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 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.

Bibliographic Details

Main Authors:	Elbers, Chris, van der Weide, Roy
Language:	English en_US
Published:	World Bank Group, Washington, DC 2014-07
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 https://hdl.handle.net/10986/19362
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