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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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

id	okr-10986-19362
recordtype	oai_dc
spelling	okr-10986-193622021-04-23T14:03:51Z Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality Elbers, Chris van der Weide, Roy 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 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. 2014-08-15T16:15:22Z 2014-08-15T16:15:22Z 2014-07 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 English en_US Policy Research Working Paper;No. 6962 CC BY 3.0 IGO http://creativecommons.org/licenses/by/3.0/igo/ World Bank Group, Washington, DC Publications & Research :: Policy Research Working Paper Publications & Research
repository_type	Digital Repository
institution_category	Foreign Institution
institution	Digital Repositories
building	World Bank Open Knowledge Repository
collection	World Bank
language	English en_US
topic	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
spellingShingle	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 Elbers, Chris van der Weide, Roy Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
relation	Policy Research Working Paper;No. 6962
description	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.
format	Publications & Research :: Policy Research Working Paper
author	Elbers, Chris van der Weide, Roy
author_facet	Elbers, Chris van der Weide, Roy
author_sort	Elbers, Chris
title	Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
title_short	Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
title_full	Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
title_fullStr	Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
title_full_unstemmed	Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
title_sort	estimation of normal mixtures in a nested error model with an application to small area estimation of poverty and inequality
publisher	World Bank Group, Washington, DC
publishDate	2014
url	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
_version_	1764443716437671936

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

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