This paper develops asymptotic F tests robust to weak identi…cation and temporal dependence. The test statistics are modi…ed versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005), both of which are based on the continuous updating generalized method of moments. In the former case, the modi…cation involves only a multiplicative degree-of-freedom adjustment. In the latter case, the modi…cation involves an additional multiplicative adjustment that uses a J statistic for testing overidenti…cation. By adopting …xed-smoothing asymptotics, we show that both the modi…ed S statistic and the modi…ed K statistic are asymptotically F-distributed. The asymptotic F theory accounts for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the asymptotic chi-squared theory ignores. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in …nite samples.

This paper studies the implication of a fraction of the population not responding to the instrument when selecting into treatment. We show that, in general, the presence of nonresponders biases the Marginal Treatment Effect (MTE) curve and many of its functionals. Yet, we show that, when the propensity score is fully supported on the unit interval, it is still possible to restore identification of the MTE curve and its functionals with an appropriate re-weighting.

This paper studies the identification and estimation of unconditional policy effects when the treatment is binary and endogenous. We first characterize the asymptotic bias of the unconditional regression estimator that ignores the endogeneity and elaborate on the channels that the endogeneity can render the unconditional regressor estimator inconsistent. We show that even if the treatment status is exogenous, the unconditional regression estimator can still be inconsistent when there are common covariates affecting both the treatment status and the outcome variable. We introduce a new class of marginal treatment effects (MTE) based on the influence function of the functional underlying the policy target. We show that an unconditional policy effect can be represented as a weighted average of the newly defined MTEs over the individuals at the margin of indifference. Point identification is achieved using the local instrumental variable approach. Furthermore, the unconditional policy effects are shown to include the marginal policy-relevant treatment effect in the literature as a special case. Methods of estimation and inference for the unconditional policy effects are provided. In the empirical application, we estimate the effect of changing college enrollment status, induced by higher tuition subsidy, on the quantiles of the wage distribution.