Estimation of Dose-Response Functions and Optimal Doses with a Continuous Treatment

This paper considers the continuous-treatment case and develops nonparametric estimators for the average dose-response function, the treatment level at which this function is maximized (location of the maximum), and the maximum value achieved by this function (size of the maximum). These parameters are identified by assuming that selection into different levels of the treatment is based on observed characteristics. The proposed nonparametric estimators of the location and size of the optimal dose are shown to be jointly asymptotically normal and uncorrelated. More generally, these estimators can be used to estimate the location and size of the maximum of a partial mean (Newey, 1994). To illustrate the utility of our approach, the techniques developed in the paper are used to estimate the turning point of the environmental Kuznets curve (EKC) for NOx, that is, the level of per capita income at which the emissions of NOx reach their peak and start decreasing. Finally, a Monte Carlo exercise is performed partly based on the data used in the empirical application. The results show that the nonparametric estimators of the location and size of the optimal dose developed in this paper work well in practice (especially when compared to a parametric model), in some cases even for relatively small sample sizes.Continuous Treatment, Nonparametric Estimation, Partial Means, Location and Size of the Maximum, Environmental Kuznets Curve

Partial Identification of Local Average Treatment Effects with an Invalid Instrument

We derive nonparametric bounds for local average treatment effects without requiring the exclusion restriction assumption to hold or an outcome with a bounded support. Instead, we employ assumptions requiring weak monotonicity of mean potential outcomes within or across subpopulations defined by the values of the potential treatment status under each value of the instrument. We illustrate the identifying power of the bounds by analyzing the effect of attaining a GED, high school, or vocational degree on subsequent employment and weekly earnings using randomization into a training program as an invalid instrument.causal inference, instrumental variables, treatment effects, nonparametric bounds, principal stratification

Nonparametric Partial Identification of Causal Net and Mechanism Average Treatment Effects

When analyzing the causal e§ect of a treatment on an outcome it is important to un- derstand the mechanisms or channels through which the treatment works. In this paper we study net and mechanism average treatment e§ects (NATE and MATE, respectively), which provide an intuitive decomposition of the total average treatment e§ect (ATE) that enables learning about how the treatment a§ects the outcome. We derive informative non- parametric bounds for these two e§ects allowing for heterogeneous e§ects and without re- quiring the use of an instrumental variable or having an outcome with bounded support. We employ assumptions requiring weak monotonicity of mean potential outcomes within or across subpopulations deÖned by the potential values of the mechanism variable under each treatment arm. We illustrate the identifying power of our bounds by analyzing what part of the ATE of a training program on weekly earnings and employment is due to the obtainment of a GED, high school, or vocational degree.causal inference, treatment effects, net effects, direct effects, nonparametric bounds, principal stratification

Identification and Estimation of Causal Mechanisms and Net Effects of a Treatment under Unconfoundedness

An important goal when analyzing the causal effect of a treatment on an outcome is to understand the mechanisms through which the treatment causally works. We define a causal mechanism effect of a treatment and the causal effect net of that mechanism using the potential outcomes framework. These effects provide an intuitive decomposition of the total effect that is useful for policy purposes. We offer identification conditions based on an unconfoundedness assumption to estimate them, within a heterogeneous effect environment, and for the cases of a randomly assigned treatment and when selection into the treatment is based on observables. Two empirical applications illustrate the concepts and methods.causal inference, causal mechanisms, post-treatment variables, principal stratification

Unbundling the Degree Effect in a Job Training Program for Disadvantaged Youth

Government-sponsored education and training programs have the goal to enhance participants' skills so as to become more employable, productive and dependable citizens and thus alleviate poverty and decrease public dependence. While most of the literature evaluating training programs concentrates on estimating their total average treatment effect, these programs offer a variety of services to participants. Estimating the effect of these components is of importance for the design and the evaluation of labor market programs. In this paper, we employ a recent nonparametric approach to estimate bounds on the "mechanism average treatment effect" to evaluate the causal effect of attaining a high school diploma, General Education Development or vocational certificate within a training program for disadvantaged youth 16-24 (Job Corps) relative to other services pffered, on two labor outcomes: employment probability and weekly earnings. We provide these estimates for different demographic groups by race, ethnicity, gender, and two age-risk groups (youth and young adults). Our analysis depicts a positive impact of a degree attainment within the training program on employment probability and weekly earnings for the majority of its participants which in general accounts for 55 - 63 percent of the effect of the program. The heterogeneity of the key demographic subgroups is documented in the relative importance of a degree attainment and of the other services provided in Job Corps.Causal Inference, Treatment Effects, Mechanism Average Effects, Nonparametric Bounds, Potential Outcomes, Principal Stratification, Training Programs, Job Corps, Active Labor Market Policies, Labor and Human Capital, Public Economics, C14, I20, J01,

Bounds on Quantile Treatment Effects of Job Corps on Participants' Wages

This paper assesses the effect of the U.S. Job Corps (JC), the nation's largest and most comprehensive job training program targeting disadvantaged youths, on wages. We employ partial identification techniques and construct informative nonparametric bounds for the causal effect of interest under weaker assumptions than those conventionally used for point identification of treatment effects in the presence of sample selection. In addition, we propose and estimate bounds on quantile treatment effects of the program on participants' wages. In general, we find convincing evidence of positive impacts of JC on participants' wages. Importantly, we find that estimated impacts on lower quantiles of the distribution are higher, with the highest impact being in the 5th percentile where a positive effect on wages is bounded between 8.4 and 16.1 percent. These bounds suggest that JC results in wage compression within eligible participants.Job Corps, Nonparametric Bounds, Principal Stratification, Active Labor Market Programs., Labor and Human Capital, Public Economics, Research Methods/ Statistical Methods, J24, J68, C14, C21,

Bounds on Average and Quantile Treatment Effects of Job Corps Training on Wages

We assess the effectiveness of Job Corps (JC), the largest job training program targeting disadvantaged youth in the United States, by constructing nonparametric bounds for the average and quantile treatment effects of the program on wages. Our preferred estimates point toward convincing evidence of positive effects of JC on wages both at the mean and throughout the wage distribution. For the different demographic groups analyzed, the statistically significant estimated average effects are bounded between 4.6 and 12 percent, while the quantile treatment effects are bounded between 2.7 and 11.7 percent. Furthermore, we find that the program's effect on wages varies across quantiles and groups. Blacks likely experience larger impacts in the lower part of their wage distribution, while Whites likely experience larger impacts in the upper part of their distribution. Non-Hispanic Females show statistically significant impacts in the upper part of their distribution but not in the lower part.training programs, wages, bounds, quantile treatment effects

Evaluating Nonexperimental Estimators for Multiple Treatments: Evidence from Experimental Data

This paper assesses the e¤ectiveness of unconfoundedness-based estimators of mean e¤ects for multiple or multivalued treatments in eliminating biases arising from nonrandom treatment assignment. We evaluate these multiple treatment estimators by simultaneously equalizing average outcomes among several control groups from a randomized experiment. We study linear regression estimators as well as partial mean and weighting estimators based on the generalized propensity score (GPS). We also study the use of the GPS in assessing the comparability of individuals among the di¤erent treatment groups, and propose a strategy to determine the overlap or common support region that is less stringent than those previously used in the literature. Our results show that in the multiple treatment setting there may be treatment groups for which it is extremely di¢ cult to ?nd valid comparison groups, and that the GPS plays a signi?cant role in identifying those groups. In such situations, the estimators we consider perform poorly. However, their performance improves considerably once attention is restricted to those treatment groups with adequate overlap quality, with di¤erence-in-di¤erence estimators performing the best. Our results suggest that unconfoundedness-based estimators are a valuable econometric tool for evaluating multiple treatments, as long as the overlap quality is satisfactory.

Evaluating Nonexperimental Estimators for Multiple Treatments: Evidence from Experimental Data

This paper assesses the effectiveness of unconfoundedness-based estimators of mean effects for multiple or multivalued treatments in eliminating biases arising from nonrandom treatment assignment. We evaluate these multiple treatment estimators by simultaneously equalizing average outcomes among several control groups from a randomized experiment. We study linear regression estimators as well as partial mean and weighting estimators based on the generalized propensity score (GPS). We also study the use of the GPS in assessing the comparability of individuals among the different treatment groups, and propose a strategy to determine the overlap or common support region that is less stringent than those previously used in the literature. Our results show that in the multiple treatment setting there may be treatment groups for which it is extremely difficult to find valid comparison groups, and that the GPS plays a significant role in identifying those groups. In such situations, the estimators we consider perform poorly. However, their performance improves considerably once attention is restricted to those treatment groups with adequate overlap quality, with difference-in-difference estimators performing the best. Our results suggest that unconfoundedness-based estimators are a valuable econometric tool for evaluating multiple treatments, as long as the overlap quality is satisfactory.multiple treatments, nonexperimental estimators, generalized propensity score

Estimating the Effects of Lenght of Exposure to Traning Program: The Case of Job Corps

Length of exposure to a training program is important in determining the labor market outcomes of participants. Employing methods to estimate the causal effects from continuous treatments, we provide insights regarding the effects of different lengths of enrollment to Job Corps (JC)— America’s largest and most comprehensive job training program for disadvantaged youth. We semiparametrically estimate average causal effects (on the treated) of different lengths of exposure to JC, using the “generalized propensity score” under the assumption that selection into different lengths is based on a rich set of observed covariates. “Placebo tests” are performed to gauge the plausibility of this assumption. We find that the estimated effects are increasing in the length of training, and that the marginal effects of additional training are decreasing with length of enrollment. We also document differences in the estimated effects of length of exposure across different demographic groups, which are particularly large between males and females. Finally, our results suggest an important “lock-in” effect in JC training.Training Programs, Continuous Treatments, Generalized Propensity Score, Dose-Response Function