GMM Based Inference with Standard Stratified Samples when the Aggregate Shares are Known

We show how to do efficient moment based inference using the generalized method of moments (GMM) when data is collected by standard stratified sampling and the maintained assumption is that the aggregate shares are known.

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.