Browsing by Subject "Treatment effects"

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Essays on Causal Inference with Endogeneity and Missing Data
(2017-05) Feng, Qian, Ph. D.; Donald, Stephen G.; Abrevaya, Jason; Xu, Haiqing; Carvalho, Carlos M.
This dissertation strives to devise novel yet easy-to-implement estima- tion and inference procedures for economists to solve complicated real world problems. It provides by far the most optimal solutions in situations when sample selection is entangled with missing data problems and when treatment effects are heterogenous but instruments only have limited variations. In the first chapter, we investigate the problem of missing instruments and create the generated instrument approach to address it. Specifically, When the missingness of instruments is endogenous, dropping observations can cause biased estimation. This chapter proposes a methodology which uses all the data to do instrumental variables (IV) estimation. The methodology provides consistent estimation with endogenous missingness of instruments. It firstly forms a generated instrument for every observation in the data sample that: a) for observations without instruments, the new instrument is an imputation; b) for observations with instruments, the new instrument is an inverse propensity score weighted combination of the original instrument and an imputation. The estimation then proceeds by using the generated instruments. Asymptotic theorems are established. The new estimator attains the semiparametric efficiency bound. It is also less biased compared to existing procedures in the simulations. As an illustrative example, we use the NLSYM data set in which IQ scores are partially missing, and demonstrate that by adopting the new methodology the return to education is larger and more precisely estimated compared to standard complete case methods. In the second chapter, we provide Lasso-type of procedures for reduced form regression with many missing instruments. The methodology takes two steps. In the first step, we generate a rich instrument set from the many missing instruments and other observed data. In the second step, IV estimation is conduced based on the generated instrument set. Specifically, the (very) many generated instruments are used to approximate a “pseudo” optimal instrument in the reduced form regression. The approach has been shown to have efficiency gains compared to the generated instrument estimator developed in the first chapter. We also compare the finite sample behavior of the new estimator with other Lasso estimator and demonstrate the good performance of the proposed estimator in the Monte Carlo experiments. The third chapter estimates individual treatment effects in a triangular model with binary–valued endogenous treatments. This chapter is based on the previous joint work with Quang Vuong and Haiqing Xu. Following the identification strategy established in (Vuong and Xu, forthcoming), we propose a two-stage estimation approach. First, we estimate the counterfactual outcome and hence the individual treatment effect (ITE) for every observational unit in the sample. Second, we estimate the density of individual treatment effects in the population. Our estimation method does not suffer from the ill-posed inverse problem associated with inverting a non–linear functional. Asymptotic properties of the proposed method are established. We study its finite sample properties in Monte Carlo experiments. We also illustrate our approach with an empirical application assessing the effects of 401(k) retirement programs on personal savings. Our results show that there exists a small but statistically significant proportion of individuals who experience negative effects, although the majority of ITEs is positive.
Essays on causal mediation analysis
(2024-05) Lee, Jung Hyub; Abrevaya, Jason; Brendan Kline; Shakeeb Khan; Haiqing Xu
This dissertation consists of three chapters on causal mediation analysis. The first two chapters propose new estimation approaches for direct and indirect effects in a semiparametric model, and the third chapter studies regression discontinuity design that incorporates indirect effects. In the first chapter, we consider a unifying framework to test for direct and indirect treatment effects in nonlinear models. Specifically, we extend a generalized linear-index model to incorporate endogenous treatments and endogenous mediators. We propose a kernel-weighted Kendall's tau statistics, which is a nonparametric rank correlation estimator, to test the significance of the direct and indirect effects of endogenous treatments on the outcome variable mediated by endogenous mediators. The proposed semiparametric model allows for treatments and mediators to be discrete, continuous, or neither of these two (e.g., censored or truncated). For the indirect effect, we construct two distinct kernel-weighted Kendall's tau statistics that capture the effect of (i) the treatment on the mediator, and (ii) the mediator on the outcome. In the second chapter, we address the issue of testing indirect effects in the generalized regression model. Also, we suggest Monte Carlo simulation results and empirical results using the new method. Unfortunately, standard joint hypothesis tests using these statistics are severely under-sized, a problem that has been noted for linear causal mediation models. To address the problem, we apply a new testing method (van Garderen and van Giersbergen (2020)) that has correct size. As an empirical illustration, we assess the effect of education level on social functioning mediated by individual income, using the British Household Panel Survey data. In the third chapter, we suggest a sharp regression discontinuity model that allows an indirect effect from the intermediate characteristics. These characteristics are determined by the treatment status and random type of each individual. We analyze RD treatment effect represented as a weighted average form and the mean expected outcome at the cutoff in the presence of intermediate characteristics. Especially, we derive bounds on the treatment effect under inequality restrictions on expected outcomes conditioned on the intermediate characteristics. Finally, we suggest a simple extension of the estimation method that incorporates the indirect effect based on local linear regression. Monte Carlo experiments validate the finite sample performance of the suggested estimation method.
Using multisite instrumental variables to estimate treatment effects and treatment effect heterogeneity
(2020-04-29) Runyon, Christopher Ryan; Pustejovsky, James E.; Beretvas, Susan N; Sales, Adam C; Whittaker, Tiffany A
Multisite randomized trials (MSTs) are an attractive research design to test the efficacy of an educational program at scale. Population models examining data from MSTs can provide information on the range of possible treatment effects that sites (such as schools) can expect from an educational program, even for those sites not included in the study. However, when some individuals at a site do not comply with their treatment assignment, conventional multilevel and meta-analytic estimation methods do not provide information on the effect of actually participating in the educational program. Instrumental variables (IV) is a method that can produce consistent estimates of the causal effect of participating in an educational program for those individuals that comply with their treatment assignment, an estimand called the complier-average treatment effect (CATE). IV methods for single-site trials are well understood and widely-used. Recently multisite IV models have been proposed to estimate the CATE and CATE heterogeneity across a population of sites, but the performance of these estimators has not been examined in a simulation study. Using Monte Carlo simulation, the current study examines the performance of three IV estimators and two conventional estimators in recovering the CATE and CATE heterogeneity under simulation conditions that resemble multisite trials of well-known educational programs.