In this paper we examine the finite sample performance of two estimators one developed by Blundell, Chen, and Kristensen (2007) (BCK) and the other by Gagliardini and Scaillet (2007) (TIR). This paper focuses on the generalization and expansion of these estimators to a full nonparametric specification with multiple regressors. In relation to the classic weak instruments literature, we provide intuition on the examination of instruments relevance when the structural function is assumed to be unknown. Simulations indicate that both estimators perform quite well in higher dimensions. This research also provides insights on the performance of bootstrapped confidence intervals for both estimators. We document that the BCK estimator's coverage probabilities are near their nominal levels even in small samples as long as the sieve order of expansion is restricted. The coverage probability for the TIR estimator's bootstrapped confidence intervals are near their nominal levels even when the order of sieve approximation is large. These results suggest that in small samples the TIR estimator has a much smaller bias then the BCK estimator but its variance is much larger. We provide two empirical examples. One is the classic wage returns to education example and the other looks at the relationship of corruption and GDP to economic growth. Results here suggests that the impact of corruption on growth depends nonlinearly on a countries level of development.


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