ECLAC approach to poverty mapping
Transcript of ECLAC approach to poverty mapping
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ECLAC approach to poverty mappingEl enfoque de CEPAL en el mapeo de la pobreza
Andrés Gutiérrez
2021
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SDG / ODS
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1.1 By 2030, eradicate extreme poverty for allpeople everywhere.
1.2 By 2030, reduce at least by half the proportionof men, women and children of all ages living inpoverty in all its dimensions according to nationaldefinitions.
1.1. De aquí a 2030, erradicar para todas laspersonas y en todo el mundo la pobreza extrema.
1.2. De aquí a 2030, reducir al menos a la mitad laproporción de hombres, mujeres y niños de todaslas edades que viven en la pobreza en todas susdimensiones con arreglo a las definicionesnacionales.
No Poverty / Poner fin a la pobreza
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Sustainable Development Goal indicators should bedisaggregated, where relevant, by income, sex, age,race, ethnicity, migratory status, disability andgeographic location, or other characteristics, inaccordance with the Fundamental Principles of OfficialStatistics.
Global indicator framework for the SustainableDevelopment Goals (A/RES/71/313).
Desglosar los ODS por ingreso, sexo, edad, raza,etnicidad, estado migratorio, discapacidad y ubicacióngeográfica, de conformidad con los PrincipiosFundamentales de las Estadísticas Oficiales.
Marco de indicadores globales para los Objetivosde Desarrollo Sostenible (A/RES/71/313).
Leave no one behind / No dejar a nadie atrás
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Household surveys limitations and the use of auxiliaryinformation
Limitaciones de las encuestas de hogares y el uso de información auxiliar
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Surveys that depend on a large sample size and aproper sampling strategy rely on a robust inferentialsystem that provides precise and exact estimation inplanned domains.
When the sample size of the survey is not enough, it isnecessary to resort to external auxiliary information(censuses, administrative records, satellite images) sothat a precise and exact inferential system can bebuilt.
Las encuestas que dependen de un buen tamaño demuestra y una estrategia de muestreo adecuada sebasan en un sistema inferencial sólido queproporciona una estimación precisa y exacta en losdominios planificados.
Cuando el tamaño muestral de la encuesta no essuficiente para sustentar la inferencia estadísticarequerida para algunos subgrupos de interés, esnecesario recurrir a información auxiliar externa paraque en conjunto se puede construir un sistemainferencial preciso y exacto.
¿What is it all about? / ¿De qué se trata?
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When the sample size does not allow obtainingreliable direct estimates for some domains of interest,the following options can be addressed:
1. Increase the sample size: this option raises costs,and it is unfeasible.
2. Use statistical methodologies that involveexternal auxiliary information to obtain reliableestimates (not direct) in the subgroups ofinterest, while keeping the survey sample size.
Cuando el tamaño de la muestra no permite obtenerestimaciones directas confiables para algunosdominios de interés, se pueden abordar las siguientesopciones:
1. Incrementar el tamaño de la muestra: esta opcióneleva los costos y es inviable.
2. Utilizar metodologías estadísticas que involucreninformación auxiliar externa para obtenerestimaciones confiables (no directas) en lossubgrupos de interés, mientras se mantiene eltamaño de la muestra de la encuesta.
Solutions / Soluciones
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Borrowing strength / Tomando fuerza prestada
Source: Methodology of Modern Business Statistics (2014).
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SAE methodologies in ECLAC
Metodologías SAE en la CEPAL
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SAE methodologies / Metodologías SAE
Source: adaptation from Rahman (2008).
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SAE estimators used in ECLAC could be divided intotwo main types:
1. Estimators based on area models2. Estimators based on unit models
The choice of the method that should be used in theestimation of the domains of interest is madedepending on the level at which the auxiliaryinformation is found (at the domain or aggregationlevel - at the household or person level)
Los estimadores de SAE se dividen en dos tiposprincipales:
1. Estimadores basados en modelos de área2. Estimadores basados en modelos de unidad
La escogencia del método que se debe utilizar en laestimación de los dominios de interés se realizadependiendo del nivel en el que se encuentre lainformación auxiliar (a nivel de dominio o agregación- a nivel de hogar o persona)
Two types of methods / Dos clases de métodos
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Area-level models
Modelos de áreas
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The sample size in each area is not planned inadvance (since the sampling scheme follows atwo-stage sampling).Any estimation of relative indicators (means andproportions) will have to make use of a ratio-typeestimator: random numerator and randomdenominator.
El tamaño de muestra en cada área difícilmentees planificado de antemano (pues el esquema demuestreo es bietápico: UPM - Vivienda).Cualquier estimación de indicadores relativos(medias, proporciones) tendrá que usar unestimador de razón: numerador y denominadoraleatorios.
When the sample size is not largeenough, none of the above estimators will be preciseneither consistent.
Cuando el tamaño de muestra no es losuficientemente grande, entonces ninguno de losanteriores estimadores será preciso, ni consistente.
Direct estimators / Estimadores directos
θDird = AV(θ
Dird ) = ∑
s∑
s
∑sdwkyk
∑sdwk
∆kl
πkl
ek
πk
el
πl
nd = #(sd) nd = #(sd)
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We will model the Direct Estimator so that in the areaswhere there is not enough sample, strength will beborrowed from the other areas.
Vamos a modelar el indicador directo para que en lasáreas en las que no haya suficiente muestra se tomefuerza prestada de las otras áreas.
Following (some) Bayes rule, we have that: De la regla de Bayes, se tiene que:
Direct estimators / Estimadores directos
θDird = θd + εd εd ∼ N(0, Var(θ
Dird ))
θd = x′dβ + ud ud ∼ N(0, σ2
u)
θDird = x′
dβ + ud + εd
θd|θDird ∼ N (θFH
d , σ2dFH
)θFH
d = E(θd|θDird ) = γdθDir
d+ (1 − γd)x′
dβ
σ2dFH
= V ar(θDir
d )γd
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We like the Bayesian way / Nos gusta el enfoque bayesiano
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We like the Bayesian way / Nos gusta el enfoque bayesiano
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Beta-logistic model for poverty / Modelo beta-logístico para la pobreza
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parameters { vector[p] beta; real<lower=0> sigma2_v; vector[N1] v;}
transformed parameters{ vector[N1] LP; real<lower=0> sigma_v; vector[N1] theta; LP = X * beta + v; sigma_v = sqrt(sigma2_v); for (i in 1:N1) { theta[i] = inv_logit(LP[i]); }}
model { vector[N1] a; vector[N1] b; for (i in 1:N1) { a[i] = theta[i] * phi[i]; b[i] = (1 - theta[i]) * phi[i]; } // priors beta ~ normal(0, 100); sigma2_v ~ inv_gamma(0.0001, 0.0001); // likelihood y ~ beta(a, b); v ~ normal(0, sigma_v);}
generated quantities { vector[N2] y_pred; vector[N2] thetapred; for (i in 1:N2) { y_pred[i] = normal_rng(Xs[i] * beta, sigma_v); thetapred[i] = inv_logit(y_pred[i]); }
And, we like STAN / Nos gusta STAN
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Unit-level models
Modelo de unidades
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ECLAC uses a unit-level model with adjustment tothe complex sampling design for the estimationof average income.
This model was first proposed by Guadarrama,Molina, and Rao (2018) and it induces anapproximation of the best empirical predictor(Pseudo-EBP) based on the model with nestederrors (Molina and Rao, 2010).
La CEPAL utiliza un modelo de nivel de unidad conajuste al diseño complejo de muestreo para laestimación del ingreso promedio.
Este modelo fue propuesto por Guadarrama,Molina y Rao (2018) e induce una aproximacióndel mejor predictor empírico (Pseudo-EBP)basado en el modelo con errores anidados(Molina y Rao, 2010).
The GMR model / El modelo GMR
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The GMR model / El modelo GMR
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This method assumes that the transformed incomevariable follows the model:
Este método asume que la variable de ingresostransformados sigue el modelo:
Where:
is the vector of regression coefficients, is the area random effect, and
are the errors for individuals inthe d-th area and are considered independentfrom the random effects.
En donde:
es el vector de coeficientes de regresión, es el efecto de área, y
son los errores del modelo paralos individuos del área d-ésima.
The nested-error model / El modelo de errores anidados
y∗di = log (ydi + c) y∗
di = log (ydi + c)
y∗di = x′
diβ + ud + edi; i = 1, … , Nd, d = 1, … , D,
β
udiid∼ N (0, σ2
u)edi
iid∼ N (0, σ2e )
β
udiid∼ N (0, σ2
u)edi
iid∼ N (0, σ2e )
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Since follows a normal distribution, the conditionaldistribution will also be a normal distributionparameterized as follows:
Dado que sigue una distribución normal, ladistribución condicional también seránormal parametrizada de la siguiente manera:
To avoid the bias induced by ignoring the samplingdesign in the model, the parameters of the abovedistribution may consistently be estimated byincluding the sampling weights .
Para evitar el sesgo inducido al ignorar el diseño demuestreo en el modelo, los parámetros de ladistribución anterior se pueden estimarconstantemente incluyendo los pesos de muestreo
.
Weigthed estimation / Estimación ponderada
ydydr | yds
ydydr | yds
ydr|yds ∼ N (µdr|s, Vdr|s) con d = 1, … , D
wkd
wkd
µdr|s = Xdrβ + γd(y dw − x′dwβ)1Nd−nd
Vdr|s = (σ2e + σ
2
u(1 − γd))1Nd−nd
1TNd−nd
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Since it is not possible to identify and link the units ofthe sample with those of the census, then theapproach used is a Census-EB type, as follows:
Como no es posible identificar y vincular las unidadesde la muestra con las del censo, el enfoque utilizadoes de tipo Census-EB, de la siguiente manera:
We consider a Monte Carlo simulation procedure toestimate the poverty indicators since often theexpectation that defines the bestpredictor cannot be calculated analytically.
Consideramos un procedimiento de simulación deMonte Carlo para estimar los indicadores de lapobreza, ya que a menudo la esperanza que define el mejor predictor no se puede calcularanalíticamente.
Monte Carlo estimation / Estimación de Monte Carlo
~θd = ∑
i∈rd
E(I ydi<z|yds)1
Nd
E(I ydi<z|yds) E(I ydi<z|yds)
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Some maps
Algunos mapas
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Processes in production of SAE / Procesos en la producción SAE
Source: adaptation from Kolenikov (2014).
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Perú
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Colombia
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Chile
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Leaving no one behind
No dejando a nadie detrás
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Colombia: age and education / edad y educación
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México: ethnicity and education / étnia y educación
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México: sex and education / sexo y educación
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