OLS and 2SLS in Randomized and Conditionally Randomized Experiments

2018 ◽  
Vol 238 (3-4) ◽  
pp. 243-293 ◽  
Author(s):  
Jason Ansel ◽  
Han Hong ◽  
and Jessie Li
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Randomized Experiments ◽  
Adaptive Randomization ◽  
Working Paper ◽  
Average Treatment ◽  
Local Average Treatment Effect ◽  
Effect Parameter ◽  
Multiple Treatments ◽  
Local Average

Abstract We investigate estimation and inference of the (local) average treatment effect parameter when a binary instrumental variable is generated by a randomized or conditionally randomized experiment. Under i.i.d. sampling, we show that adding covariates and their interactions with the instrument will weakly improve estimation precision of the (local) average treatment effect, but the robust OLS (2SLS) standard errors will no longer be valid. We provide an analytic correction that is easy to implement and demonstrate through Monte Carlo simulations and an empirical application the interacted estimator’s efficiency gains over the unadjusted estimator and the uninteracted covariate adjusted estimator. We also generalize our results to covariate adaptive randomization where the treatment assignment is not i.i.d., thus extending the recent contributions of Bugni, F., I.A. Canay, A.M. Shaikh (2017a), Inference Under Covariate-Adaptive Randomization. Working Paper and Bugni, F., I.A. Canay, A.M. Shaikh (2017b), Inference Under Covariate-Adaptive Randomization with Multiple Treatments. Working Paper to allow for the case of non-compliance.

scholarly journals Instrumental variable estimation of truncated local average treatment effects

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249642
Author(s):  
Byeong Yeob Choi
Keyword(s):  
Treatment Effect ◽  
Instrumental Variable ◽  
Propensity Scores ◽  
Real Data ◽  
Target Population ◽  
Average Treatment Effect ◽  
Average Treatment ◽  
Local Average Treatment Effect ◽  
Local Average Treatment Effects ◽  
Local Average

Instrumental variable (IV) analysis is used to address unmeasured confounding when comparing two nonrandomized treatment groups. The local average treatment effect (LATE) is a causal estimand that can be identified by an IV. The LATE approach is appealing because its identification relies on weaker assumptions than those in other IV approaches requiring a homogeneous treatment effect assumption. If the instrument is confounded by some covariates, then one can use a weighting estimator, for which the outcome and treatment are weighted by instrumental propensity scores. The weighting estimator for the LATE has a large variance when the IV is weak and the target population, i.e., the compliers, is relatively small. We propose a truncated LATE that can be estimated more reliably than the regular LATE in the presence of a weak IV. In our approach, subjects who contribute substantially to the weak IV are identified by their probabilities of being compliers, and they are removed based on a pre-specified threshold. We discuss interpretation of the proposed estimand and related inference method. Simulation and real data experiments demonstrate that the proposed truncated LATE can be estimated more precisely than the standard LATE.

scholarly journals Instruments with Heterogeneous Effects: Bias, Monotonicity, and Localness

2020 ◽  
Vol 8 (1) ◽  
pp. 182-208
Author(s):  
Nick Huntington-Klein
Keyword(s):  
Treatment Effect ◽  
Treatment Effects ◽  
Weighted Average ◽  
Small Sample ◽  
Average Treatment Effect ◽  
Average Treatment ◽  
Local Average Treatment Effect ◽  
Heterogeneous Effects ◽  
The Impact ◽  
Local Average

AbstractIn Instrumental Variables (IV) estimation, the effect of an instrument on an endogenous variable may vary across the sample. In this case, IV produces a local average treatment effect (LATE), and if monotonicity does not hold, then no effect of interest is identified. In this paper, I calculate the weighted average of treatment effects that is identified under general first-stage effect heterogeneity, which is generally not the average treatment effect among those affected by the instrument. I then describe a simple set of data-driven approaches to modeling variation in the effect of the instrument. These approaches identify a Super-Local Average Treatment Effect (SLATE) that weights treatment effects by the corresponding instrument effect more heavily than LATE. Even when first-stage heterogeneity is poorly modeled, these approaches considerably reduce the impact of small-sample bias compared to standard IV and unbiased weak-instrument IV methods, and can also make results more robust to violations of monotonicity. In application to a published study with a strong instrument, the preferred approach reduces error by about 19% in small (N ≈ 1, 000) subsamples, and by about 13% in larger (N ≈ 33, 000) subsamples.

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