Partial identification in microeconometrics

We intend to apply the general instrument variable (GIV) method to derive the set of both average treatment effect (ATE) and local average treatment effects (LATE) in nonparametric instrumental variable models for discrete outcomes and discrete endogenous variables. Single equation instrumental variable models for binary outcomes and discrete endogenous variables could not be point-identified generally. In this kind of setting, the two stage least squares (2SLS) method is commonly used to secure point-identification by specifying linear parametric restrictions. The
advantage of 2SLS method is that we can easily compute the consistent estimator for local average treatment effects (LATE) under the restrictions of Imbens and Angrist (1994). However, if we want to estimate other useful treatment effects' parameters such as average treatment effects (ATE) or quantile treatment effects (QTE), we have to put some additional restrictions to maintain point identification which sounds untenable, for example, assuming the treatment response as homogenous. Instead of using unsound assumptions to complete the incomplete models with point identification, we can consider of econometric models that allow for partial identification. We can obtain a set of values for the parameters of interest which are observationally equivalent given the data, and the range of the set may be non-trivial enough to get valuable information without making further restrictions. In this circumstance, we can consider a nonparametric threshold-crossing model. By using the general instrument variable (GIV) method proposed by Chesher and Rosen (2017), the average treatment effects (ATE) can be set-identified. To apply this method, I may use the dataset of the British Household Panel Survey and UK Census Longitudinal Studies. I want to use these datasets to analyse the crime rate and the high school dropout rate. In this research, I decided to first use the more restrictive point identifying 2SLS model, and then compare it with the results of GIV method. We may find the 2SLS estimation of LATE lies in the set of GIV estimation. We can also compare the result of using different instrument variables. Finally, we may also analyse the inference on the identified set by using the method proposed by Chernozhukov et al. (2013b, 2015) and the method proposed by Belloni, Bugni and Chernozhukov (2018). This research could provide a more conservative and robust point of view on policy-related micro-econometrics problems compared to the traditional methods.