Using matching, instrumental variables and control functions to estimate economic choice models

This paper investigates four topics. (1) It examines the different roles played by the propensity score (probabilitiy of selection) in matching, instrumental variable and control functions methods. (2) It contrasts the roles of exclusion restrictions in matching and selection models. (3) It characterizes the sensivity of matching to the choice of conditioning variables and demonstrates the greater robustness of control function methods to misspecification of the conditioning variables. (4) It demonstrates the problem of choosing the conditioning variables in matching and the failure of conventional model selection criteria when candidate conditioning variables are not exogenous.