This book reviews recent approaches for partial identification of average treatment effects with instrumental variables in the program evaluation literature, including Manski’s bounds, bounds based on threshold crossing models, and bounds based on the Local Average Treatment Effect (LATE) framework. It compares these bounds across different sets of assumptions, surveys relevant methods to assess the validity of these assumptions, and discusses estimation and inference methods for the bounds. The book also reviews some empirical applications employing bounds in the program evaluation literature. It aims to bridge the gap between the econometric theory on which the different bounds are based and their empirical application to program evaluation.

Average treatment effect (ATE) is a measure that is frequently used in empirical analysis for measuring the impact of a policy amendable treatment on an outcome variable. Identification and estimation of the ATE have been of concern in empirical studies, as individuals are often only observed for one of the two treatment states in non-experimental data and the selection of treatment is often endogenous. This thesis studies the identification and estimation of the ATE of a binary treatment variable on a binary outcome variable. It particularly focuses on the implication of recent theoretical developments in the literature of partial identification to the econometric estimation of policy relevant effects in empirical applications.The notion of partial identification relates to the idea that in certain situations such as limited observability, more than one data generating process (DGP), or model, can give rise to the same data set we observe; these models are said to be observationally equivalent. In such circumstances policy relevant measures such as the ATE can not be point identified. It is only possible to set identify the measure by estimating an identified set (or bound) for such measures where all values in the set are consistent with the data.The analysis in the thesis is divided to three parts. The first part assumes that data is generated from a particular DGP with an additive error and a parametric distribution. It is found that the bias in the ATE estimator arising from a mis-specified error distribution is not significantly large if we have reasonable sample size and IV strength, even though there may be more significant biases for the model coefficients estimators. We also show that under this regime, the ATE can still be estimated reasonably well even without the existence of instrumental variables (IVs), relying on the assumed functional form and sample size for identification. The main part of the analysis is carried out in the remaining chapters under the partial identification framework. Performances of the estimated ATE bounds from four different estimation methods are compared by using the Hausdorff distance and Euclidean distance. It is found that for all sample sizes in the simulation, the easy to implement parametric methods yield better estimates than nonparametric methods. The strength of IVs also plays an important role on the partial identification of the ATE. The width of the identified set drops as the instrument strength grows. If an extremely strong instrumental variable is available, we may be able to achieve point identification of the ATE (the upper bound and lower bound will overlap). The simulation results further confirms that estimators from parametric methods are robust with regard to instrument strength, while the nonparametric estimators will deviate significantly from the true when the instrument strength is relatively small. Finally the point identification and partial identification of the ATE are applied to a real world data set to study the impact of the private health insurance status on dental service utilisation in Australia.The analysis in the thesis shows that conventional empirical analysis assuming a bivariate probit model could be misleading by estimating a much smaller range for the policy effect. This thesis illustrates with practical applications how various bound analysis of the ATE can be carried out and can provide more robust estimates for policy effects under much broader assumptions for the DGP.

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pretreatment variables, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the pre-treatment variables. Rosenbaum and Rubin (1983, 1984) show that adjusting solely for differences between treated and control units in a scalar function of the pre-treatment, the propensity score, also removes the entire bias associated with differences in pre-treatment variables. Thus it is possible to obtain unbiased estimates of the treatment effect without conditioning on a possibly high-dimensional vector of pre-treatment variables. Although adjusting for the propensity score removes all the bias, this can come at the expense of efficiency. We show that weighting with the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to efficient estimates of the various average treatment effects. This result holds whether the pre-treatment variables have discrete or continuous distributions. We provide intuition for this result in a number of ways. First we show that with discrete covariates, exact adjustment for the estimated propensity score is identical to adjustment for the pre-treatment variables. Second, we show that weighting by the inverse of the estimated propensity score can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score. Finally, we make a connection to results to other results on efficient estimation through weighting in the context of variable probability sampling.

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

This paper considers the use of instrumental variables to estimate the mean effect of treatment on the treated, the mean effect of treatment on randomly selected persons and the local average treatment effect. It examines what economic questions these parameters address. When responses to treatment vary, the standard argument justifying the use of instrumental variables fails unless person-specific responses to treatment do not influence decisions to participate in the program being evaluated. This requires that individual gains from the program that cannot be predicted from variables in outcome equations do not influence the decision of the persons being studied to participate in the program. In the likely case in which individuals possess and act on private information about gains from the program that cannot be fully predicted by variables in the outcome equation, instrumental variables methods do not estimate economically interesting evaluation parameters. Instrumental variable methods are extremely sensitive to assumptions about how people process information. These arguments are developed for both continuous and discrete treatment variables, and several explicit economic models are presented.

Comparative effectiveness research (CER) is the generation and synthesis of evidence that compares the benefits and harms of alternative methods to prevent, diagnose, treat, and monitor a clinical condition or to improve the delivery of care (IOM 2009). CER is conducted to develop evidence that will aid patients, clinicians, purchasers, and health policy makers in making informed decisions at both the individual and population levels. CER encompasses a very broad range of types of studies—experimental, observational, prospective, retrospective, and research synthesis. This volume covers the main areas of quantitative methodology for the design and analysis of CER studies. The volume has four major sections—causal inference; clinical trials; research synthesis; and specialized topics. The audience includes CER methodologists, quantitative-trained researchers interested in CER, and graduate students in statistics, epidemiology, and health services and outcomes research. The book assumes a masters-level course in regression analysis and familiarity with clinical research.