Aspects of identification and partial identification of average treatment effect in binary outcome models

Abstract

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.