|
Abstract:
|
Researchers often use instrumental variables (IV) techniques to estimate causal effects in non-experimental settings. When a single instrument is available, such estimation typically assumes that the treatment variable has a linear effect on the outcome of interest, which can lead to misleading conclusions when the effect is in fact nonlinear. We consider the task of estimating the nonlinear effect of a discrete endogenous regressor when a single instrumental variable is available. When the instrument takes on at least as many values as the endogenous regressor, the level-specific effects are generally identified and could in principle be estimated with a generalized method of moments estimator. However, the finite sample performance of this estimator is typically quite poor. We suggest a regularization scheme that increases precision by biasing the estimated causal response function towards the one implied by the linear IV estimator. We use simulations to show that this can achieve a useful approximation of nonlinear effects in situations where alternative estimators do not. Finally, we discuss inference and choice of the regularization parameter.
|
