2sCOPE-GAM: Instrument-Free Copula Approach for Endogeneity in Additive Models

Music City Center 

While causal inference is central to many empirical analyses, endogeneity often complicates it. Classical instrumental variable (IV) methods addressing endogeneity require valid instruments and often assume linear relationships between the outcome and both endogenous and exogenous regressors. However, these linearity assumptions can be restrictive for many real-world applications, leading to biased estimates when relationships are inherently nonlinear. Copula-based approaches, such as copula endogeneity correction, offer instrument-free solutions but are similarly limited by their linearity assumptions. This paper introduces a flexible two-stage Copula Generalized Additive Model (2sCOPE-GAM) to address endogeneity without instruments while accommodating nonlinear relationships. Expressly, 2sCOPE-GAM assumes a linear relationship between the outcome and the endogenous regressor while allowing nonlinear relationships between the outcome and exogenous regressor through GAM. Through theoretical development, simulation and empirical data, we demonstrate the efficacy of our approach in accurately estimating causal effects in the presence of endogeneity and nonlinear relationships.

Endogeneity

Copula

2 stage estimation

Generalized additive model 

Health Policy Statistics Section