Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment

We revisit the problem of estimating the local average treatment effect (LATE) and the local average treatment effect on the treated (LATT) when control variables are available, either to render the instrumental variable (IV) suitably exogenous or to improve precision. Unlike previous approaches, our doubly robust (DR) estimation procedures use quasi-likelihood methods weighted by the inverse of the IV propensity score - so-called inverse probability weighted regression adjustment (IPWRA) estimators. By properly choosing models for the propensity score and outcome models, fitted values are ensured to be in the logical range determined by the response variable, producing DR estimators of LATE and LATT with appealing small sample properties. Inference is relatively straightforward both analytically and using the nonparametric bootstrap. Our DR LATE and DR LATT estimators work well in simulations. We also propose a DR version of the Hausman test that compares different estimates of the average treatment effect on the treated (ATT) under one-sided noncompliance

Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect

In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie (2003)'s kappa theorem. Our framework presumes a binary endogenous explanatory variable ("treatment") and a binary instrumental variable, which may only be valid after conditioning on additional covariates. We argue that one of the Abadie estimators, which we show is weight normalized, is likely to dominate the others in many contexts. A notable exception is in settings with one-sided noncompliance, where certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. We use a simulation study and three empirical applications to illustrate our findings. In applications to causal effects of college education using the college proximity instrument (Card, 1995) and causal effects of childbearing using the sibling sex composition instrument (Angrist and Evans, 1998), the unnormalized estimates are clearly unreasonable, with "incorrect" signs, magnitudes, or both. Overall, our results suggest that (i) the relative performance of different kappa weighting estimators varies with features of the data-generating process; and that (ii) the normalized version of Tan (2006)'s estimator may be an attractive alternative in many contexts. Applied researchers with access to a binary instrumental variable should also consider covariate balancing or doubly robust estimators of the LATE

Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects

We show that when the propensity score is estimated using a suitable covariate balancing procedure, the commonly used inverse probability weighting (IPW) estimator, augmented inverse probability weighting (AIPW) with linear conditional mean, and inverse probability weighted regression adjustment (IPWRA) with linear conditional mean are all numerically the same for estimating the average treatment effect (ATE) or the average treatment effect on the treated (ATT). Further, suitably chosen covariate balancing weights are automatically normalized, which means that normalized and unnormalized versions of IPW and AIPW are identical. For estimating the ATE, the weights that achieve the algebraic equivalence of IPW, AIPW, and IPWRA are based on propensity scores estimated using the inverse probability tilting (IPT) method of Graham, Pinto and Egel (2012). For the ATT, the weights are obtained using the covariate balancing propensity score (CBPS) method developed in Imai and Ratkovic (2014). These equivalences also make covariate balancing methods attractive when the treatment is confounded and one is interested in the local average treatment effect

How distinctive is the Foreign Language Enjoyment and Foreign Language Classroom Anxiety of Kazakh learners of Turkish?

The present study focuses on foreign language enjoyment (FLE) and foreign language classroom anxiety (FLCA) of 592 learners of Turkish as a foreign language (FL) in Kazakhstan. Mean levels of FLE and FLCA were found to be similar to previous studies in different settings with different target languages. In contrast with previous literature, a weak positive correlation was found between FLE and FLCA and the gender effect went in the opposite direction, with male participants reporting more FLCA than female participants. Multiple regression analyses revealed that FLE and FLCA were more strongly predicted by learners’ attitude toward Turkish and teacher-related variables than by learner-internal variables, confirming previous research outside Kazakhstan. Attitude toward the FL, teacher’s friendliness, strictness and frequency of use of the FL, attitude toward the teacher, participant’s age and FL exam result explained a total of 25% of variance in FLE. Differing slightly from previous studies, FLCA was found to be only weakly predicted (6% of variance) by some learner-internal variables (FL exam result, attitude toward the FL) as well as teacher-centred variables (friendliness, strictness). The findings suggest that variation in FLE and FLCA among Kazakh learners of Turkish is quite similar to that established in other contexts

Doubly Robust Estimation of Causal Effects with Multivalued Treatments

Abstract: This paper provides doubly robust estimators for treatment effect parameters which are defined in multivalued treatment effect framework. We apply this method on a unique data set of British Cohort Study (BCS) to estimate returns to different levels of schooling. Average returns are estimated for entire population, as well as conditional on having a specific educational achievement. The analysis is carried out for female and male samples separately to capture possible gender differences. The results indicate that, on average, the percentage wage gain due to higher education versus any other lower educational attainment is higher for highly educated females than highly educated males.