Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality

Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality

This paper proposes a method for estimating distribution functions that are associated with the nested errors in linear mixed models. The estimator incorporates Empirical Bayes prediction while making minimal assumptions about the shape of the erro...

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Bibliographic Details
Main Authors: Elbers, Chris, van der Weide, Roy
Format: Policy Research Working Paper
Language:English
en_US
Published: World Bank Group, Washington, DC 2014
Subjects:
ANALYSIS OF VARIANCE
ASYMPTOTIC DISTRIBUTION
BENCHMARK
BIASES
BOOTSTRAP
CENTRAL LIMIT THEOREM
COMMON VARIANCE
COVARIANCE
DEPENDENT VARIABLE
DESCRIPTIVE STATISTICS
DEVELOPED COUNTRIES
DEVELOPING COUNTRIES
DEVELOPMENT ECONOMICS
DEVELOPMENT POLICY
DEVELOPMENT RESEARCH
DISTRIBUTION FUNCTION
DISTRIBUTION FUNCTIONS
DISTRIBUTIONAL ASSUMPTIONS
ECONOMIC REVIEW
ECONOMICS
EMPIRICAL APPLICATION
EMPIRICAL SUPPORT
EQUATIONS
ERROR
ERROR TERM
ERROR TERMS
ESTIMATION METHOD
EXPECTED VALUE
FINITE SAMPLE
FUNCTIONAL FORM
GINI INDEX
GOODNESS-OF-FIT
HETEROSKEDASTICITY
HOUSEHOLD DATA
HOUSEHOLD INCOME
HOUSEHOLD MEMBERS
HOUSEHOLD SIZE
INCOME DATA
INCOME DISTRIBUTION
INCOME INEQUALITY
INDEPENDENT VARIABLES
INEQUALITY MEASUREMENT
INEQUALITY WILL
LINEAR FUNCTION
LINEAR MODELS
LOG INCOME
LOG LIKELIHOOD FUNCTION
LOG-LIKELIHOOD FUNCTION
MATHEMATICS
MATRIX
MAXIMUM LIKELIHOOD
MAXIMUM LIKELIHOOD ESTIMATION
MEASUREMENT ERROR
MOMENT CONDITION
MONTE CARLO SIMULATION
NON-LINEAR FUNCTION
NORMAL DENSITY
NORMAL DISTRIBUTION
OPTIMIZATION
PARAMETER VECTOR
PER CAPITA INCOME
PER CAPITA INCOMES
POINT ESTIMATES
POLICY DISCUSSIONS
POLICY RESEARCH
POVERTY ALLEVIATION
POVERTY LINE
POVERTY LINES
POVERTY RATE
POVERTY RATES
PRECISION
PREDICTION
PREDICTIONS
PROBABILITIES
PROBABILITY
PROBABILITY DENSITY
PROBABILITY DENSITY FUNCTION
PROBABILITY DISTRIBUTION
PROBABILITY DISTRIBUTION FUNCTION
PUBLIC ECONOMICS
PUBLIC GOODS
RANDOM EFFECTS
RANDOM VARIABLE
RANDOM VARIABLES
REGRESSION MODEL
SAMPLE SIZE
SKEWNESS
STANDARD DEVIATION
STANDARD ERRORS
STRUCTURAL MODEL
Online Access:http://documents.worldbank.org/curated/en/2014/07/19756129/estimation-normal-mixtures-nested-error-model-application-small-area-estimation-poverty-inequality
http://hdl.handle.net/10986/19362
Description
Summary:This paper proposes a method for estimating distribution functions that are associated with the nested errors in linear mixed models. The estimator incorporates Empirical Bayes prediction while making minimal assumptions about the shape of the error distributions. The application presented in this paper is the small area estimation of poverty and inequality, although this denotes by no means the only application. Monte-Carlo simulations show that estimates of poverty and inequality can be severely biased when the non-normality of the errors is ignored. The bias can be as high as 2 to 3 percent on a poverty rate of 20 to 30 percent. Most of this bias is resolved when using the proposed estimator. The approach is applicable to both survey-to-census and survey-to-survey prediction.

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