Independence, Monotonicity, and Latent Index Models: An Equivalence Result

By E. Vytlacil. 2002

519 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8ee1e57d732d93c2b705f4d68aaf78ef38323df5

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Citations in the corpus

Extrapolate-Ing: External Validity and Overidentification in the Late Framework (2010, unknown): “IV using z as an instrument for the effect of d on y with no covariates is the Wald (1940) estimator.”
Fuzzy Differences-in-Differences (2015, background): “(Treatment participation equation) D = 1{V ≥ vGT }, with V ⊥⊥ T |G. Assumption 3 imposes a latent index model for the treatment (see, e.g., Vytlacil, 2002), where V may be interpreted as a unit’s propensity to be treated, and where the threshold for treatment participation depends both on time and…”
Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New Environments (2007, methodology): “…P(z) in the conditioning sets.197 196 To show that the monotonicity assumption implies a separable latent index model, one can follow the proofs of Vytlacil (2002) with the sole modification of replacing P(z) = Pr(D = 1 | Z = z) with Pr(D(z) = 1), where D(z) is the indicator variable for whether…”
Tolerating defiance? Local average treatment effects without monotonicity (2017, background): “Finally, to draw inference on the ATE I refer the reader to Shaikh and Vytlacil (2005). In their Theorem 7.”
Beyond LATE with a Discrete Instrument (2017, methodology): “With Z stochastically independent of (U0, U1, UD) given X, the model of equations (2) and (3) implies and is implied by the standard IV assumptions of conditional independence and monotonicity (see Vytlacil 2002; Heckman 2010).”
Program evaluation and causal inference with high-dimensional data (2013, background): “It has an equivalent formulation in terms of a simultaneous equation model with a binary endogenous variable; see Vytlacil (2002) and Heckman and Vytlacil (1999).”
Minimax regret treatment choice with covariates or with limited validity of experiments (2012, methodology): “It is essentially equivalent to imposing a threshold crossing model for selection into treatment, with treatment assignment working as an instrument (Vytlacil (2002)).”
Using Instrumental Variables for Inference About Policy Relevant Treatment Effects (2018, unknown): “Vytlacil (2002) showed that, given I.1, the assumption that the index of the selection equation is additively separable as in (2) is equivalent to the assumption that Z0 affects D monotonically in the sense introduced by Imbens and Angrist (1994).”
Program evaluation with high-dimensional data (2013, background): “See also Belloni et al. (2014a) which deals with the partially linear model in detail and thus covers this linear example as a special case.”
Understanding Instrumental Variables in Models with Essential Heterogeneity (2006, unknown): “As a consequence of Vytlacils (2002) theorem, under assumptions (A-1)-(A-5), LATE can be written as”
Beyond LATE with a discrete instrument. Heterogeneity in the quantity-quality interaction of children (2012, methodology): “Using the method of local instrumental variables (LIV), the MTE can be identi ed and estimated under the standard IV assumptions of conditional independence and monotonicity (see Vytlacil, 2002; Heckman, 2010).”
Non-Cognitive Child Outcomes and Universal High Quality Child Care (2010, unknown): “For us to identify a meaningful parameter by using IV, we need an additional assumption, monotonicity, see Angrist, Imbens, and Rubin (1996) and Vytlacil (2002).”
The microeconometric estimation of treatment effects—An overview (2006, background): “In fact, in a recent paper Vytlacil (2002) shows that the identifying assumptions for the selection model are equivalent to those invoked by Imbens and Angrist (1994) in the linear instrumental variables context.”