Data collection, weighting, and modeling techniques to estimate consistent population parameters

Empirical research studies regularly encounter sampling-related challenges that can impact the validity and reliability of model estimation results. This paper presents a comprehensive examination of the implications of nonrandom sampling for estimator consistency and asymptotic efficiency. Through theoretical and simulation-backed support, we underscore the importance of adopting appropriate sampling and estimation methods in two broad scenarios. First, we demonstrate that achieving range variation in exogenous variables, rather than strict population representativeness, is crucial for estimating individual-level causal relationships when sampling is based only on observed exogenous variables. Second, we investigate the efficacy of weighting approaches when sampling is endogenous and use a joint modeling approach to accommodate unobserved self-selection effects where traditional weighting approaches prove inadequate. Our proposed approach accommodates unobserved correlations and successfully recovers true population parameters when the joint distribution of exogenous variables in the population is known. The methodology also shows improved performance compared to existing methods even when only the population marginal distribution of exogenous variables is available. Notably, our simulation experiments extend beyond the conventional linear regression framework to include binary outcomes, providing crucial insights for nonlinear choice modeling applications. The findings underscore the importance of carefully considering sampling mechanisms and their implications for model estimation, while offering practical guidance for researchers facing various sampling-related challenges in empirical studies.