. In order to measure agricultural land-use we use the Global Hybrid dataset (0611-2012 V2) produced by Fritz et al. (2015), which estimates the percentage share of land used for agriculture within a one square kilometer pixel. Expert assessment of five existing global land cover products along with national and subnational crop statistics as inputs provides the likelihood of a pixel indicating agricultural land use. By mul-

> 12Large scale (1:10 million) vector data are available for download from: http://www.naturalearthdata.com/downloads/

> 13Similarly, Verdin et al. (2007) derive slope measures at 30-arc-seconds derived from the 3-arcseconds SRTM data.

40
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<!-- Start of picture text --> median NDVI<br>0.113 - 0.468<br>0.469 - 0.517<br>Mm 0.518 - 0.562<br>Ml 0.563 - 0.618<br>ME 0.619 - 0.829<br><!-- End of picture text --> <!-- Start of picture text --> PET<br>1314.5- 1505.5<br>1505.6 - 1557.6<br>M§) 1557.7- 1599.5<br>MMB 1599.6- 1636.5<br>MM 1636.6- 1912.9<br><!-- End of picture text -->
database (FGGD). The FGGD 2005 data includes a suitability index for rain-fed crops measured at a spatial resolution of 5 arc-minutes (10 km) (Van Velthuizen et al. 2007).<sup>16</sup> We also include the production of plant biomass using the measurement of Net Primary Productivity (NPP), which is the result of all the carbon used in photosynthesis minus the loss of carbon from the maintenance respiration. Google Earth Engine provides the cloud-corrected MODIS product (MOD17A3) data at 1km spatial resolution summarized at the annual level from the 45 8-day Net Photosynthesis (PSN) products. Evaluating the mean level at the administrative level yields the variable _npp_ .

Naidoo and Iwamura (2007) derive a global map of gross economic rents from agricultural lands (in 2000 US dollars per hectare per year) by integrating spatial information on crop productivity, livestock density, and producer prices from FAOSTAT (http://faostat.fao.org; accessed June 2005). We extract these economic rents by pixel and summarize the mean over the administrative unit ( _agr_ _~~o~~ pp_ _~~c~~ st_ ).

# **Climate:**

Climate provides the initial conditions to agricultural production and human settlement. Increasing change in climate will arguably affect conditions to support agricultural production. In a low production scenario, Hertel et al. (2010) find that the prices for major staples rise 10–60% by 2030, which would have heterogenous impacts on the poor depending on local changes in agricultural production and the sources of income for households in the area. In the case of drought and urban floods, Winsemius et al. (2015) find evidence that the poor already are overexposed to natural hazards of floods and droughts and are vulnerable to changes in climate.

BioClim is a global gridded database at 30 arc-second (1km2) spatial resolution of bioclimatic variables that are derived from monthly temperature and rainfall values from cleaned weather station data and elevation. The bio-physical model interpolates these meteorological variables and provides derivative variables of seasonality over the base period of 1960 to 1991 (Hijmans et al. 2005)<sup>17</sup> . We extract these 1km2 pixels for annual mean temperature ( _bio1_ in degrees Celsius * 10), temperature seasonality ( _bio4_ in standard deviation * 100), annual precipitation ( _bio12_ in mm * 10), precipitation seasonality ( _bio15_ in coefficient of variation * 10), precipitation of wettest quarter ( _bio16_ in mm * 10) and precipitation in driest quarter ( _bio17_ in mm). We aggregate the data to obtain mean values for each administrative area. In Figure A2.4 (left panel), we see the effect of elevation in the higher temperature of the Great Rift Valley

> 16We modified negative values that represent pixels classified as urban, closed forest or irrigated to equal zero for the mean calculations by administrative area.

> 17For the interpolation of noisy multi-variate meteorological data, the authors use thin plate smoothing splines from the ANUSPLIN program with latitude, longitude, and elevation as independent variables.

44
<!-- Start of picture text --> \<br>rela<br>:<br>‘8<br>biot<br>162.4 - 199.8<br>199.9 - 208.5<br>Ml 208.6 - 219.0<br>MH 219.1 - 234.6<br>MB 234.7 - 264.0<br><!-- End of picture text --> <!-- Start of picture text --> }<br>; &<br>q<br>* ’ a<br>bio4 ' }<br>1350 - 1921<br>1922 - 2197<br>Ml 2198- 2415<br>Ml 2416- 2670<br>Ml 2671 - 3015<br><!-- End of picture text -->
measures the amount of evaporation that would occur given sufficient water resources over the period 1950 to 2000. This variable is labeled _pet_ and plotted in Figure A2.3 (right panel).

In addition, we extract an aridity index and potential evapo-transpiration from models created by Trabucco and Zomer (2009). The models use data from WorldClim (Hijmans et al. 2005) as input parameters. The global mean Aridity index is Mean Annual Precipitation divided by Mean Annual Potential Evapo-Transpiration for the period from 1950 to 2000. High values of this index represent humid conditions, while low values represent arid conditions. A generalized climate classification scheme by UNEP (1997) suggests: hyper arid and arid are values less than 0.2, semi-arid has values 0.2-0.5 and dry sub-humid and humid have values above 0.5.<sup>19</sup>

# **Environment:**

The environment provides context to human settlements and surrounding economic activities. Land cover provides important information on the extent and type of human activity. We use the MODIS land cover products to select the crop and urban areas from the Annual International Geosphere-Biosphere Programme (IGBP) classification. These data area are the result of both supervised classifications of MODIS Terra and Aqua reflectance data and subsequent post-processing refinements for specific classes from prior knowledge and ancillary information. We select the crop and urban classes: _crop_ and _urb_ . The forest data are from Hansen et al. (2013) version 1.6 that provide both the stock of the forest from 2000, which is defined as “Tree canopy cover for year 2000, defined as canopy closure for all vegetation taller than 5m in height”, and forest loss, which is defined as “a stand-replacement disturbance (a change from a forest to non-forest state)”: _forloss_ and _forest_ .

To measure pollution, we use the fine particulate matter (PM 2.5) of air pollution data estimated from a model that excludes dust and sea-salt particles (van Donkelaar et al., 2015). The model uses geographically weighted regressions along with monitoring and satellite data, including: aerosol composition and land use information. We obtain the mean ( _pm25_ ), sum ( _pm25_ _~~s~~ um)_ and standard deviation ( _pm25_ _~~s~~ d_ ) for each administrative unit.

# **Socio-economic: Night time lights**

Night time lights (NTL) data, the visible light emitted from earth at night captured by satellites, are found to correlate strongly with population density and economic activity (e.g. Ebener et al., 2005; Henderson et al., 2012). The NTL high gain data come from the Defense Meteorological Satellite Program DMSP-OLS, which are made

> 19See Table 2 in CGIAR-CSI _Global Aridity Index (Global-Aridity)_ and _Global Potential EvapoTranspiration (Global-PET)_ Climate Database (2009)

46
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ban areas play an important role in providing service delivery, which in turn influences poverty. Different measures of urbanity have been proposed in the literature (e.g Dijkstra and Poelman, 2014; Aubrecht et al., 2016; Roberts et al., 2017). We take advantage of geospatial subnational gridded global data to measure travel time to major cities, the agglomeration index, population count, and built-up area.

We construct population density and totals from two main sources of global model population distribution data: Landscan (e.g. Bright et al., 2013) and GHS-Pop (Freire et al., 2016).<sup>21</sup> Landscan is a model that uses dasymetric and spatial modeling methods to estimate population. The model takes advantage of multiple sources of spatial microdata including land cover, road, slopes and urban areas data, and population census data. Figure A2.6 illustrates the spatial distribution of the total population across the enumeration area.

GHSpop data are derived from a raster-based dasymetric model estimating global population. Using newly processed LandSat data to provide multiple periods in time (1975, 1990, 2000 and 2014), this model leverages newly available built-up data (GHSBUILT) to define the locations where the GHSpop allocates population. The estimates of population are from the highest number of spatial units available to account for the total population known across subnational areas. We construct the following variables of total population within the administrative unit: _GHS_ _~~p~~ optot_ _~~1~~ 975_ , _GHS_ _~~p~~ optot_ _~~1~~ 990_ , _GHS_ _~~p~~ optot_ _~~2~~ 000_ , and _GHS_ _~~p~~ optot_ _~~2~~ 014_ . GHS-BUILT at 300m spatial resolution is the source of built-up area within each administrative unit from which we derive the variables: _GHSL_ _~~b~~ uilt_ _~~k~~ m2_ _~~1~~ 975_ , _GHSL_ _~~b~~ uilt_ _~~k~~ m2_ _~~1~~ 990_ , _GHSL_ _~~b~~ uilt_ _~~k~~ m2_ _~~2~~ 000_ , and _GHSL_ _~~b~~ uilt_ _~~k~~ m2_ _~~2~~ 014_ .

The share of urban population within an administrative unit is constructed as follows. We first define urban population as the number of people within a given threshold of density from the 2014 GHS population grid ( _ghspop14_ ) and the Landscan 2012 population grid ( _lpop12_ ). Next we use the World Urban Prospects estimates of the urban share at the country level provided by the World Bank World Development Indicators to inform a population density threshold that sums to the estimated urban share at the country level<sup>22</sup> . Finally, we construct the share of urban population that meet these density criteria within the administrative unit as the urban share of total population ( _urban_ _~~l~~ pop12_ ).

# **Socio-economic: Travel time and accessibility**

Transport infrastructure enables improved economic growth by lowering costs of moving goods and people. Nelson (2008) derives the travel time from all land area to

> 21For a recent review of gridded population datasets see Leyk et al. (2019).

> 22Another method of country consistent urban rates from World Urbanization Prospects is the iUrban method by Aubrecht et al. (2016).

48
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area level and label it _ai50k2000_ . Roberts et al. (2017) provide an updated AI circa 2010 using the newer travel time model and the population model from Landscan 2012 ( _ai50k2010)_ . We construct the variable of the total population in the AI for each period and, subsequently, the share of population in an AI out of the total population of the administrative area, respectively _ai50k2000_ _~~l~~ pop04_ and _ai50k2010_ _~~l~~ pop12_ .

# **Appendix 3: ELL (log) consumption model**

||Coefcient|Std. Err.|
|---|---|---|
|Intercept|10.5881|(0.1237)|
|EA<br>M<br>~~H~~HD<br>~~H~~AS<br>BICYCLE|-0.1779|(0.0595)|
|EA<br>M<br>~~H~~HD<br>~~H~~AS<br>CAR|1.2011|(0.2212)|
|EA<br>M<br>~~H~~HD<br>~~H~~AS<br>PHONE|0.2678|(0.0836)|
|EA<br>M<br>~~H~~HD<br>~~H~~AS<br>TV|-0.4604|(0.1471)|
|EA<br>M<br>~~H~~OH<br>~~R~~ESID<br>5YR|0.1522|(0.0797)|
|EA<br>M<br>~~H~~OH<br>~~T~~R<br>~~S~~ENA|-0.3658|(0.0513)|
|EA<br>M<br>~~H~~OH<br>~~T~~R<br>~~T~~UMBUKA|0.1242|(0.0555)|
|EA<br>R<br>~~C~~HLDBRN<br>LSTYR<br>~~F~~EM<br>~~3~~0<br>~~4~~5|0.2403|(0.0688)|
|HHD<br>~~A~~GE<br>00<br>05<br>~~A~~LL<br>~~0~~|0.1749|(0.0199)|
|HHD<br>~~A~~GE<br>00<br>05<br>~~A~~LL<br>~~1~~|0.0722|(0.0155)|
|HHD<br>~~A~~GE<br>06<br>15<br>~~A~~LL<br>~~0~~0|0.0715|(0.0207)|
|HHD<br>~~A~~GE<br>06<br>15<br>~~A~~LL<br>~~0~~1|0.0649|(0.0167)|
|HHD<br>~~A~~GE<br>65<br>ALL<br>~~0~~|0.0352|(0.0214)|
|HHD<br>~~C~~OOK<br>WOOD<br>~~O~~THER<br>1|-0.1877|(0.0276)|
|HHD<br>~~E~~DU<br>SECONDARY<br>~~0~~|-0.0814|(0.0261)|
|HHD<br>~~F~~LOOR<br>~~S~~OFT<br>~~1~~|-0.1754|(0.0203)|
|HHD<br>~~H~~AS<br>~~B~~ICYCLE<br>1|0.098|(0.0136)|
|HHD<br>~~H~~AS<br>~~C~~OOKER<br>~~1~~|0.1738|(0.0467)|
|HHD<br>~~H~~AS<br>~~F~~RIDGE<br>1|0.2897|(0.0444)|
|HHD<br>~~H~~AS<br>~~I~~TN<br>1|0.1469|(0.0126)|
|HHD<br>~~H~~AS<br>~~R~~ADIO<br>~~1~~|0.1934|(0.0134)|
|HHD<br>~~H~~AS<br>~~T~~V<br>~~1~~|0.2631|(0.027)|
|HHD<br>~~O~~CCUPIED<br>~~0~~6<br>~~1~~5<br>~~0~~|0.034|(0.0154)|
|HHD<br>~~R~~OOF<br>~~G~~RASS<br>1|-0.1072|(0.0181)|
|HHD<br>~~R~~OOMS<br>01|-0.2334|(0.0236)|
|HHD<br>~~R~~OOMS<br>02|-0.1608|(0.019)|

50
||Coefcient|Std. Err.|
|---|---|---|
|HHD<br>~~R~~OOMS<br>03|-0.0815|(0.0182)|
|HHD<br>~~S~~IZE<br>~~0~~1|1.2754|(0.0375)|
|HHD<br>~~S~~IZE<br>~~0~~2|0.7781|(0.0336)|
|HHD<br>~~S~~IZE<br>~~0~~3|0.5297|(0.0273)|
|HHD<br>~~S~~IZE<br>~~0~~4|0.3551|(0.0223)|
|HHD<br>~~S~~IZE<br>~~0~~5|0.21|(0.0196)|
|HHD<br>~~S~~IZE<br>~~0~~6|0.1046|(0.0187)|
|HHD<br>~~T~~OIL<br>NONE<br>1|-0.2377|(0.032)|
|HHD<br>~~T~~OIL<br>PIT<br>~~1~~|-0.1515|(0.0262)|
|HHD<br>~~W~~ALL<br>MUDBRCK<br>~~1~~|-0.0376|(0.0146)|
|HOH<br>AGE<br>~~L~~N|-0.0597|(0.0236)|
|HOH<br>EDU<br>~~P~~RIMARY<br>~~1~~|0.1332|(0.0208)|
|HOH<br>EDU<br>~~S~~ECONDARY<br>~~1~~|0.1766|(0.0346)|
|HOH<br>EDU<br>~~S~~OMEPRIM<br>~~1~~|0.1047|(0.0157)|
|HOH<br>EDU<br>~~S~~OMESEC<br>~~1~~|0.2069|(0.023)|
|HOH<br>EDU<br>~~T~~ERTIARY<br>~~1~~|0.2779|(0.0455)|
|HOH<br>OCCUPIED<br>~~1~~|0.117|(0.0194)|
|HOH<br>OCC<br>PRIVATE<br>~~1~~|-0.0605|(0.0209)|
|HOH<br>OCC<br>SELFAGRO<br>~~1~~|-0.0588|(0.0146)|
|HOH<br>RELIG<br>MUSLIM<br>1|0.0513|(0.0203)|
|STRATA<br>~~1~~|0.3166|(0.0796)|
|STRATA<br>~~2~~|0.4951|(0.0722)|
|STRATA<br>~~3~~|0.5221|(0.0714)|
|STRATA<br>~~4~~|-0.0796|(0.0465)|
|STRATA<br>~~5~~|0.2127|(0.0272)|
|TA<br>~~R~~EMOTE100K|-0.017|(0.0098)|
|~~U~~RBAN$HHD<br>~~H~~AS<br>BICYCLE<br>~~1~~1|-0.125|(0.0353)|
|~~U~~RBAN$HHD<br>~~H~~AS<br>RADIO<br>11|-0.0983|(0.0339)|
|~~U~~RBAN$HHD<br>~~R~~OOF<br>GRASS<br>~~1~~1|0.1054|(0.0475)|
|~~U~~RBAN$HHD<br>~~R~~OOMS<br>~~1~~01|-0.4033|(0.0682)|
|~~U~~RBAN$HHD<br>~~R~~OOMS<br>~~1~~02|-0.2877|(0.0563)|
|~~U~~RBAN$HHD<br>~~R~~OOMS<br>~~1~~03|-0.2806|(0.0543)|
|~~U~~RBAN$HHD<br>~~R~~OOMS<br>~~1~~04|-0.1993|(0.0535)|
|~~U~~RBAN$HHD<br>~~W~~ALL<br>MUDBRCK<br>~~1~~1|-0.0967|(0.0386)|

51
Coefficient Std. Err.

Table 9: ELL household (log) consumption regression model

||Coefcient|Std. Err.|
|---|---|---|
|Intercept|-4.3293|(0.0726)|
|STRATA<br>1|0.0265|(0.1417)|
|STRATA<br>2|-0.2575|(0.1435)|
|STRATA<br>3|-0.2739|(0.1332)|
|STRATA<br>4|0.2134|(0.0946)|
|STRATA<br>5|0.2481|(0.064)|
|TA<br>REMOTE100K|-0.062|(0.0262)|

Table 10: ELL heteroskedasticity model

# **References**

- Alderman, H., Babita, M., Demombynes, G., Makhatha, N. and Ozler, B.<sup> ̈</sup> (2002). How low can you go? combining census and survey data for mapping poverty in south africa. _Journal of African Economies_ , **11,** number 2, 169–200.

- Allen, R. G., Pereira, L. S., Raes, D. and Smith, M. (1998). Crop evapotranspirationguidelines for computing crop water requirements. Irrigation and drainage paper 56. FAO, Rome.

- Anselin, L. (2001). _Spatial econometrics_ , A companion to theoretical econometrics, 310330 edn.

- Araujo, M., Ferreira, F., Lanjouw, P. and Ozler, B. (2008). Local inequality and project choice: Theory and evidence from ecuador. _Journal of Public Economics_ , **92,** 1022–1046.

- Aubrecht, C., Gunasekera, R., Ungar, J. and Ishizawa, O. (2016). Consistent yet adaptive global geospatial identification of urban–rural patterns: The iurban model. _Remote Sensing of Environment_ , **187,** 230–240.

- Baird, S., McIntosh, C. and Ozler, B. (2013). The regressive demands of demand-driven development. _Journal of Public Economics_ , **106,** 27–41.

52
- Bazzi, S. (2017). Wealth heterogeneity and the income elasticity of migration. _American Economic Journal: Applied Economics_ , **9,** 219–255.

- Bedi, T., Coudouel, A. and Simler, K. (2007). _More than a pretty picture: using poverty maps to design better policies and interventions_ . World Bank Publications.

- Bell, K. and Bockstael, N. (2000). Applying the generalized-moments estimation approach to spatial problems involving microlevel data. _Review of Economics and Statistics_ , **82,** 72–82.

- Berg, C., Blankespoor, B., Li, Z. and Selod, H. (2017). Travel time to major cities. mimeo. The World Bank.

- Blumenstock, J., Cadamuro, G. and On, R. (2015). Predicting poverty and wealth from mobile phone metadata. _Science_ , **350,** 1073–1076.

- Blumenstock, J. E. (2016). Fighting poverty with data. _Science_ , **353,** 753–754.

- Bosco, C., Alegana, V., Bird, T., Pezzulo, C., Bengtsson, L., Sorichetta, A. and Wetter, E. (2017). Exploring the high-resolution mapping of gender-disaggregated development indicators. _Journal of The Royal Society Interface_ , **14** .

- Bourguignon, F. (2017). _The globalization of inequality_ . Princeton and Oxford: Princeton University Press.

- Bright, E. A., Rose, A. N. and Urban, M. L. (2013). _LandScan 2012: High Resolution Global Population Data_ , US Department of Energy: http://www. ornl. gov/landscan edn. UT-Battelle, LLC. Oak Ridge National Laboratory.

- Burke, M., Driscoll, A., Lobell, D. and Ermon, S. (2021). Using satellite imagery to understand and promote sustainable development. _Science_ , **371** .

- Chander, G., Markham, B. L. and Helder, D. L. (2009). Summary of current radiometric calibration coefficients for landsat mss, tm, etm+, and eo-1 ali sensors. _Remote Sensing of Environment_ , **113,** number 5, 893–903.

- Crost, B., Felter, J. and Johnston, P. (2014). Aid under fire: Development projects and civil conflict. _American Economic Review_ , **104,** 1833–1856.

- Demombynes, G. and Ozler, B. (2005). Crime and local inequality in south africa. _Journal of Development Economics_ , **76,** 265–292.

53
- Dijkstra, L. and Poelman, H. (2014). A harmonised definition of cities and rural areas: the new degree of urbanisation. Regional Working Paper. European Comission Directorate-General for Regional and Urban Policy.

- Donaldson, D. and Storeygard, A (2016). The view from above: Applications of satellite data in economics. _Journal of Economic Perspectives_ , **30,** number 4, 171–198.

- Ebener, S., Murray, C., Tandon, A. and Elvidge, C. C. (2005). From wealth to health: modelling the distribution of income per capita at the sub-national level using nighttime light imagery. _International Journal of Health Geographics_ , **4,** number 1.

- Elbers, C., Fujii, T., Lanjouw, P., Ozler, B. and Yin, W. (2007). Poverty alleviation through geographic targeting: How much does disaggregation help? _Journal of Development Economics_ , **83,** number 1, 198–213.

- Elbers, C., Lanjouw, J. and Lanjouw, P. (2003). Micro–level estimation of poverty and inequality. _Econometrica_ , **71,** number 1, 355–364.

- Elbers, C., Lanjouw, J. and Lanjouw, P. (2005). Crime and local inequality in south africa. _Journal of Economic Geography_ , **5,** 101–118.

- Elbers, C., Lanjouw, P., and Leite, P. (2008). Brazil within brazil: Testing the poverty mapping methodology in minas gerais. Policy Research Working Paper 4513. The World Bank.

- Elbers, C. and van der Weide, R. (2014). Estimation of normal mixtures in a nested error model with an application to small area estimation of poverty and inequality. Policy Research Working Paper 6962. The World Bank.

- Elvidge, C.C., Hsu, F. C., Baugh, K. E. and Ghosh, T. (2013). _National Trends in Satellite Observed Lighting: 1992-2012_ , O. Weng (ed), Global Urban Monitoring and Assessment Through Earth Observation edn. CRC Press.

- Engstrom, R., Hersh, J. and Newhouse, D. (2021). Poverty from space: Using highresolution satellite imagery for estimating economic well-being. _World Bank Economic Review_ .

- Ferreira, F. H. G., Chen, S., Dabalen, A. L., Dikhanov, Y. M., Hamadeh, N., Jolliffe, D. M., Narayan, A., Prydz, E. B., Revenga, A. L., Sangraula, P., Serajuddin, U. and Yoshida, N. (2015). A global count of the extreme poor in 2012 : data issues, methodology and initial results. Policy Research Working Paper 7432. The World Bank.

54
- Fischer, G., Nachtergaele, F. O., Prieler, S., Teixeira, E., T ́oth, G., Van Velthuizen, H., Verelst, L. and Wiberg, D. (2012). Global agro-ecological zones (gaez v3. 0) - model documentation. Technical Report. FAO, Rome.

- Freire, S., MacManus, K., Pesaresi, M., Doxsey-Whitfield, E. and Mills, J. (2016). _Development of new open and free multi-temporal global population grids at 250 m resolution_ , Geospatial Data in a Changing World; Association of Geographic Information Laboratories in Europe (AGILE) edn. AGILE.

- Fritz, S., See, L., McCallum, I., You, L., Bun, A., Moltchanova, E., Havlik, P. and Co. (2015). Mapping global cropland and field size. _Global change biology_ , **21,** number 5, 1980–1992.

- Fujii, T. (2010). Micro-level estimation of child undernutrition indicators in cambodia. _World Bank Economic Review_ , **24,** number 3, 520–553.

- Fujii, T. and van der Weide, R. (2020). Is predicted data a viable alternative to real data? _World Bank Economic Review_ .

- Gibson, J., Le, T. and Kim, B. (2017). Prices, engel curves, and time-space deflation: Impacts on poverty and inequality in vietnam. _World Bank Economic Review_ , **31,** 504–530.

- Goldberger, A. S. (1962). Best linear unbiased prediction in the generalized linear regression model. _Journal of the American Statistical Association_ , **57,** 369–375.

- Hansen, M.C., Potapov, P.V., Moore, R., Hancher, M., Turubanova, S. A., Tyukavina, A., Thau, D., Stehman, S.V., Goetz, S.J., Loveland, T.R. and Kommareddy, A. (2013). High-resolution global maps of 21st-century forest cover change. _Science_ , **342,** 850–853.

- Henderson, C. (1953). Estimation of variance and covariance components. _Biometrics_ , **9,** 226–253.

- Henderson, J. V., Storeygard, A. and Weil, D. N. (2012). Measuring economic growth from outer space. _American Economic Review_ , **102,** number 2, 994–1028.

- Hertel, T. W., Burke, M. B. and Lobell, D. B. (2010). The poverty implications of climate-induced crop yield changes by 2030. _Global Environmental Change_ , **20,** number 4, 577–585.

- Hijmans, R. J., Cameron, S., Parra, J., Jones, P. G., Jarvis, A. and Richardson, K. (2005). _WorldClim_ , version 1.3 edn. University of California, Berkeley.

55
- Imran, M., Stein, A. and Zurita-Milla, R. (2014). Investigating rural poverty and marginality in burkina faso using remote sensing-based products. _International Journal of Applied Earth Observation and Geoinformation_ , **26,** 322–334.

- Jarvis, A., Reuter, H. I., Nelson, A. and Guevara, E. (2008). _Hole-filled seamless SRTM data_ , version 4, available at: http://srtm. csi. cgiar.org edn. International Center for Tropical Agriculture (CIAT).

- Jean, N., Burke, M., Xie, M., Davis, W. M., Lobell, D. B. and Ermon, S. (2016). Combining satellite imagery and machine learning to predict poverty. _Science_ , **353,** 790–794.

- Kelejian, H. and Prucha, I. (2010). Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. _Journal of Econometrics_ , **157,** 53–67.

- Kilic, T., Serajuddin, U., Uematsu, H. and Yoshida, N. (2017). Costing household surveys for monitoring progress toward ending extreme poverty and boosting shared prosperity. Policy Research Working Paper 7951. The World Bank.

- Lee, K. and Braithwaite, J. (2022). High-resolution poverty maps in sub-saharan africa. _World Development_ , **159** .

- Leyk, S., Gaughan, A. E., Adamo, S. B., Sherbinin, A. D., Balk, D., Freire, S. and Comenetz, J. (2019). The spatial allocation of population: a review of large-scale gridded population data products and their fitness for use. _Earth System Science Data_ , **11,** number 3, 1385–1409.

- Maloney, W. and Caicedo, F. (2015). The persistence of (subnational) fortune. _Economic Journal_ , **126,** 2363–2401.

- Marx, B., Stoker, T. and Suri, T. (2019). There is no free house: Ethnic patronage in a kenyan slum. _American Economic Journal: Applied Economics_ , **11,** 36–70.

- Molina, I. and Rao, J. (2010). Small area estimation of poverty indicators. _Canadian Journal of Statistics_ , **38,** 369–385.

- Naidoo, R. and Iwamura, T. (2007). Global-scale mapping of economic benefits from agricultural lands: Implications for conservation priorities. _Biological Conservation_ , **140,** number 1-2, 40–49.

56
- Nelson, A. (2008). _Travel time to major cities: A global map of Accessibility_ , Global Environment Monitoring Unit edn. Joint Research Centre of the European Commission, Ispra Italy.

- Nhu, C. and Noy, I. (2020). Measuring the impact of insurance on urban earthquake recovery using nightlights. _Journal of Economic Geography_ , **20,** 857–877.

- NSO (2012). Third integrated household survey 2010-2011 - final report. Technical Report. Malawi National Statistical Office (NSO) and The World Bank.

- Nunn, N. and Puga, D. (2012). Ruggedness: The blessing of bad geography in africa. _Review of Economics and Statistics_ , **94,** number 1, 20–36.

- Perez-Heydrich, C., Warren, J. L., Burgert, C. R. and Emch, M. (2013). Guidelines on the use of DHS GPS data edn. ICF International.

- Pinkovskiy, M. and Sala-i Martin, X. (2016). Lights, camera ... income! illuminating the national accounts-household surveys debate. _The Quarterly Journal of Economics_ , **131,** number 2, 579–631.

- Pokhriyal, N. and Jacques, D. C. (2017). Combining disparate data sources for improved poverty prediction and mapping. _Proceedings of the National Academy of Sciences_ , **114,** E9783–E9792.

- Pratesi, M. and Salvati, N. (2008). Small area estimation: the eblup estimator based on spatially correlated random area effects. _Statistical Methods and Applications_ , **17,** 113–141.

- Ravallion, M. (2018). Inequality and globalization: A review essay. _Journal of Economic Literature_ , **56,** number 2, 620–642.

- Roberts, M., Blankespoor, B., Deuskar, C. and Stewart, B. (2017). Urbanization and development: is latin america and the caribbean different from the rest of the world? Policy Research Working Paper 8019. The World Bank.

- Searle, S., Casella, G. and McCulloch, C. (1992). _Variance components_ . New York: Wiley.

- Steele, J. E., Sundsøy, P. R., Pezzulo, C., Alegana, V. A., Bird, T. J., Blumenstock, J. and Hadiuzzaman, K. N. (2017). Mapping poverty using mobile phone and satellite data. _Journal of The Royal Society Interface_ , **14** .

57
- Tarozzi, A. (2011). Can census data alone signal heterogeneity in the estimation of poverty maps? _Journal of Development Economics_ , **95,** 170–185.

- Tarozzi, A. and Deaton, A. (2009). Using census and survey data to estimate poverty and inequality for small areas. _Review of Economics and Statistics_ , **91,** 773–792.

- Teluguntla, P., Thenkabail, P., Xiong, J., Gumma, M.K., Giri, C., Milesi, C., Ozdogan, M., Congalton, R., Tilton, J., Sankey, T.R., Massey, R., Phalke, A. and Yadav, K. (2015). _Global Cropland Area Database (GCAD) derived from Remote Sensing in Support of Food Security in the Twenty-first Century: Current Achievements and Future Possibilities_ , Vol. II edn. Land Resources: Monitoring, Modelling, and Mapping, Remote Sensing Handbook edited by Prasad S. Thenkabail. In Press.

- Trabucco, A. and Zomer, R. J. (2009). _Global aridity index (global-aridity) and global potential evapo-transpiration (global-PET) geospatial database_ . CGIAR Consortium for Spatial Information.

- Uchida, H. and Nelson, A. (2008). Agglomeration index: towards a new measure of urban concentration. Background paper for the World Bank’s World Development Report 2009. The World Bank.

- Van der Weide, R. (2014). Gls estimation and empirical bayes prediction for linear mixed models with heteroskedasticity and sampling weights: A background study for the povmap project. Policy Research Working Paper 7028. The World Bank.

- Van der Weide, R., Rijkers, B., Blankespoor, B. and Abrahams, A. (2018). Obstacles on the road to palestinian economic growth. Policy Research Working Paper 8385.

- Van Donkelaar, A., Martin, R. V., Brauer, M. and Boys, B. L. (2015). Use of satellite observations for long-term exposure assessment of global concentrations of fine particulate matter. _Environmental health perspectives_ , **123,** number 2, 135–143.

- Van Veelen, M. and van der Weide, R. (2008). A note on different approaches to index number theory. _American Economic Review_ , **98,** 1722–1730.

- Van Velthuizen, H., Huddleston, B., Fischer, G., Salvatore, M., Ataman, E., Nachtergaele, F. O., Zanetti, M. and Bloise, M. (2007). Mapping biophysical factors that influence agricultural production and rural vulnerability. Woking Paper 11. FAO, Rome.

- Watmough, G. R., Atkinson, P. M., Saikia, A. and Hutton, C. W. (2016). Understanding the evidence base for poverty–environment relationships using remotely sensed satellite data: an example from assam, india. _World Development_ , **78,** 188–203.

58
- Watmough, G. R., Marcinko, C. L., Sullivan, C., Tschirhart, K., Mutuo, P. K., Palm, C. A. and Svenning, J. C. (2019). Socioecologically informed use of remote sensing data to predict rural household poverty. _Proceedings of the National Academy of Sciences_ , **116,** number 4, 1213–1218.

- Weiss, D. J., Atkinson, P. M., Bhatt, S., Mappin, B., Hay, S. I. and Gething, P. W. (2014). An effective approach for gap-filling continental scale remotely sensed timeseries. _ISPRS Journal of Photogrammetry and Remote Sensing_ , **98,** 106–118.

- Winsemius, H. C., Jongman, B., Veldkamp, T. I., Hallegatte, S., Bangalore, M. and Ward, P. J. (2015). Disaster risk, climate change, and poverty: assessing the global exposure of poor people to floods and droughts. Technical Report.

- Wu, J., He, S., Peng, J., Li, W. and Zhong, X. (2013). Intercalibration of dmsp-ols night-time light data by the invariant region method. _International journal of remote sensing_ , **34,** 7356–7368.

- Zhao, X., Yu, B., Liu, Y., Chen, Z., Li, Q., Wang, C. and Wu, J. (2019). Estimation of poverty using random forest regression with multi-source data: A case study in bangladesh. _Remote Sensing_ , **11,** number 4.

- Zhu, Z., Bi, J., Pan, Y., Ganguly, S., Anav, A., Xu, L. and Myneni, R. (2013). Global data sets of vegetation leaf area index (lai) 3g and fraction of photosynthetically active radiation (fpar) 3g derived from global inventory modeling and mapping studies (gimms) normalized difference vegetation index (ndvi3g) for the period 1981 to 2011. _Remote sensing_ , **5,** number 2, 927–948.

- Zomer, Robert J, Trabucco, Antonio, Bossio, Deborah A and Verchot, Louis V (2008). Climate change mitigation: A spatial analysis of global land suitability for clean development mechanism afforestation and reforestation. _Agriculture, ecosystems & environment_ , **126,** number 1-2, 67–80.

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