Estimating Marginal Treatment Effects using Parametric and Semiparametric Methods

Abstract

We describe the new command margte, which computes marginal and average treatment effects for a model with a binary treatment and a continuous outcome given selection on unobservables and returns. Marginal treatment effects differ from average treatment effects in instances where the impact of treatment varies within a population in correlation with unobserved characteristics. Both parametric and semiparametric estimation methods can be used with margte, and we provide evidence from a Monte Carlo simulation for when each is preferable.

Do Cellmates Matter? A Causal Test of the Schools of Crime Hypothesis With Implications for Differential Association and Deterrence Theories

“…At supported propensity scores, marginal prison peer effects can be estimated via local linear regression. With full support, an average prison peer effect can be calculated by integrating over the marginal prison peer effects (Brave and Walstrum, 2014;Heckman, Urzúa, and Vytlacil, 2006;Rosenbaum and Rubin, 1983).…”

“…To clarify the essential heterogeneity problem in the context of the schools of crime hypothesis, we develop a prison peer effect model based on the potential outcomes framework, which we follow Brave and Walstrum (2014) in depicting as regression equations. For a detailed econometric account of essential heterogeneity, please see Heckman, Urzúa, and Vytlacil (2006).…”

The heterogeneous causal effects of neonatal care: a model of endogenous demand for multiple treatment options based on geographical access to care

“…MTEs are estimated semi-parametrically (Brave & Walstrum, 2014;Heckman & Vytlacil, 1999) and plotted relative to p. We estimate alternative MTEs under the parametric probit treatment choice model with propensity score derived from the cumulative normal distribution function and K Y (p) in 6 replaced by the expression -(σ 1 ρ 1 -σ 0 ρ 0 )φ where σ j ρ j is the covariance of potential outcome with NICU (j=1) or non-NICU (j=0) and the φ the standard normal density function value for the linear index of covariates X and instrumental variables (Appendix 3). We tested for the existence of unobserved selection by prognosis (H0: ρ 1 = 0 in the parametric probit treatment model), where infants who have worse unobserved prognosis may be more likely to be born in NICU than infants with better prognosis, and selection by returns (H0: ∂K Y (p)/∂p = 0 in 7 or σ 1 ρ 1 -σ 0 ρ 0 = 0 in the parametric probit model (Heckman, Urzua, & Vitlacyl, 2006), where infants with unobserved characteristics predisposing them to benefit more from treatment are more likely to be born in NICU (Appendix 3).…”

“…where the Greek symbols now represent parameters to be estimated for the two outcome equations, one parameter set for the potential outcome under NICU (δ Y1 ) and another for the potential outcome under non-NICU care (δ Y0 ) (Rubin, 2005). The MTE is the derivative of the expected outcome EY with respect to p (Brave & Walstrum, 2014),…”

Dynamic corporate risk management: Motivations and real implications

“…In our application, estimation of the parameters follows the parametric method proposed by Brave and Walstrum (2014) by using the MARGTE command (See also Heckman, Urzua, and Vytlacil (2006b) � ( = , = ) = 1 + � − 0 � + � 1 � + 0 � � ′ + ( � 1 − � 0 )Φ −1 ( ).…”