Philip Shaw, Michael Andrew Cohen, Tao Chen
November 18, 2015

### Abstract

This paper investigates recent developments in the literature on nonparametric instrumental variables estimation and considers the practical importance of the features of these estimators in the context of typically applied econometric models. Our primary focus is on the estimation of econometric models with endogenous regressors, and their marginal effects, without a known functional form. We develop an estimator for the marginal effects and investigate its finite sample performance. We show that when instruments are weak, in the classic sense, the nonparametric estimates of the marginal effect outperforms the classic two-stage least squares estimator, even when the model is correctly specified. When the instruments are strong, we show that the nonparametric estimator for the partial effects is still effective compared to the two-stage least squares estimator even as the number of IVs increases. We also investigate bandwidth choice and find that a rule-of-thumb bandwidth performs relatively well. Whereas cross-validation leads to a better fit when the number of instruments is small, as the number of instruments increases the rule-of-thumb standard actually results in better model fit. In an empirical application we estimate the work-horse aggregate logit demand model, discuss the required nonparametric identification properties, and document the differences between nonparametric and parametric specifications on the estimation of demand elasticities.