Linearity In Instrumental Variables Estimation: Problems And Solutions
The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant across all margins. This paper investigates the problems caused by the linearity restriction in IV estimation, and discusses possible remedies. The authors first examine the biases due to nonlinearity in the commonly used tests for non-zero treatment effects, selection bias, and instrument validity. Next, they consider three applications where theory suggests a nonlinear relationship, yet previous research has used linear IV estimators.