Sebastian Juhl

Most instrumental variable analyses (IVs) employ a Two-Stage-Least-Squares (2SLS) estimator, whereby the predicted values of the instrumented variable (X_i) are generated by a linear regression of X_i on the instrument(s) Z_i. Theory often dictates monotone but not necessarily linear relationships, hence the effect of Z_i on X_i may not be properly depicted by a linear specification. We propose a way of increasing instrument strength and thus boosting efficiency in the first stage of IV estimation. In particular we show that the predicted values obtained from a series of local non-parametric smoothing techniques are better suited to capture this effect. Monte Carlo evidence suggests that non-parametric first-stage improves efficiency without violating the orthogonality of the errors guaranteed by the OLS. Bootstrapping can account for the uncertainty of the second-level estimates. We demonstrate the usefulness of the method with three empirical applications from development economics, international political economy and political psychology.