Regression analysis using survey data with endogenous design

This paper discusses the influence of the sampling design on the estimation of a linear regression model. Particularly, sampling designs will be discussed which are dependent on the values of the endogenous variable in the population: endogenous (or “informative”) designs. A consistent estimator of the regression coefficients is given. Its variance is the sum of a sampling design component and a disturbance term component. Also, model-free regression is briefly discussed. The model-free regression estimator is the same as the model estimator in the case of an endogenous design.