Small Area Estimation of General Indicators in Off-Census Years

TL;DR

The paper tackles small-area estimation of general indicators when census auxiliary data are outdated by introducing the Survey Empirical Best (SEB) predictor, which leverages a larger contemporaneous unit-level survey to supply auxiliary information. Building on a two-level mixed-model framework, SEB combines a SB predictor based on the larger survey with estimated model parameters, and is designed to remain unbiased as the auxiliary sample grows, approaching the Census EB (CEB) predictor in the limit. A total MSE estimator incorporating both model and design uncertainty from the larger survey is proposed, with a parametric bootstrap to obtain naive and corrected positive MSE estimates. Through simulations and an application to Colombian poverty mapping, SEB demonstrates solid performance: it matches the nearly optimal EB when census data are current and substantially outperforms direct estimators when census data are obsolete, while providing reliable MSE assessment.

Abstract

We propose small area estimators of general indicators in off-census years, which avoid the use of deprecated census microdata, but are nearly optimal in census years. The procedure is based on replacing the obsolete census file with a larger unit-level survey that adequately covers the areas of interest and contains the values of useful auxiliary variables. However, the minimal data requirement of the proposed method is a single survey with microdata on the target variable and suitable auxiliary variables for the period of interest. We also develop an estimator of the mean squared error (MSE) that accounts for the uncertainty introduced by the large survey used to replace the census of auxiliary information. Our empirical results indicate that the proposed predictors perform clearly better than the alternative predictors when census data are outdated, and are very close to optimal ones when census data are correct. They also illustrate that the proposed total MSE estimator corrects for the bias of purely model-based MSE estimators that do not account for the large survey uncertainty.

Figures (16)

• Figure 1: Percent RB and RRMSE of DIR, FH, EB, and SEB estimators of poverty gap $F_{1,d}$ for each area $d$, with outdating parameter $\lambda = 0.2$ and $n_d'=10\,n_d$.
• Figure 2: Percent RB and RRMSE of DIR, FH, EB, and SEB estimators of poverty gap $F_{1,d}$ for each area $d$, with outdating parameter $\lambda = 0$ and $n_d'=10\,n_d$.
• Figure 3: True total MSE of the SEB predictor of poverty gap, $F_{1,d}$, and empirical expectations of $\hbox{mse}_{T,na}(\hat{\delta}_d^{SEB})$ and $\hbox{mse}_{T,cp}(\hat{\delta}_d^{SEB})$ obtained with $B=500$, for each area, for $n_d'=10\,n_d$.
• Figure 4: Normal QQ-plots of (A) predicted area effects and (B) unit-level residuals from initial model.
• Figure 5: Normal QQ-plots of (A) predicted area effects and (B) unit-level residuals from working model.

Theorems & Definitions (3)

• Proposition 1
• Proposition 2
• Proposition 3