M-quantile models with application to poverty mapping |
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Authors: | Nikos Tzavidis Nicola Salvati Monica Pratesi Ray Chambers |
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Institution: | (1) Centre for Census and Survey Research, University of Manchester, Manchester, M13 9PL, UK;(2) Dipartimento di Statistica e Matematica Applicata all’Economia, Università di Pisa, Via Ridolfi 10, Pisa, 56124, Italy;(3) Centre for Statistical and Survey Methodology, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia |
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Abstract: | Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately,
cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation,
using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models
are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random
effects models that include random area effects to account for between area variations. However, such models also depend on
strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow
for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models
was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction
of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do
not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate
for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality.
The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation
of the distribution function of the study variable within the small area of interest both under an M-quantile and a random
effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small
area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the
2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of
poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption
expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are
in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of
inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology
and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile
estimation framework through design-based simulations based on two realistic survey data sets containing small area information
and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function. |
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Keywords: | Distribution function Quantile regression Inequality measure Poverty assessment Robust inference |
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