Original Article Till Koebe, Department of Economics, Freie Universität
Berlin, Garystrasse 21, 14195 Berlin, Germany<EMAIL_ADDRESS>The
authors did not receive any specific funding for this work.

# Intercensal updating using structure-preserving methods and satellite
imagery

Till Koebe  Department of Economics, Freie Universität Berlin, Berlin, Germany
Alejandra Arias-Salazar  Department of Economics, Freie Universität Berlin,
Berlin, Germany  Natalia Rojas-Perilla  Department of Economics, Freie
Universität Berlin, Berlin, Germany  Timo Schmid  Department of Economics,
Freie Universität Berlin, Berlin, Germany

###### Abstract

Censuses are fundamental building blocks of most modern-day societies, yet
collected every ten years at best. We propose an extension of the widely
popular census updating technique Structure Preserving Estimation by
incorporating auxiliary information in order to take ongoing subnational
population shifts into account. We apply our method by incorporating satellite
imagery as additional source to derive annual small-area updates of
multidimensional poverty indicators from 2013 to 2020 for a population at
risk: female-headed households in Senegal. We evaluate the performance of our
proposal using data from two different census periods.

###### keywords:

Multidimensional poverty, Official statistics, Small area estimation, SPREE

##  1 Introduction

The estimation and monitoring of key statistical indicators are essential for
the definition and adequate execution of public policies. How many young women
without educational attainment currently live in district A? Answers to
questions like this inform local policy-making on a daily basis. On a global
scale, the 2030 Agenda for Sustainable Development highlights the need for
information to be disaggregated not only geographically, but also along other
dimensions such as sex, age, and employment status to identify and reach the
most vulnerable in a society ([42]). Statistical systems around the world
increasingly face growing demand for statistical information with specific
quality characteristics such as disaggregation, periodicity and relevance in
order to guide policy decisions, since these require a more nuanced and up-to-
date picture than national-level indicators can provide. However, serving this
demand appropriately remains a challenge in developing countries: censuses are
collected every ten years at best for a limited scope of indicators. Household
surveys are usually conducted more frequently covering a broad range of
indicators, although they may not provide representative results at higher
levels of disaggregation. In addition, data collection costs for both
instruments scale unfavourably with the sample size. While some countries can
link statistical data with high-quality administrative records in order to
fill gaps, e.g. using small area estimation methods ([27, 33, 39]), many
others lack appropriate administrative data systems to do so.

To overcome the shortage of geographically disaggregated data, academic
literature has seen a rise of approaches in recent years that use non-
traditional (big) data sources. In particular, night-time lights and land use
information captured by satellites, as well as mobility and social network
insights via mobile phone metadata, are increasingly used for estimating
disaggregated key statistical indicators related to economic growth ([6, 16,
28]), literacy ([38, 35]), population density ([15, 4, 23, 36]) or poverty
([20, 29, 43]). The United Nations (UN) recommends using satellite imagery to
prioritize and check geospatial processes such as the delineation of
enumeration areas during census preparation ([41]). It further supports the
construction of population grids as a common spatial reference system as
proposed by [37, 10, 5].

While these approaches can increase spatial granularity by assuming that
correlations captured for large areas also hold for small areas, they suffer
of five major shortcomings: First, they still require disaggregated
statistical data from surveys or censuses for training and model fitting,
ideally captured at the same point in time. Second, only variables of interest
that correlate with covariates from the novel data source can be modelled
appropriately. Third, little research has been done so far to investigate
whether these inferential relationships also hold over time. Fourth, some of
the novel data sources are privately owned, e.g. high resolution satellite
imagery and mobile phone metadata. Creating reliable long-term access options,
a precondition for embedding them in statistical business processes, is an
institutional and legal challenge on its own. Fifth, many new approaches use
sophisticated machine learning in combination with data generated in processes
beyond the control of statistical offices. Adopting them would require a major
paradigm shift in the work of official statisticians. However, and most likely
given the capacity constraints many statistical offices in the world face, it
discourages adoption altogether.

Another strain of research, usually known as updating, intercensal or
postcensal estimation methods, focuses on the periodicity of statistical data
by tackling the problem of the time-gap between two sources of information.
Traditional demographic techniques such the component method ([40]) and the
vital rates method or regression symptomatic procedures ([32]) build on long-
term trends around fertility, mortality, and migration and have been
extensively used to obtain postcensal population estimates, often called
population projections. Most of these techniques rely on survey information,
therefore limiting the level of spatial granularity for which population
updates can be provided. Large-area population estimates are then distributed
to small areas via the proportion method ([40]), i.e. fixed population shares
captured in the latest census. Population shifts within these large areas,
e.g. induced by urbanization, desertification or internal conflicts are thus
not accounted for. Hence, the lack of disaggregated, frequent, relevant,
reliable, and timely statistics is still largely unsolved.

The structure preserving estimation (SPREE) method has been widely used to
produce intercensal estimates for disaggregated population counts ([30]).
Unemployment ([25]), occupational classification ([17]) and poverty estimation
([19]) are examples of the application of this method and its extensions. In
SPREE, disaggregated postcensal estimates are generated by updating the
margins (called the allocation structure) of a census composition (called the
association structure). The updated margins, i.e. the distribution of the
variable of interest (e.g. poverty status by sex) and the population sizes for
each domain, are usually provided by recent survey data. In case population
sizes by domains cannot be sufficiently generated due to sampling design
constraints, population projections as described above can be used instead
([24]).

In this paper, we provide a unified framework for the two aforementioned, so
far mainly disparate, fields of research - using novel data sources to add
spatial granularity and updating existing census structures with long-term
trends and recent data to add disaggregation, periodicity, and reliability.
Specifically, we study the potential benefit of including auxiliary data in
the SPREE process by strengthening the population estimates in local areas.
The aim is relaxing rigid assumptions on the subnational population allocation
between census rounds by tracking population changes across small areas over
time using auxiliary information without jeopardizing the compelling
simplicity of the SPREE approach. We also provide uncertainty estimates for
the postcensal predictions based on our approach following a semiparametric
bootstrap procedure. We apply the proposed methodology in a case study in
Senegal. Since its latest census in 2013, Senegal has started to roll out a
nation-wide social safety net program to lift families out of poverty
including cash transfers for up to every fourth Senegalese household ([12,
2]). Therefore, we expect that the only source of commune-level data on
multidimensional poverty, the census 2013 data, has become quickly outdated
and therefore is ill-suited for further local policy guidance. In a first
step, we validate the value added of our proposed methodology by updating the
census 2002 to 2013 and comparing the results with the actual census 2013.
Finally, using data from census 2013, multiple rounds of major household
surveys, population projections, and satellite imagery-based population
estimates we retrieve annual point predictions including corresponding mean
squared error (MSE) estimates of the multidimensional headcount ratio for the
552 communes in Senegal up to 2020.

The document has the following structure: a summary of SPREE is included in
Section 2 as well as the proposed updating strategy which incorporates
auxiliary information such as satellite imagery. MSE estimates for
corresponding point estimates are also provided. Section 3 is dedicated to
introduce the case study and the data sources used in both the validation and
the application. In Section 4 we present the simulation exercise to validate
our proposal. Section 5 summarises the application results in which we provide
small-area-level updates of the multidimensional headcount ratio for several
postcensal years in Senegal. Conclusions and further research questions are
presented in Section 6.

##  2 Methodology

The method proposed to obtain updated indicators in small areas by including
auxiliary information is described in this section. After a brief introduction
to SPREE, we present the main scientific contribution of this paper:
incorporating auxiliary information to improve the accuracy of small-area
census updates by relaxing the assumption of fixed population margins between
census years.

###  2.1 Structure Preserving Estimation (SPREE)

SPREE is an updating technique for intercensal population compositions. In
general, population compositions can be thought of as multiway contingency
tables. We denote the composition of interest as $Y_{aj,t}$ with $a=1,\dots,A$
representing the target areas i.e. small areas and $j=1,\dots,J$ representing
the categories of interest, e.g. poor/non-poor, at time $t=1,\dots,T$.
Consequently, $Y_{a,t}$ represents the row margins, i.e. population sizes for
each area, and $Y_{j,t}$ the column margins, i.e. distribution of the
categories of interest at national level (global totals) since the last
census. Here, we assume the initial population composition to be generated at
time $t=0$. Since that is usually the year of the latest census, we simply
call it the census composition. For better legibility, we denote the census
year without a time index, e.g. $Y_{aj}$ instead of $Y_{aj,0}$. Further, we
assume that smaller areas are disjoint subsets of larger areas (as it is
commonly the case for administrative areas) which we denote with
$k=1,\dots,K$.

In order to illustrate how a census composition can be updated via the
margins, we describe it as a log-linear model (here for a two-way case such as
poverty status by area):

$\log{Y_{aj}}=\alpha^{Y}_{0}+\alpha^{Y}_{a}+\alpha^{Y}_{j}+\alpha^{Y}_{aj},$

where $\alpha^{Y}_{0}$ represents the overall mean, $\alpha^{Y}_{a}$ the main
effect of areas, $\alpha^{Y}_{j}$ the main effect of categories, and
$\alpha^{Y}_{aj}$ the interaction term also known as the association
structure. The definition of these parameters can be found in detail in most
of the SPREE literature (see e.g. [24]). Following the original proposal of
[30], two basic structures are required to apply this methodology: an
association structure $\alpha^{Y}_{aj}$ which provides information about the
interaction between areas (rows) and categories (columns), and an allocation
structure represented by $\alpha^{Y}_{0}$, $\alpha^{Y}_{a}$ and
$\alpha^{Y}_{j}$ that provides information about area and category terms.
Generally, in order to capture the association structure appropriately, each
combination of areas and categories (called cells) must be backed by
sufficient data. Especially for countries lacking effective administrative
data systems, censuses are the only source of information at that level of
detail as surveys usually suffer of sample size constraints. Consequently, the
census composition is only available every ten years at best for many
countries in the world and therefore the association structure is assumed to
be constant between census years
$\big{(}\alpha^{Y}_{aj,t}=\alpha^{Y}_{aj}\big{)}$. Usually the allocation
structure is gathered from direct survey estimates, however, spatial
disaggregation here is often limited by the lack of reliable subnational
population margins.

The fitting process in the original SPREE model is achieved via the iterative
proportional fitting (IPF) algorithm ([7]), where reliable survey row
$\big{(}\hat{Y}_{a,t}\big{)}$ and column margins $\big{(}\hat{Y}_{j,t}\big{)}$
are fitted to a census composition ($Y_{aj}$). Then, the iterative process to
obtain the updated point estimates is indicated as in [24] as:

$\hat{Y}_{aj,t}=\text{IPF}\big{(}Y_{aj},\hat{Y}_{a,t},\hat{Y}_{j,t}\big{)}.$
(1)

There are some basic limitations to this methodology:

  1. (a)

the survey(s) used to generate $\hat{Y}_{j,t}$ and $\hat{Y}_{a,t}$ must
contain the same variable definition as the census or a high correlate of it
([13]),

  2. (b)

the survey margins must follow the same disaggregation scheme as defined in
the census (areas/categories),

  3. (c)

the margin totals $\sum_{a=1}^{A}\hat{Y}_{a,t}$ and
$\sum_{j=1}^{J}\hat{Y}_{j,t}$ need to add up perfectly,

  4. (d)

only categorical variables are allowed (e.g. poverty status = poor/not poor).

The literature on SPREE methodology can be roughly summarised into three
groups: a) original SPREE as defined by [30] and the proposal of [26] to
formulate SPREE under the generalized linear model (GLM) framework, b) SPREE
extensions focused on bias reduction as suggested by [46] and later extended
by [24] through incorporating cell-specific random effects and informative
sampling design and c) SPREE extensions to account for situations where the
variable of interest is not available in the census ([19]). As far as we know,
the only work that uses additional sources of information besides one census,
survey data, and population projections is [25] who consider a second census
composition for updating ethnicity categories by age groups in England in
2011. While the population census provided information for all age groups, a
scholar census offered better information for children between five and 15
years old. The authors studied the possibilities of updating the estimates
considering that one of the age groups has two different data sources
available. Nonetheless, the authors did not observe improvements by using this
additional source of information. However, they point to the need for further
research to better understand the potential value added of auxiliary
information in SPREE. Moreover, to the best of our knowledge, all studies in
this field assume the presence of reliable and up-to-date population margins
for the areas of interest, which may not be ubiquitously available in many
small-area settings.

###  2.2 SPREE with auxiliary information

Our contribution here is straight-forward: as demographic projections and
surveys usually provide reliable population totals only for large areas
($\hat{Y}_{k,t}$), a common-place method uses fixed population proportions
$p_{k_{a}}$ captured in $t=0$ for distributing large-area counts to small
areas:

$\hat{Y}_{a,t}=\hat{Y}_{k,t}\cdot
p_{a}\quad\text{with}\quad\sum_{a=1}^{A}p_{a}=\sum_{a=1}^{A}\frac{Y_{a}}{Y_{k}}=1\quad\forall\quad
a\subseteq k.$ (2)

We relax this obviously strong assumption that subnational population shares
remain fixed between censuses by using auxiliary information to track
population changes dynamically for small areas over time. Consequently, we
replace $p_{a}$ with $\hat{p}_{a,t}$, so Equation 2 becomes:

$\hat{Y}_{a,t}=\hat{Y}_{k,t}\cdot\hat{p}_{a,t}\quad\text{with}\quad\sum_{a=1}^{A}\hat{p}_{a,t}=\sum_{a=1}^{A}\frac{\hat{Y}_{a,t}^{\text{Aux}}}{\hat{Y}_{k,t}^{\text{Aux}}}=1\quad\forall\quad
a\subseteq k,$ (3)

where $\hat{Y}_{a,t}^{\text{Aux}}$ and $\hat{Y}_{k,t}^{\text{Aux}}$ represent
the population sizes of small areas $a$ and large areas $k$ at time $t$
estimated using auxiliary data. Notice that it may be possible to rely on
$\hat{Y}_{a,t}^{\text{Aux}}$ only to estimate $\hat{Y}_{a,t}$. However,
demographic projections and surveys capture information on population
whereabouts for large areas in a statistically rigorous and reliable manner
and are therefore used as regional-level benchmarks through dasymetric mapping
([37]). This allows us to combine the benefits from both auxiliary data and
statistical data. First, reliable counts are distributed to smaller areas not
covered so far. Second, only information on the within-area distribution of
counts are used from auxiliary information, not on the totals. This makes
SPREE for small areas less prone to quality issues in the auxiliary data.

Besides administrative records, big data sources such as mobile phone metadata
and satellite imagery appear to be promising auxiliary information in SPREE.
For satellite imagery, five characteristics make it a suitable candidate for
that: Satellite imagery provides virtually 1) global coverage at 2) high
spatial resolutions for 3) frequent time intervals on 4) human-made impact in
a 5) structured and - at least to some extent - harmonised way. In regard to
population changes, built settlement growth, and changes in night-time lights
may constitute the potentially most relevant indicators on human impact from
satellite imagery. Data products from remote sensing are currently rapidly
evolving in terms of quality and user-friendliness. Examples for open-access
data products from remote sensing are the Copernicus program ([8]) and [45].

###  2.3 Assessment of uncertainty

The original SPREE approach assumes that the association structure is fixed
and therefore only the allocation structure provides a variation component.
While [30] propose linearization or replication techniques to account for the
introduced uncertainty, [31], [18] and [24] provide also analytical
approximations for the variance of the estimator and other measures of
uncertainty for SPREE and its extensions. In contrast, the data generating
process of auxiliary data in general and specifically the population margins
derived from satellite imagery is usually not known and it has to be expected
that uncertainty in these data sources follows complex, non-trivial patterns.
For example, satellite imagery run through multiple stages of data processing
with dependencies to other data sources such as OpenStreetMaps ([37]) before
providing population estimates. To some extent, this complexity also holds
true for uncertainty in demographic projections. As we assume the uncertainty
stemming from external sources like satellite imagery to be non-negligible,
but also non-trivial, we opt to follow the replication idea proposed by [30]
which is also the basis of some MSE alternatives suggested in [24] instead of
pursuing an analytical strategy that may require strong assumptions on some of
the sources of uncertainty. Therefore, we propose an empirical approximation
of the uncertainty based on a semiparametric bootstrap in order to give some
indication on the trustworthiness of a point estimate while acknowledging that
it most likely captures only a fraction of the total variation. Since the
allocation structure is constructed based on auxiliary data, population
projections and survey data, a fully parametric approach is not
straightforward. For this reason and to avoid misspecification issues, the
column and row margin are resampled in an non-parametric way, where the column
margin is provided by direct survey estimates and the row margin is derived
from auxiliary information. Following existing literature (see e.g. [24]),
census data is replicated following a multinomial distribution. In addition,
we account for the stochastic nature of the overall population by resampling
the population of each area using a Poisson distribution. This step is
complementary and intended for use cases where census counts are subject to
uncertainty, e.g. due to quality issues or the availability of only a census
sample. To summarize, the steps to obtain the MSE of the updated estimates
$\hat{Y}_{aj,t}$ via a mixed semiparametric bootstrap are as follows:

  1. (a)

obtain the point estimate $\hat{Y}_{aj,t}$ from Equation 1 using the row
margin $\hat{Y}_{a,t}$ as defined in Equation 3 and compute
$\hat{\pi}_{aj,t}=\frac{\hat{Y}_{aj,t}}{\hat{Y}_{a,t}}$,

  2. (b)

for $b=1,\dots,B$:

    1. (i)

create population composition $\hat{Y}_{aj,t}^{\text{Mult},b}$ following a
multinomial distribution, denoted by
$\text{Multinom}\Big{(}\hat{Y}_{a,t}^{\text{Pois},b},\hat{\pi}_{aj,t}\Big{)}$,
where the row margins $\hat{Y}_{a,t}^{\text{Pois},b}$ are obtained assuming a
Poisson distribution, defined by
$\text{Pois}\big{(}\lambda=\hat{Y}_{a,t}\big{)}$,

    2. (ii)

generate auxiliary-based row margin $\hat{Y}_{a,t}^{b}$ by resampling from
$\hat{Y}_{a,t}$,

    3. (iii)

generate survey-based column margin $\hat{Y}_{j,t}^{b}$ by resampling from
$\hat{Y}_{j,t}$,

    4. (iv)

apply SPREE (Equation 1) for each replicate, generating $B$ updated
compositions
$\hat{Y}_{aj,t}^{b}=\text{IPF}\Big{(}\hat{Y}_{aj,t}^{\text{Mult},b},\hat{Y}_{a,t}^{b},\hat{Y}_{j,t}^{b}\Big{)}$,

  3. (c)

the MSE of $\hat{Y}_{aj,t}$ is estimated as:

$\widehat{MSE}\big{(}\hat{Y}_{aj,t}\big{)}=\frac{1}{B}\sum_{b=1}^{B}\Big{(}\hat{Y}_{aj,t}^{b}-\hat{Y}_{aj,t}^{\text{Mult},b}\Big{)}^{2}.$

##  3 Case study: multidimensional poverty in Senegal

In 2013, the Senegalese government launched a nation-wide family security
benefits program as part of a wider social safety net initiative. Officially
termed Programme National de Bourses de Sécurité Familiale (PNBSF), the goal
of the ongoing program is ‘to contribute to the fight against the
vulnerability and social exclusion of families through integrated social
protection in order to promote their access to social transfers and to
strengthen, among other things, their educational, productive and technical
capacities’ ([12]). Its main component are cash transfers to disadvantaged
families that in turn commit to schooling, keeping vaccination records and
registering newborns and children in civil status ([2]). The cash transfers
(100,000 FCFA, i.e. approximately 180 USD per year and household) are
accompanied by coordination, communication, and evaluation activities. After a
one-year pilot phase with 50,000 poor or vulnerable Senegalese households in
2013, the program was scaled up to 250,000 households in 2014 and onwards. A
further extension to a total of 400,000 households - that is approximately
every fourth household in Senegal - is currently underway. Consequently, it
can be expected that poverty-related measures for small areas in Senegal will
have become quickly outdated since the latest census in 2013. Even though the
program efficiency is monitored including a large-scale baseline survey
considering treatment and control group, this does not provide a
representative view on socio-economic development in Senegal in general and
for sub-groups in the 552 communes of Senegal, specifically.

The aim of the case study is to provide annual census updates of
multidimensional poverty for small areas in Senegal until 2020 to inform about
main drivers of multidimensional poverty for a specific sub-group: individuals
living in female-headed households. To make sure our methodology adds value
vis-à-vis existing approaches, we validate our proposal using censuses from
2002 and 2013. As we combine multiple sources of data in this case study, we
first introduce them together with the target indicator - the headcount ratio
of the multidimensional poverty index - in this section before presenting the
validation results in Section 4 and the application results in Section 5. The
full code for this paper is available on GitHub:
https://github.com/tilluz/Auxiliary-SPREE

###  3.1 Geography of Senegal

Senegal is administratively divided in 14 régions (NUTS1), 45 départements
(NUTS2), 103 arrondissements (NUTS3) and 552 communes (NUTS4). The total
population was at 13.5 million in 2013 and projected to be at 16.2 million in
2020. We choose the 552 communes as target domains in the application as they
represent the level of administration responsible for the provision of public
services in the decentralization efforts set out in the national development
plan of Senegal (Plan Sénégal Émergent) ([11]). Since a number of land reforms
have taken place in Senegal between 2002 and 2013, the smallest common
denominator in terms of administrative boundaries for analysis between 2002,
and 2013 is the NUTS3 level (103 arrondissement) of the census 2002
Recensement Général de la Population et de l’Habitat (RGPH 2002). For
evaluation, we consequently aggregate the data of the census 2013 Recensement
Général de la Population et de l’Habitat, de l’Agriculture et de l’Elevage
(RGPHAE 2013) from the 552 communes to the 103 arrondissements. Figure 1 shows
an overlay of the two administrative structures.

Figure 1: Overlay of RGPH 2002 (grey) and the RGPHAE 2013 (green).
The 552 communes from the RGPHAE 2013 are perfect subsets of the 103
arrondissements of the RGPH 2002.

###  3.2 Multidimensional poverty in Senegal

The global multidimensional poverty index (MPI) for Senegal based on [3] is
calculated considering the incidence of poverty $H$ and the average
deprivation share $D$:

$\text{MPI}=H\times D.$

The MPI varies from 0 to 1 on a continuous scale, where 1 represents the
highest level of MPI poverty. As SPREE requires the target indicator to be
categorical, we focus on the incidence $H$ (also called MPI headcount ratio)
in this case study. The MPI headcount ratio is defined as the proportion of
people identified as multidimensional poor. It is calculated based on the
(weighted) number of deprivations that they experience (also called
deprivation score). The MPI is composed of ten indicators measuring different
dimensions of deprivation. A household with a deprivation score of at least
1/3 is considered multidimensional poor. The deprivation indicators $I_{i}$
with the respective weight $w_{i}$ are summarized in Table 1.

Dimension |  Indicator ($i$) |  Weight ($w_{i}$) | Available
---|---|---|---
Health | Nutrition | 1/6 | No
| Child mortality* | 1/6 | Yes
Education | Years of schooling | 1/6 | Yes
| School attendance | 1/6 | Yes
Living standards | Cooking fuel | 1/18 | Yes
| Sanitation | 1/18 | Yes
| Drinking water | 1/18 | Yes
| Electricity | 1/18 | Yes
| Housing | 1/18 | Yes
| Assets | 1/18 | Yes
Table 1: Dimensions and weights for measuring the MPI.
*As data on ‘nutrition’ is not available, ‘child mortality’ receives the full weight of the ‘health’ dimension (1/3).

The percentage contribution $\phi$ of indicator $i$ to the overall MPI
headcount ratio $H$ is defined as:

$\phi_{i}=w_{i}*\frac{H_{i}}{H}.$

Indicator-specific contributions to the overall MPI headcount ratio are
particularly interesting for policy-making as they rank drivers of
multidimensional poverty along the usual responsibilities of line ministries
(e.g. education, energy, health, infrastructure etc.) in a simple-to-visualize
and easy-to-understand manner. For more details, we refer to [3]. Although the
survey data used in this application provide information for all MPI
indicators, the census data lacks of the ‘nutrition’ indicator from the
‘health’ dimension. Even though the situation when there is lack of
information in the census can be addressed within SPREE as shown by [19], we
focus on the nine remaining indicators for the sake of simplicity. Therefore,
the indicator ‘child mortality’ in the ‘health’ dimension receives a weight of
1/3 instead of 1/6 (see Table 1). The multidimensional headcount ratio ($H$)
in 2013 is shown for subgroups by région in Table 2 and by commune in Figure
2.

Figure 2: MPI headcount ratio in 2013 by commune.
The unweighted commune-level MPI headcount ratio in Senegal in 2013 averages at 0.75 (white) with a minimum at 0.1 (dark brown) and a maximum at 1 (dark green). Région | $H$ | $H_{\text{female}}$ | Région | $H$ | $H_{\text{female}}$
---|---|---|---|---|---
Dakar | 51.8 | 50.3 | Louga | 69.9 | 57.4
Diourbel | 69.7 | 58.5 | Matam | 80.6 | 70.7
Fatick | 75.8 | 62.9 | Saint-Louis | 68.6 | 59.7
Kaffrine | 81.9 | 65.5 | Sedhiou | 84.6 | 74.2
Kaolack | 72.6 | 58.4 | Tambacounda | 85.6 | 71.8
Kedougou | 81.8 | 72.7 | Thies | 64.2 | 55.8
Kolda | 82.7 | 65.9 | Ziguinchor | 65.3 | 61.1
Table 2: Regional-level MPI headcount ratios by sub-group from 2013 census.
Headcount ratios are given for the overall population ($H$) and the population
living in a female-headed household ($H_{\text{female}}$).

###  3.3 Data sources

####  3.3.1 Recensement Général de la Population et de l’Habitat, de
l’Agriculture et de l’Elevage (RGPHAE) 2013

Data collection for the latest census took place between November 19th, 2013
and December 14th, 2013. Unit-level data of the population and housing census
with 10% of the households sampled within each of the 17,145 census districts
is provided for scientific use via the microdata portal of the Agence
Nationale de la Statistique and de la Démographie (ANSD) - the Senegalese
national statistical office. The RGPHAE 2013 provides data for all MPI
indicators but not for ‘nutrition’. Some indicators suffer of item nonreponse
that apparently do not follow a missing completely at random (MCAR) scheme.
Table 3 provides an overview over the missing data treatment in the RGPHAE
2013, where can be seen that the population part of RGPHAE 2013 exhibits
large-scale item-nonresponse. The strong imputation effects in these
indicators are somehow expected due their respective definition. A household
is deprived in the indicator ‘child mortality’ if any child has died in the
household. Thus, the higher the coverage of individuals within the household,
the more likely it is to fulfill the criteria of deprivation. Same holds for
the indicator ‘school attendance’, which defines a household as deprived if
any school-aged child is not attending school up to class eight. The contrary
holds for the indicator ‘years of schooling’, which defines a household as
deprived if no household member has completed six years of schooling. The more
household members are covered, the more likely it is for a household not to
fulfill the criteria of deprivation. We address the item nonresponse by
imputing missing values in a single imputation using chained equations (see
e.g. [44]). Even though we acknowledge that imputation introduces additional
uncertainty, we do not explicitly account for it as this goes beyond the scope
of the paper. Consequently, we put it as further research.

Indicator | % missing | % deprived | % deprived (imputed)
---|---|---|---
Nutrition | - | - | -
Child mortality | 65.4 | 27.9 | 53.6
Years of schooling | 60.6 | 15.1 | 11.3
School attendance | 60.6 | 40.8 | 57.4
Cooking fuel | 0.0 | 65.8 | 65.8
Sanitation | 0.0 | 30.8 | 30.8
Drinking water | 0.0 | 15.7 | 15.7
Electricity | 0.0 | 38.9 | 38.9
Housing | 0.0 | 26.2 | 26.2
Assets | 0.0 | 16.6 | 16.6
Table 3: Missing MPI data and imputation effects in the RGPHAE 2013.

####  3.3.2 Recensement Général de la Population et de l’Habitat (RGPH) 2002

Similar to RGPHAE 2013, the Recensement Général de la Population et de
l’Habitat 2002 (RGPH 2002) data is available at the unit-level with 10% of the
households sampled within each of the census districts for scientific use via
the microdata portal of ANSD. As with RGPHAE 2013 data, missing values are
treated by single imputation using chained equations.

####  3.3.3 Household survey data

In this case study, we use data from Senegalese Demographic and Health Surveys
(DHS) collected for the years 2013 and beyond. The DHS program is mainly
funded by the United States Agency for International Development (USAID) with
the aim of provide accurate and reliable indicators of population, health, and
nutrition at national, residence (urban-rural) and regional levels (NUTS1).
Details on the respective survey rounds are summarized in Table 4.

Year | Contract phase | Data collection | Sample size | Clusters
---|---|---|---|---
2013 | VI | Jan-Oct | 4 174 | 200
2014 | VII | Jan-Oct | 8 406 | 400
2015 | VII | Jan-Oct | 4 511 | 214
2016 | VII | Jan-Oct | 4 437 | 214
2017 | VII | Apr-Dec | 8 380 | 400
2018 | VIII | Jun-Dec | 4 592 | 214
2019 | VIII | Apr-Dec | 4 538 | 214
Table 4: Description of the DHS data set available.

Indicator definitions and/or response options slightly differ between DHS
surveys and RGPHAE 2013 leading to differences in the results as shown in
Figure 3 and Table 5. For example, while the DHS surveys provide data on the
time travelled for safe drinking water, RGPHAE 2013 does not. Therefore, we do
not account for the time travelled in the respective indicator even though it
has a major impact on the deprivation score for drinking water in Senegal.
Nevertheless, regional-level correlations between indicators of the DHS 2013
and RGPHAE 2013 are generally quite strong with an average of 0.68 ranging
from 0.40 for ‘assets’ to 0.99 for ‘cooking fuel’.

Indicator | RGPHAE | DHS
---|---|---
2013 | ’13 | ’14 | ’15 | ’16 | ’17 | ’18 | ’19
Child mortality | 53.9 | 41.4 | 39.9 | 39.4 | 36.0 | 37.6 | 36.1 | 32.2
Years of schooling | 10.0 | 36.2 | 36.1 | 40.0 | 38.6 | 33.0 | 34.8 | 37.0
School attendance | 64.4 | 80.8 | 79.7 | 74.4 | 76.5 | 76.8 | 76.8 | 77.9
Cooking fuel | 75.8 | 81.0 | 78.7 | 79.0 | 74.0 | 22.5 | 20.9 | 21.3
Sanitation | 35.2 | 42.1 | 41.1 | 45.4 | 41.4 | 36.5 | 30.5 | 31.8
Drinking water | 17.5 | 24.1 | 21.7 | 25.2 | 23.2 | 22.5 | 21.9 | 23.4
Electricity | 43.3 | 47.0 | 43.3 | 41.7 | 37.0 | 38.3 | 33.8 | 29.4
Housing | 27.9 | 26.5 | 26.9 | 22.4 | 22.5 | 21.8 | 14.8 | 15.1
Assets | 12.4 | 11.5 | 11.0 | 12.5 | 12.4 | 11.5 | 10.0 | 10.8
MPI headcount | 68.4 | 69.0 | 67.9 | 67.5 | 64.7 | 59.3 | 58.1 | 57.8
Table 5: Overview over indicator-specific headcount ratios by data source.
Figure 3: Distribution of household-level deprivation scores by data source.
Cutoffs are 0.2 (vulnerable to multidimensional poverty), 0.33 (MPI-poor) and
0.5 (severely MPI-poor), respectively.

Differences between the categories available to create the MPI indicators lead
also to differences in the distribution of the deprivation scores when
comparing RGPHAE 2013 and the DHS 2013. For instance, while the census asks
whether public sanitation facilities are used, the DHS asks whether sanitation
facilities are shared (which could also occur privately among a small number
of households).

####  3.3.4 Demographic projections

Demographic projections inform about the possible future demographic
composition of a country. Usually, demographic projections take the latest
census as base population and use hypotheses on the future development of
fertility, mortality and migration in a country. In Senegal, demographic
projections are produced by ANSD disaggregated by 5-year age groups, gender,
region, and urban status based on RGPHAE 2013 using the software SPECTRUM
following the cohort component method ([40]):

$\text{pop}_{t1}=\text{pop}_{t_{0}}+(\text{births}_{t_{1}}-\text{deaths}_{t_{1}})+(\text{immigration}_{t_{1}}-\text{emigration}_{t_{1}}).$

Population projections are made on the regional level, which are then
distributed via fixed population shares determined during the census year to
lower administrative levels (proportion method ([40])). As reliable regional-
level data on migration is not available, the migration pattern captured in
the census is treated as static over time. For estimating current fertility
and death trends, the ANSD uses regional-level survey data, usually from the
latest DHS. For details on the methodology applied to create population
projections in Senegal, we refer to [1].

####  3.3.5 Satellite Imagery

In this case study, we use satellite imagery provided by [45] for estimating
dynamic subnational population shares on a frequent basis. The idea behind
this is to account for population shifts occurring within regions that are so
far not captured via the proportion method. By using the Dakar région as
example, Figure 4 shows the evolution of the population shares from 2002 to
2013. Figure 4(a) shows how the population shares have changed based on
population counts from RGPH 2002 and RGPHAE 2013, and Figure 4(b) shows
changes in the population shares based on RGPH 2002 and satellite imagery-
derived population estimates from WorldPop. The proportion method (not
depicted) assumes fixed population shares, i.e. horizontal lines, across
years.

(a) RGPHAE 2013

(b) Satellite imagery-based population estimates

Figure 4: Development of the small-area population shares between 2002 and
2013 for the Dakar region.
The within-region population shares always add up to 100%.

WorldPop data are provided in tagged image file format (TIFF) with a pixel
representing roughly a 100m $\times$ 100m grid square in an open data
repository under CC4.0 licence ([45]). We aggregate the pixel values via their
centroids to the respective administrative areas in Senegal. For discussions
on the impact of allocation uncertainty across different area systems we refer
to [21] and [14]. While WorldPop already provides population estimates for
Senegal in their open data repository, we opt to slightly modify their
approach to align it with our case study. The reasons for this are two-fold:
First, the original approach maps RGPHAE 2013 data dasymetrically via a pixel-
level weighting layer derived from a hierarchical random forest model trained
on départment-level data from the same census and satellite imagery-based
covariates from 2013. As Figures 5(a) to 5(d) show, accuracy of the satellite
imagery-derived population estimates steeply decline for small areas, hinting
at little spatial robustness of the underlying estimation method. Second,
temporal trends in the relationship between population numbers and satellite
imagery-based covariates are not accounted for as model training took place at
one point in time. For example, while there were on average 1.41 inhabitants
per pixel identifying a built-settlement in 2002, this number reduced to 0.88
in 2013. While reasons for that could be manifold (e.g. growth in buildings
not used for housing or in per capita housing space) it shows that this could
lead to an under- or over-estimation of the population count in 2002 depending
on the direction and size of the coefficient.

(a) Régions (14)

(b) Départments (45)

(c) Arrondissements (103)

(d) Communes (552)

(e) Régions (14)

(f) Départments (45)

(g) Arrondissements (103)

(h) Communes (552)

Figure 5: Accuracy of satellite imagery-based population estimates across
geographies.
Satellite imagery-derived population estimates (predicted) are compared with
RGPHAE 2013 population counts (actual) for original WorldPop estimates trained
on département-level (a-d) and recalculated estimates trained on the commune-
level (e-h).

In contrast, the validation study sets out to update RGPH 2002 tables to 2013,
so training needs to take place on 2002 data to make the dynamic population
shares comparable to the fixed approach. Moreover, as modelling exercises
generally benefit from additional data points, we extend the training phase
from originally 45 départements to 103 arrondissements and 552 communes in the
validation study and the application, respectively. Comparing Figures 5(a) to
5(d) with Figures 5(e) to 5(h) illustrate nicely that this holds true in our
case study as well. For further details on the covariates, the preprocessing
of the satellite imagery-derived indicators and the hierarchical random forest
model used in WorldPop, we refer to [37] and [9]. Table 6 summarizes the
different approaches.

Approach | Training level | Prediction level | Distribution level
---|---|---|---
WorldPop | Département, 2013 | Pixel, 2013 | Département, 2013
Validation | Arrondissement, 2002 | Arrondissement, 2013 | Région, 2013
Application | Commune, 2013 | Commune, 2013-20 | Région, 2013-20
Table 6: WorldPop population estimates and their modifications.

For the validation study, we modify the original approach to fit the time
window 2002 to 2013 and to make the results comparable with the proportion
method and the application setup. Specifically, we use arrondissement-level
data from 2002 (RPGH 2002 and satellite imagery-based covariates from 2002)
for fitting the hierarchical random forest model. This way, we make better use
of more fine-granular training data and we align the time window for training
of the dynamic and the fixed approach. In a next step, we predict the
weighting layer for the arrondissement-level of the year 2013 using satellite
imagery-based covariates from 2013 and use it for distributing regional-level
RGPHAE 2013 population counts to the arrondissements. This allows us to
account for both spatial and temporal uncertainty in the evaluation. In
addition, initial tests indicate that creating the weighting layer for very
small areas, i.e. pixels, introduces much instability also seen in large-area
aggregates (see Figure 5). For example, population estimates for 2013 using
the validation setup described above with an arrondissement-level weighting
layer correlates highly at $\rho=0.93$ with the RGPHAE 2013 population counts.
In contrast, population estimates derived the same way, but with a pixel-level
weighting layer correlate at $\rho=0.33$. Therefore, we strike a balance here
between spatial disaggregation and robustness by opting for small areas for
which we can do both training and testing on. In addition, we compared the
accuracy of the population estimates from the hierarchical Bayes approach
proposed by [22] with the results from the hierarchical random forest,
however, without improvements in accuracy.

For the application, we use the approach from the validation study, but apply
it on the commune-level for the years 2013 to 2020. Specifically, region-level
population projections are mapped to communes using a commune-level weighting
layer derived from a hierarchical random forest model trained on commune-level
RGPHAE 2013 counts. Not all covariates are available on an annual basis until
2020. In these cases, we consider the latest data available for weighting
layer prediction.

##  4 Validation

The contribution of this paper is to allow subnational population shares to
vary over time (in contrast to fixed shares via the proportion method). For
example, 2% of the population of area A lives in small area A1 during the
first census. The proportion method assumes that also in the following years
2% of the population of area A will live in small area A1, regardless of the
actual situation on the ground. Thus, the subnational population shares are
considered as fixed. In contrast, we propose to use auxiliary data to capture
subnational population shifts during census years. Thus, the subnational
population shares can vary over time; we consider them to be dynamic.
Arrondissement-level population shares within regions have changed
significantly between 2002 and 2013 with growth rates ranging from -91% to
+48% with the absolute change averaging at 15.7%. Figure 4(a) illustrates the
true changes in population shares for the ten arrondissements within the
région Dakar. Fixed population shares would require the lines to be
horizontal, however, this assumption clearly does not hold. The question then
is if auxiliary information, in our case satellite imagery, are capable to
capture that change more accurately and whether better accuracy translates
into the expected improvements for census updating. Concerning the first
point, Figure 4(b) gives initial indication for Dakar that this might be the
case.

To examine the overall value added of the proposed methodology we use two
census periods in which we update the earlier census (denoted without a time
index) to the year of later census (which we denote with a time index $t$) and
evaluate our contribution vis-à-vis existing approaches. Specifically, we
update the arrondissement-level MPI headcount ratio disaggregated by sex of
the head of household extracted from RGPH 2002 to 2013. To do so, we use the
DHS 2013 for updating the column margins and RGPH 2002 and population
estimates from satellite imagery for updating the row margins with fixed and
dynamic population shares, respectively. The updated MPI headcount ratios are
evaluated against results from RGPHAE 2013 in terms of relative bias and
relative root MSE (RMSE) across arrondissements using $R=500$ simulation
rounds. Therefore, we generate $R=500$ replicates of the census composition
$Y_{aj}$ from RGPH 2002 assuming an independent multinomial distribution in
each small area $a$ with parameters $Y_{a}^{\text{Pois},r}$ and $\pi_{aj}$.
The population row margin is represented as $Y_{a}^{\text{Pois},r}$ and is
obtained using a Poisson distribution $\text{Pois}(\lambda=Y_{a})$ for each
small area $a$ independently. The second parameter is defined as
$\pi_{aj}=\frac{Y_{aj}}{Y_{a}}$. This same process is applied to the
composition from RGPHAE 2013 ($Y_{aj,t}$) that we use for evaluating the
updated MPI headcount ratios. Since the idea is to compare the performance of
SPREE using the dynamic approach (Equation 3) in contrast to the fixed
approach (Equation 2), row margins are generated in two ways: For the fixed
approach, we calculate the arrondissement-level population count of 2013
$\hat{Y}_{a,t}^{r}$ using regional-level population counts $\hat{Y}_{k,t}$
from demographic projections and arrondissement-level population shares
$p_{a}^{r}$ from each census composition replicate $Y_{aj}^{r}$ as described
in Equation 2. For the dynamic approach, we generate $R=500$ replicates of the
population estimates $\hat{Y}_{a,t}^{\text{Aux}}$ created using the
hierarchical random forest approach described in Section 3.3.5. Following
Equation 3, we use the estimated population shares $\hat{p}_{a,t}^{r}$ to
distribute regional-level population counts $\hat{Y}_{k,t}$ to get
arrondissement-level population counts $\hat{Y}_{a,t}^{r}$ for each simulation
round $r$. Then, we obtain $R=500$ replicates of the column margin
$\hat{Y}_{j,t}$ by simple resampling from each primary sampling unit of the
DHS 2013. Finally, we use $Y_{aj}^{r}$, $\hat{Y}_{j,t}^{r}$ and the respective
$\hat{Y}_{a,t}^{r}$ to generate arrondissement-level point estimates
$\hat{Y}_{aj,t}^{r}$ of the MPI headcount ratio in 2013, which we then compare
against $Y_{aj,t}^{r}$ from RGPHAE 2013 using the relative bias and empirical
RMSE defined as:

$\text{Relative
bias}\left(\hat{Y}_{aj,t}\right)=\frac{\frac{1}{R}\sum_{r=1}^{R}\left(\hat{Y}^{r}_{aj,t}-Y^{r}_{aj,t}\right)}{\frac{1}{R}\sum_{r=1}^{R}Y^{r}_{aj,t}},$

and

$\text{Relative
RMSE}\left(\hat{Y}_{aj,t}\right)=\frac{\sqrt{\frac{1}{R}\sum_{r=1}^{R}\left(\hat{Y}^{r}_{aj,t}-Y^{r}_{aj,t}\right)^{2}}}{\frac{1}{R}\sum_{r=1}^{R}Y^{r}_{aj,t}}.$

Naturally, fixed population shares provide very good accuracy for areas
exhibiting little change and poor accuracy for areas exhibiting large
fluctuations in the inter-censal population. This pattern indicates that
dynamic population margins may be able to improve estimates for areas with
large changes in population shares. Table 7 supports both hypotheses by
grouping the arrondissement-level accuracy measurements into quartiles along
the true population change.

Quartile | Relative Bias (in %)
---|---
dynamic | fixed
Lowest | 17.95 | 28.99
2nd | 18.41 | 9.98
3rd | 7.57 | -5.44
Highest | 0.68 | -19.60
Table 7: Accuracy of estimated population shares in 2013.
Arrondissements ordered by changes in the true population share between 2002
and 2013. The accuracy is evaluated against the true population shares from
RGPHAE 2013.

For example, for the 50% of the 103 arrondissements with the smallest changes
in population shares between 2002 and 2013 (2nd and 3rd group), the fixed
approach outperforms the dynamic approach. For the arrondissements exhibiting
the strongest changes in population share, the dynamic approach provides
better accuracy than the fixed approach. A potential reason why both
approaches, but especially the dynamic approach, exhibit a tendency to
overestimate the changes in the population shares is that the underlying
population counts are naturally left-censored at zero. This may induce an
upward bias in the population estimates, especially for sparsely populated
areas and for population margins with comparatively high volatility.

In total, considering satellite imagery-based population estimates for
updating the population margin in SPREE provides more accurate population
shares for 42 of the 103 arrondissements in this validation study. Therefore,
we see indication that satellite imagery-based population estimates can
improve existing approaches used in census updating for deriving small area
population margins.

One limitation here is that the knowledge on the question of which small areas
show large changes of subnational population shares is usually not known ex-
ante. Intuitively, one approach to overcome this could be to use dynamic
population shares for areas for which the estimated changes are large.
However, volatile satellite imagery-based population margins make this an
imperfect selection criteria. Therefore, we opt for a more conservative
approach in the application by selecting those small areas for which to use
the dynamic population shares that are situated within those 25% of regions
showing the strongest population changes following the regional-level
estimates from the official population projections.

Figure 6 and Table 8 show the results of the simulation. The overall
correlation of the estimated MPI headcount ratio for 2013 and the true
headcount ratio of 2013 as depicted in Figure 6 is moderate for both
proportion types. While the Pearson correlation coefficient reflects the
overall results from Table 7, the differences between the dynamic and fixed
approach are less striking. A potential reason is that SPREE builds on
multiple inputs (represented by the allocation structure and the association
structure), so changes in one of the inputs may not affect the SPREE output to
the same extent.

Figure 6: Correlation of estimated and true arrondissement-level MPI headcount
ratio in 2013.
Arrondissements are grouped along the quartiles of the changes in true
population shares between 2002 and 2013.

Looking at the relative bias and the relative RMSE in Table 8, the dynamic
approach performs better in most of the cases. The comparatively higher
relative bias in the second group can potentially be explained with zero
counts in the underlying census composition. As SPREE performs less well in
the presence of zero counts and as half of the zero counts in the census
composition are located in the second group a deterioration of model
performance can be expected.

Relative bias (in %)
---
Quartile | Type | Q2.5 | Q25 | Median | Mean | Q75 | Q97.5
Lowest | Dynamic | -29.55 | -11.94 | 1.23 | -1.96 | 7.60 | 22.13
| Fixed | -28.92 | -10.39 | 3.94 | -0.24 | 8.64 | 22.87
2nd | Dynamic | -14.00 | 4.69 | 15.79 | 15.32 | 27.94 | 43.22
| Fixed | -13.57 | 5.05 | 16.87 | 16.02 | 28.55 | 43.38
3rd | Dynamic | -24.44 | -0.60 | 2.58 | 6.89 | 16.88 | 36.99
| Fixed | -24.15 | 0.19 | 4.40 | 7.74 | 17.18 | 38.17
Highest | Dynamic | -30.54 | -6.72 | 1.74 | 3.82 | 18.93 | 34.55
| Fixed | -29.83 | -4.28 | 5.50 | 5.58 | 19.37 | 34.83
Relative RMSE (in %)
Quartile | Type | Q2.5 | Q25 | Median | Mean | Q75 | Q97.5
Lowest | Dynamic | 7.99 | 13.15 | 17.42 | 18.70 | 23.82 | 32.71
| Fixed | 8.44 | 12.76 | 17.42 | 18.23 | 21.96 | 32.12
2nd | Dynamic | 9.12 | 13.81 | 22.51 | 24.09 | 34.36 | 50.96
| Fixed | 8.76 | 14.23 | 22.55 | 24.25 | 34.60 | 51.02
3rd | Dynamic | 5.91 | 10.02 | 18.36 | 19.99 | 28.46 | 42.52
| Fixed | 5.82 | 9.93 | 18.40 | 20.04 | 28.55 | 43.25
Highest | Dynamic | 9.06 | 16.03 | 23.16 | 23.59 | 30.25 | 43.14
| Fixed | 8.90 | 16.73 | 22.61 | 23.64 | 32.06 | 43.54
Table 8: Performance of the 2013 census updates for the MPI headcount ratio in
Senegal, across arrondissements.

A possible reason why the differences between the dynamic and the fixed
approach are less striking in terms of relative RMSE is that the resampling
procedure of the respective population margins differs. While the fixed
population margin is solely derived from census data, which is resampled
following a Poisson and a Multinomial distribution in our setup, the procedure
to obtain the dynamic population margin based on satellite imagery considers a
simple resampling in order to account for potential non-trivial uncertainty in
the pre-processing. This may lead to efficiency losses in the dynamic
approach.

In summary, the results of the validation study show that the dynamic approach
using satellite imagery from WorldPop as auxiliary information can improve the
accuracy of both the population margin (relative bias) and the census updates
(in Pearson correlation coefficient), especially for areas with large changes
in population shares. For those areas with minor changes in their population
shares, the fixed approach is recommended.

##  5 Application

In this section we present the results of our case study where we produce
updated MPI headcount ratios for all 552 communes in Senegal for the years
2013 to 2020. We apply the semiparametric bootstrap procedure with $B=100$
explained in Section 2.3 to obtain uncertainty measures for the estimated MPI
headcount ratios.

Has the multidimensional headcount ratio of individuals living in female-
headed households improved more or less than the one in male-headed households
since 2013? As shown in Table 2, individuals living in female-headed
households in Senegal are less likely to be multidimensional poor than
individuals living in male-headed households. Consequently, it is expected
that female-headed households may profit on average less from the social
safety net program PNBSF. Figure 7 depicts the difference of growth rates in
the MPI headcount ratio between individuals living in female-headed households
and individuals living in male-headed households using the year 2013 as
baseline. The figure and the national-level point estimates of the MPI
headcount ratio $H$ in Tables 9 and 10 confirm that the MPI headcount ratio of
female-headed households has improved on average less since 2013 than of male-
headed households (represented by the shades of brown in Figure 7).

(a) 2013

(b) 2014

(c) 2015

(d) 2016

(e) 2017

(f) 2018

(g) 2019

(h) 2020

Figure 7: Evolution of the updated MPI headcount ratio of individuals living
in female-headed households vs. male-headed households.

Table 9 shows that the estimated MPI headcount ratio for female-headed
households has been constantly decreasing from 2013 to 2020, with a greater
reduction between 2016 and 2018. As of 2018, the incidence of multidimensional
poverty of this specific population in Senegal has remained stagnant (61%).
The corresponding coefficients of variation (CV) indicate that the updated
incidence of multidimensional poverty are acceptable considering traditional
thresholds (below 20%).

Year | H | Coefficient of variation (in %)
---|---|---
(est.) | Q2.5 | Q25 | Median | Mean | Q75 | Q97.5
2013 | 0.70 | 0.13 | 5.26 | 9.67 | 12.68 | 14.22 | 29.18
2014 | 0.69 | 0.08 | 3.77 | 7.19 | 7.55 | 10.04 | 21.21
2015 | 0.69 | 0.08 | 4.46 | 8.08 | 9.25 | 12.01 | 20.94
2016 | 0.69 | 0.08 | 4.26 | 8.18 | 9.11 | 12.93 | 21.42
2017 | 0.65 | 0.06 | 3.80 | 6.69 | 6.93 | 9.49 | 16.12
2018 | 0.61 | 0.09 | 6.33 | 10.81 | 10.69 | 14.18 | 24.52
2019 | 0.61 | 0.13 | 6.52 | 10.62 | 11.08 | 13.88 | 28.72
2020 | 0.61 | 0.12 | 6.62 | 10.52 | 10.98 | 13.89 | 27.65
Table 9: Estimated headcount ratio and its coefficient of variation for
female-headed households, across communes.

In comparison, the MPI headcount ratio for male-headed households (see Table
10) decreased by 13 percentage points over the same period of time showing
considerable smaller CVs than the female-headed households. This result is
expected since the the sample size of male-headed households is considerably
larger (approximately 77.7% of Senegalese households are headed by men).

Year | H | Coefficient of variation (in %)
---|---|---
(est.) | Q2.5 | Q25 | Median | Mean | Q75 | Q97.5
2013 | 0.77 | 0.66 | 2.17 | 3.95 | 4.43 | 6.29 | 9.77
2014 | 0.77 | 0.51 | 1.61 | 2.85 | 3.38 | 4.96 | 7.67
2015 | 0.77 | 0.61 | 2.08 | 3.74 | 4.44 | 6.64 | 9.91
2016 | 0.74 | 0.58 | 2.44 | 4.40 | 4.96 | 7.38 | 10.90
2017 | 0.68 | 0.84 | 2.56 | 3.94 | 4.20 | 5.97 | 8.11
2018 | 0.66 | 0.86 | 3.32 | 5.48 | 6.03 | 8.93 | 12.14
2019 | 0.64 | 1.42 | 4.06 | 6.13 | 6.45 | 8.86 | 12.32
2020 | 0.64 | 1.45 | 4.06 | 6.11 | 6.50 | 8.99 | 12.48
Table 10: Estimated headcount ratio and its coefficient of variation for male-
headed households, across communes.

Looking at the indicator-specific contributions to the MPI headcount ratio at
a national-level, decreases in multidimensional poverty are mainly due to
improved living conditions (see Figure 8(a)). Notably, deprivation in the
indicator on ‘years of schooling’ has increased for individuals living in
female-headed households with ‘school attendance’ remaining a main driver of
multidimensional poverty.

In order to drill down to local realisations of national-level trends, we
apply SPREE following the hybrid approach laid out in Section 4, i.e. apply
the dynamic approach in those areas with bigger changes in their population
shares and the fixed approach for those with less changes. Specifically, the
regions Kaffrine, Matam and Tambacounda show the highest population change.
Thus, we apply the dynamic margins for the 105 communes located in these
regions. Figure 8(b) illustrates the development of indicator-specific
contributions to the commune-level MPI headcount ratio of the commune ‘Yoff’
in the region Dakar from 2013 to 2020 as an example. While in Yoff living
conditions as drivers of multidimensional poverty steadily declined over the
years similar to the national trend, also school attendance has improved,
however, still remaining the biggest driver of commune-level MPI poverty.

(a) Senegal

(b) Yoff, Dakar, Senegal

Figure 8: Indicator-specific contributions to the uncensored MPI headcount
ratio for individuals living in female-headed households in Senegal and in the
commune Yoff located in the region Dakar, specifically.

In this setting neither direct nor indirect evaluation of commune-level census
updates is possible due to the lack of appropriate commune-level evaluation
data after the census year 2013 on the one hand and due to the fact that SPREE
results reproduce region-level survey results by design on the other.

##  6 Conclusion

This study has demonstrated in a case study how auxiliary information such as
satellite imagery can be used to potentially improve the availability of
relevant key statistics for small areas between census years by strengthening
the population margins especially in regions exhibiting strong population
growth. This is particularly important for local-level policy-making as
censuses and surveys fail to provide reliable and up-to-date data on small
areas. This study has laid out a path to fill this gap by proposing a unified
framework to combine established census updating techniques with recent
approaches that add spatial granularity to existing data using novel data
sources. We discussed both power and limitations of the proposal by providing
annual MPI headcount ratio updates including indicator-specific contributions
for the years 2013 to 2020 in the 552 communes of Senegal.

First and foremost, the value added vis-à-vis existing census updating
methodologies is largely determined by the quality of the auxiliary data. The
simulation showed that conveniently preprocessed remote sensing products such
as the population grids including the corresponding covariates currently still
lack the spatial robustness needed to add value to existing approaches. While
this challenge is likely to be solved in the mid-term by the rapidly evolving
market of remote sensing products, it may require considerable effort in the
short-term to overcome this quality gap.

Second, rigorously addressing the uncertainty involved in the estimation
process demands further research as for many promising auxiliary data sources
the data generating process is beyond the control of a national statistical
office. In addition, census and survey inputs sometimes require imputation to
address high levels of non-response. While we took a first step in this paper
to capture parts of the uncertainty by resampling the inputs, it would be
interesting to incorporate uncertainty in the explanatory variables and
effects from (multiple) imputation more formally.

Third, as we showcased in the case study, slightly varying definitions of the
indicator of interest across data sources may induce additional uncertainty
into the updating process, so harmonisation along the lines of [19] is clearly
advised. This approach could also be used to obtain a complete MPI when some
of the components are not present in the census, which is the case in the
setup of this paper.

Fourth, under the SPREE approach, census, survey and auxiliary data must have
the same structure in terms of the disaggregation dimensions. However,
considering that a census is conducted in long intervals, accounting for re-
structurings such as land reforms that alter the administrative delineation,
takes relevance. High-resolution population grids allow for a re-allocation of
the population across different geographies under certain assumptions,
however, a more general approach is desirable.

Fifth, the applicability of the SPREE could also increase significantly by
allowing for non-categorical indicators and non-linear relationships. Here,
copulas as used in [34] may provide a powerful vehicle to generalize SPREE
further.

## Conflict of interest

The authors have declared that no competing interests exist.

## References

  * Agence Nationale de la Statistique et de la Démographie [2013] Agence Nationale de la Statistique et de la Démographie (2013) Rapport Projection de la Population du Senegal 2013-2063.  Tech. rep., Agence Nationale de la Statistique et de la Démographie.  URL: http://www.ansd.sn/ressources/publications/Rapport_projection_version_12fev06.pdf.
  * Agence Nationale de la Statistique et de la Démographie [2015] — (2015) Enquête de Mise à jour du Registre National Unique des Ménages Vulnérables.  URL: http://anads.ansd.sn/index.php/catalog/143.
  * Alkire et al. [2019] Alkire, S., Kanagaratnam, U. and Suppa, N. (2019) The Global Multidimensional Poverty Index (MPI) 2019.  Oxford Poverty and Human Development Initiative, University of Oxford, 47, OPHI MPI Methodological Note 47.  URL: https://www.ophi.org.uk/wp-content/uploads/OPHI_MPI_MN_47_2019_vs2.pdf.
  * Bonafilia et al. [2019] Bonafilia, D., Gill, J., Kirsanov, D. and Sundram, J. (2019) Mapping for humanitarian aid and development with weakly-and semi-supervised learning.  Tech. rep., Facebook.  URL: https://bit.ly/2PxK5dx.
  * Boo et al. [2020] Boo, G., Darin, E., Thomson, D. R. and Tatem, A. J. (2020) A grid-based sample design framework for household surveys.  Gates Open Research, 4.  URL: https://gatesopenresearch.org/articles/4-13/v1.
  * Chen and Nordhaus [2011] Chen, X. and Nordhaus, W. D. (2011) Using luminosity data as a proxy for economic statistics.  Proceedings of the National Academy of Sciences of the United States of America, 108, 8589–8594.  URL: http://www.ncbi.nlm.nih.gov/pubmed/21576474.
  * Deming and Stephan [1940] Deming, E. and Stephan, F. (1940) On a least squares adjustment of a sampled frequency table when the expected marginal totals are known.  The Annals of Mathematical Statistics, 11, 427–444.
  * European Union [2020] European Union (2020) Copernicus: Europe´s eyes on Earth.  URL: https://www.copernicus.eu/en.
  * Fick and Hijmans [2017] Fick, S. E. and Hijmans, R. J. (2017) WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas.  International Journal of Climatology, 37, 4302–4315.  URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/joc.5086.
  * Freire et al. [2016] 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.  AGILE.  URL: http://publications.jrc.ec.europa.eu/repository/handle/JRC100523.
  * Gouvernement du Sénégal [2014] Gouvernement du Sénégal (2014) Plan Senegal Emergent.  Tech. rep., Gouvernement du Sénégal.  URL: https://www.sec.gouv.sn/sites/default/files/PlanSenegalEmergent_0.pdf.
  * Gouvernement du Sénégal [2017] — (2017) Programme National de Bourses de Sécurité Familiale (PNBSF).  URL: https://bit.ly/3h8mUCl.
  * Green et al. [1998] Green, A., Haslett, S. and Zingel, C. (1998) Small Area Estimation Given Regular Updates of Census Auxiliary Variables.  In Proceedings of the New Techniques and Technologies for Statistics Conference, 206–211.
  * Groß et al. [2020] Groß, M., Kreutzmann, A. K., Rendtel, U., Schmid, T. and Tzavidis, N. (2020) Switching between Different Non-Hierachical Administrative Areas via Simulated Geo-Coordinates: A Case Study for Student Residents in Berlin.  Journal of Official Statistics, 36, 297–314.
  * Harvey [2002] Harvey, J. T. (2002) Estimating census district populations from satellite imagery: Some approaches and limitations.  International Journal of Remote Sensing, 23, 2071–2095.  URL: https://www.tandfonline.com/doi/abs/10.1080/01431160110075901.
  * Henderson et al. [2012] Henderson, J. V., Storeygard, A. and Weil, D. N. (2012) Measuring economic growth from outer space.  American Economic Review, 102, 994–1028.  URL: http://pubs.aeaweb.org/doi/10.1257/aer.102.2.994.
  * Hidiroglou and Lavallee [2009] Hidiroglou, M. A. and Lavallee, P. (2009) Sampling and Estimation in Business Surveys.  In Handbook of Statistics: Design, Methods and Applications (eds. D. Pfeffermann and C. R. Rao), vol. 29 A, chap. Sampling a, 441–470. Elsevier.
  * Isidro [2010] Isidro, M. (2010) Intercensal updating of small area estimates.  Ph.D. thesis, Massey University.
  * Isidro et al. [2016] Isidro, M., Haslett, S. and Jones, G. (2016) Extended structure preserving estimation (ESPREE) for updating small area estimates of poverty.  Annals of Applied Statistics, 10, 451–476.
  * Jean et al. [2016] 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.  URL: http://www.ncbi.nlm.nih.gov/pubmed/27540167.
  * Koebe [2020] Koebe, T. (2020) Better coverage, better outcomes? Mapping mobile network data to official statistics using satellite imagery and radio propagation modelling.  PLoS ONE, 15, e0241981.  URL: https://dx.plos.org/10.1371/journal.pone.0241981.
  * Leasure et al. [2020] Leasure, D. R., Jochem, W. C., Weber, E. M., Seaman, V. and Tatem, A. J. (2020) National population mapping from sparse survey data: A hierarchical Bayesian modeling framework to account for uncertainty.  Proceedings of the National Academy of Sciences, 117, 24173–24179.
  * Leyk et al. [2019] Leyk, S., Gaughan, A. E., Adamo, S. B., de Sherbinin, A., Balk, D., Freire, S., Rose, A., Stevens, F. R., Blankespoor, B., Frye, C., Comenetz, J., Sorichetta, A., MacManus, K., Pistolesi, L., Levy, M. and Tatem, A. 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, 1385–1409.  URL: https://www.earth-syst-sci-data.net/11/1385/2019/.
  * Luna [2016] Luna, A. (2016) Multivariate Structure Preserving Estimation for Population Compositions.  Ph.D. thesis, University of Southampton.
  * Luna et al. [2015] Luna, A., Zhang, L. C., Whitworth, A. and Piller, K. (2015) Small area estimates of the population distribution by ethnic group in England: A proposal using structure preserving estimators.  Statistics in Transition, 16, 585–602.
  * Noble et al. [2002] Noble, A., Haslett, S. and Arnold, G. (2002) Small area estimation via generalized linear models.  Journal of Official Statistics, 18, 45–60.
  * Pfeffermann [2013] Pfeffermann, D. (2013) New Important Developments in Small Area Estimation.  Statistical Science, 28, 40–68.
  * Pinkovskiy and Sala-i Martin [2016] Pinkovskiy, M. and Sala-i Martin, X. (2016) Lights, Camera … Income! Illuminating the National Accounts-Household Surveys Debate.  The Quarterly Journal of Economics, 131, 579–631.  URL: https://academic.oup.com/qje/article-lookup/doi/10.1093/qje/qjw003.
  * Pokhriyal and Jacques [2017] Pokhriyal, N. and Jacques, D. C. (2017) Combining disparate data sources for improved poverty prediction and mapping.  Proceedings of the National Academy of Sciences of the United States of America, 114, E9783–E9792.  URL: http://www.ncbi.nlm.nih.gov/pubmed/29087949http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC5699027.
  * Purcell and Kish [1980] Purcell, N. J. and Kish, L. (1980) Postcensal Estimates for Local Areas (Or Domains).  International Statistical Review / Revue Internationale de Statistique, 48, 3–18.  URL: https://www.jstor.org/stable/pdf/1402400.pdf?refreqid=excelsior%3Aa8cffa0e4ad83ca4e8bd5009e1c6e060.
  * Rao [1986] Rao, J. N. K. (1986) Synthetic estimators, SPREE and the best model based predictors.  In Proceedings of the Conference on Survey Research Methods in Agriculture, 1–16. US Department of Agriculture Washington, DC.
  * Rao [2003] — (2003) Small Area Estimation.  New York: Wiley.
  * Rao and Molina [2015] Rao, J. N. K. and Molina, I. (2015) Small Area Estimation.  New York: Wiley, 2nd edn.
  * Rocher et al. [2019] Rocher, L., Hendrickx, J. M. and de Montjoye, Y. A. (2019) Estimating the success of re-identifications in incomplete datasets using generative models.  Nature Communications, 10, 1–9.  URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6650473/.
  * Schmid et al. [2017] Schmid, T., Bruckschen, F., Salvati, N. and Zbiranski, T. (2017) Constructing sociodemographic indicators for national statistical institutes by using mobile phone data: estimating literacy rates in Senegal.  Journal of the Royal Statistical Society. Series A: Statistics in Society, 180, 1163–1190.  URL: https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssa.12305.
  * Steinnocher et al. [2019] Steinnocher, K., De Bono, A., Chatenoux, B., Tiede, D. and Wendt, L. (2019) Estimating urban population patterns from stereo-satellite imagery.  European Journal of Remote Sensing, 52, 12–25.  URL: https://doi.org/10.1080/22797254.2019.1604081.
  * Stevens et al. [2015] Stevens, F. R., Gaughan, A. E., Linard, C. and Tatem, A. J. (2015) Disaggregating census data for population mapping using Random forests with remotely-sensed and ancillary data.  PLoS ONE, 10, e0107042.  URL: http://www.ncbi.nlm.nih.gov/pubmed/25689585http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC4331277.
  * Sundsøy [2016] Sundsøy, P. (2016) Can mobile usage predict illiteracy in a developing country?  arXiv preprint arXiv:1607.01337.  URL: http://arxiv.org/abs/1607.01337.
  * Tzavidis et al. [2018] Tzavidis, N., Zhang, L. C., Luna, A., Schmid, T. and Rojas-Perilla, N. (2018) From start to finish: a framework for the production of small area official statistics.  Journal of the Royal Statistical Society. Series A: Statistics in Society, 181, 927–979.  URL: https://onlinelibrary.wiley.com/doi/abs/10.1111/rssa.12364.
  * United Nations [1956] United Nations (1956) Manual III. Methods for population projections by sex and age.
  * United Nations Department of Economic and Social Affairs [2009] United Nations Department of Economic and Social Affairs (2009) Handbook on geospatial infrastructure in support of census activities.  New York, USA: United Nations Publication, st/esa/sta edn.
  * United Nations General Assembly [2015] United Nations General Assembly (2015) Res 70/1. Transforming Our World: The 2030 Agenda for Sustainable Development.  Tech. rep., United Nations General Assembly.  URL: https://www.un.org/en/development/desa/population/migration/generalassembly/docs/globalcompact/A_RES_70_1_E.pdf.
  * Weidmann and Schutte [2017] Weidmann, N. B. and Schutte, S. (2017) Using night light emissions for the prediction of local wealth.  Journal of Peace Research, 54, 125–140.  URL: http://journals.sagepub.com/doi/10.1177/0022343316630359.
  * White et al. [2011] White, I. R., Royston, P. and Wood, A. M. (2011) Multiple imputation using chained equations: Issues and guidance for practice.  Statistics in Medicine, 30, 377–399.  URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.4067.
  * WorldPop [2018] WorldPop (2018) Global High Resolution Population Denominators Project.  URL: www.worldpop.org.
  * Zhang and Chambers [2004] Zhang, L. C. and Chambers, R. L. (2004) Small area estimates for cross-classifications.  Journal of the Royal Statistical Society. Series B: Statistical Methodology, 66, 479–496.  URL: https://www.jstor.org/stable/pdf/3647538.pdf?refreqid=excelsior%3Af84bf05ab9ce21280f2f9004e9489090.