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Empirical best prediction of poverty indicators via nested error regression with high dimensional parameters

Yuting Chen, Partha Lahiri, Nicola Salvati

Abstract

The Nested Error Regression Model with High-Dimensional Parameters (NERHDP) is extended to address challenges in small area poverty estimation. A robust and flexible framework is proposed to derive empirical best predictors (EBPs) of small area poverty indicators while accommodating heterogeneity in regression coefficients and sampling variances across areas. To mitigate the computational limitations of the existing algorithm, an efficient estimation procedure is introduced, substantially reducing computation time and enhancing scalability for large datasets. A novel approach for generating area-specific poverty estimates in out-of-sample areas is also developed, improving the reliability of synthetic estimates. Uncertainty is quantified through a parametric bootstrap method specifically tailored to the extended model. Under heterogeneous data-generating scenarios, the proposed method yields lower relative bias and relative root mean squared prediction error than existing approaches. The methodology is further illustrated using data from the 2002 Albania Living Standards Measurement Survey, combined with auxiliary information from the 2001 census, to estimate poverty indicators for 374 municipalities.

Empirical best prediction of poverty indicators via nested error regression with high dimensional parameters

Abstract

The Nested Error Regression Model with High-Dimensional Parameters (NERHDP) is extended to address challenges in small area poverty estimation. A robust and flexible framework is proposed to derive empirical best predictors (EBPs) of small area poverty indicators while accommodating heterogeneity in regression coefficients and sampling variances across areas. To mitigate the computational limitations of the existing algorithm, an efficient estimation procedure is introduced, substantially reducing computation time and enhancing scalability for large datasets. A novel approach for generating area-specific poverty estimates in out-of-sample areas is also developed, improving the reliability of synthetic estimates. Uncertainty is quantified through a parametric bootstrap method specifically tailored to the extended model. Under heterogeneous data-generating scenarios, the proposed method yields lower relative bias and relative root mean squared prediction error than existing approaches. The methodology is further illustrated using data from the 2002 Albania Living Standards Measurement Survey, combined with auxiliary information from the 2001 census, to estimate poverty indicators for 374 municipalities.

Paper Structure

This paper contains 12 sections, 42 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. A review of Empirical Best Prediction for FGT measures
  3. The LSMS and Census data
  4. Nested error regression model with high dimensional parameters
  5. Estimation of the high dimensional parameters
  6. Definition and estimation of tuning parameter $\tau_i$
  7. Uncertainty measures
  8. Model-based Monte Carlo simulations
  9. Model-based simulation I
  10. Model-based simulation II
  11. Application: poverty mapping for Albania
  12. Discussion

Figures (8)

  • Figure 1: Bar chart of average percent estimated coefficient of variation of direct estimates for HCR and PG versus within-area sample size for all sampled municipalities.
  • Figure 2: Histograms of percent estimated coefficient of variation of direct estimates for HCR and PG for all sampled municipalities using 2002 LSMS data.
  • Figure 3: Box-plots displaying ratios of estimates of regression coefficients and area specific sampling variances to their corresponding true values under repeated sampling in our model-based simulation experiment.
  • Figure 4: Distributions of estimated regression coefficients fitted for each of the 213 municipalities of Albania.
  • Figure 5: Distributions of the standardized residuals by municipality.
  • ...and 3 more figures