Nonparametric IV Estimation of Local Average Treatment Effects with Covariates

By Markus Frölich. Social Science Research Network, 2007

283 citations recorded by the source corpus.

In this paper nonparametric instrumental variable estimation of local average treatment effects (LATE) is extended to incorporate confounding covariates. Estimation of local average treatment effects is appealing since their identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models. Including covariates in the estimation of LATE is necessary when the instrumental variable itself is endogenous (e.g. when the instrument is self-selected). However, all previous approaches to handle covariates in the estimation of LATE rely on parametric or semiparametric methods. In this paper, a nonparametric estimator for the estimation of LATE with covariates is suggested that is root-n asymptotically normal and efficient.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6115e5d44eeb949938f14c9136371e7eb83a66bd

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Citations in the corpus

Unconditional Quantile Treatment Effects Under Endogeneity (2007, unknown): “When the conditional distribution is estimated by local regression or by nearest neighbor regression, we obtain the estimator proposed, for example, in Frölich (2007b).”
Including Covariates in the Regression Discontinuity Design (2018, background): “Suggested Citation: Frölich, Markus; Huber, Martin (2017) : Including Covariates in the Regression Discontinuity Design, IZA Discussion Papers, No.”
Interpretable Almost Matching Exactly With Instrumental Variables (2019, methodology): “…include Bayesian methods (Imbens and Rubin, 1997), semiparametric methods (Abadie, 2003; Tan, 2006; Ogburn et al., 2015), nonparametric methods (Frölich, 2007) and deep learning methods (Hartford et al., 2017), but these methods do not enjoy the benefits of interpretability that matching…”
Nonparametric Tests for Treatment Effect Heterogeneity With Duration Outcomes (2016, unknown): “Assume that (i) (Y (0) , Y (1)) ⊥ (C (0) , C (1))| T, Z; and (ii) for t ∈ {0, 1}, P(Y (t) ≤ C (t) |X, T, Z, Y (t)) = P(Y (t) ≤ C (t) | T, Z, Y (t) ) a.s. Assumption 4.1 is standard in the literature (see, e.g., Abadie 2002, 2003; Frölich 2007).”
Tolerating defiance? Local average treatment effects without monotonicity (2017, methodology): “[368, 369, 384, 385] Angrist, J. D. and I. Fernandez-Val (2013), “ExtrapoLATE-ing: External validity and overidentification in the LATE framework.””
Partial Identification of Local Average Treatment Effects With an Invalid Instrument (2013, background): “One could combine the ideas herein with work allowing estimation of LATE when the instrument is assumed to be random conditional on a set of covariates (Hirano et al. 2000; Abadie 2003; Frölich 2007).”
Racial Bias in Bail Decisions ⇤ (2018, unknown): “[32] Frölich, Markus, “Nonparametric IV Estimation of Local Average Treatment Effects with Covariates,” Journal of Econometrics, 139 (2007), 35-75.”
Instrumental Variable Estimation of the Causal Effect of Hunger Early in Life on Health Later in Life (2016, methodology): “This estimator has first been proposed by Frölich (2007). He shows that equation (4) can be derived from the more intuitive (but not identified) expression ∫ E[Y |X=x,Z=1]−E[Y |X=x,Z=0] E[D|X=x,Z=1]−E[D|X=x,Z=0]dFX|DZ=1>DZ=0 , using Bayes’ theorem.”
Matching and semi-parametric IV estimation, a distance-based measure of migration, and the wages of young men (2011, methodology): “Frölich (2007) shows that propensity score based estimators 36 Note that for our matching estimator, the key identifying restriction only involves the potential outcome in the absence of treatment.”
Education and social capital: empirical evidence from microeconomic analyses (2010, methodology): “Recently there have been efforts to introduce covariates in LATE estimation because instruments may require conditioning on a set of covariates to be valid (e.g. Hirano et al, 2000; Abadie, 2003; Froelich, 2007).”
Estimating Conditional Average Treatment Effects (2014, methodology): “The following IV framework, augmented by covariates, is now standard in the treatment effect literature; see, for example, Abadie (2003), Frolich (2007), Hong and Nekipelov (2010), and Donald, Hsu, and Lieli (2014a).”
Direct and indirect treatment effects–causal chains and mediation analysis with instrumental variables (2014, methodology): “For ease of exposition, we assume Z1 to be binary, albeit the discussion could be extended to multi-valued instruments with bounded support as in Frölich (2007). Z2 denotes the instrument for mediator M , referred to as the second instrument hereafter, and for most of the paper it is assumed to be c”
ESTIMATION IN AN INSTRUMENTAL VARIABLES MODEL WITH TREATMENT EFFECT HETEROGENEITY (2012, methodology): “…which replaces π2 and ψ2 in (4) by their least-squares estimates, leading to P̂ = HZ⊥T; • The bias-corrected two-stage least squares estimator (Nagar, 1959; Donald and Newey, 2001), which adjusts the tsls propensity score estimator to P̂ = ((1− k)MW + kHZ⊥)T to improve its finite-sample…”
The Effect of Grandparental Support on Mothers’ Labour Market Participation: An Instrumental Variable Approach (2014, unknown): “If covariates need to be accommodated to make the assumptions more plausible, as in our case, we can think of Angrist et al. (1996) results as applying within cells defined by covariates values (Frölich, 2007).”
DOUBLY ROBUST INSTRUMENTAL VARIABLE REGRESSION (2012, methodology): “Frölich (2007) obtains some of the results of Tan (2006b) and develops a nonparametric analogue of Robinson’s semiparametric IV regression, called the nonparametric IV matching estimator, that involves nonparametric estimation of E(Yi|Xi, Zi) and E(Wi|Xi, Zi); the nonparametric IV matching…”