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

33 Pages Posted: 20 Apr 2016

See all articles by Chris Elbers

Chris Elbers

Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute - Tinbergen Institute Amsterdam (TIA)

Roy van der Weide

World Bank; World Bank - Development Research Group (DECRG)

Date Written: July 1, 2014

Abstract

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.

Keywords: Inequality

Suggested Citation

Elbers, Chris and van der Weide, Roy, Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality (July 1, 2014). World Bank Policy Research Working Paper No. 6962. Available at SSRN: https://ssrn.com/abstract=2461940

Chris Elbers (Contact Author)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Tinbergen Institute - Tinbergen Institute Amsterdam (TIA) ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Roy Van der Weide

World Bank ( email )

1818 H Street, N.W.
Washington, DC 20433
United States

World Bank - Development Research Group (DECRG)

1818 H. Street, N.W.
MSN3-311
Washington, DC 20433
United States

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