Design-Based Inference under Deep Domain Stratification: Language of Instruction and Private-Institution Choice in India's NSS 71st Round

Abstract

Large household surveys support precise national estimates but can become statistically fragile after repeated disaggregation by geography, sector, sex, age, and outcome category. This paper develops an auditable design-based framework for deciding how far such disaggregation can be taken in a stratified multistage survey. The framework is built around a nested contribution ledger that reconstructs each domain total through the first stage probability proportional to size expansion, the certainty-plus-random hamlet-group selection, and the second-stage household expansion. Nonlinear domain parameters are expressed as ratios of these totals and analyzed by first-order linearization. The two independent National Sample Survey subsamples then provide a natural replication variance estimator. A granularity-stability profile combines the resulting relative standard error with replicate support and concentration diagnostics, so that a detailed estimate is accompanied by evidence about whether the design can sustain it. Finite population unbiasedness of the total estimator, asymptotic validity of the ratio linearization, and unbiasedness of the two-subsample variance estimator for linearized totals are established. The method is illustrated with the 71st-round Social Consumption: Education survey, focusing on home language versus medium of instruction and reported reasons for preferring private educational institutions in India and Himachal Pradesh. The application preserves the substantive analysis in the original project while replacing ad hoc calculation with a reproducible inferential workflow.

102 pages , 24 Tables and 4 Histograms