Handling endogenous regressors by joint estimation using copulas

We propose a new statistical instrument-free method to tackle the endogeneity problem. The proposed method models the joint distribution of the endogenous regressor and the error term in the structural equation of interest (the structural error) using a copula method, and it makes inferences on the model parameters by maximizing the likelihood derived from the joint distribution. Similar to the "exclusion restriction" in instrumental variable methods, extant instrument-free methods require the assumption that the unobserved instruments are exogenous, a requirement that is difficult to meet. The proposed method does not require such an assumption. Other benefits of the proposed method are that it allows the modeling of discrete endogenous regressors and offers a new solution to the slope endogeneity problem. In addition to linear models, the method is applicable to the popular random coefficient logit model with either aggregate-level or individual-level data. We demonstrate the performance of the proposed method via a series of simulation studies and an empirical example.