Essays on Microeconometrics

My dissertation has three chapters which develop and apply microeconometric tech- niques to empirically relevant problems. All the chapters examines the robustness issues (e.g., measurement error and model misspecification) in the econometric anal- ysis. The first chapter studies the identifying power of an instrumental variable in the nonparametric heterogeneous treatment effect framework when a binary treat- ment variable is mismeasured and endogenous. I characterize the sharp identified set for the local average treatment effect under the following two assumptions: (1) the exclusion restriction of an instrument and (2) deterministic monotonicity of the true treatment variable in the instrument. The identification strategy allows for general measurement error. Notably, (i) the measurement error is nonclassical, (ii) it can be endogenous, and (iii) no assumptions are imposed on the marginal distribution of the measurement error, so that I do not need to assume the accuracy of the measure- ment. Based on the partial identification result, I provide a consistent confidence interval for the local average treatment effect with uniformly valid size control. I also show that the identification strategy can incorporate repeated measurements to narrow the identified set, even if the repeated measurements themselves are endoge- nous. Using the the National Longitudinal Study of the High School Class of 1972, I demonstrate that my new methodology can produce nontrivial bounds for the return to college attendance when attendance is mismeasured and endogenous.

The second chapter, which is a part of a coauthored project with Federico Bugni, considers the problem of inference in dynamic discrete choice problems when the structural model is locally misspecified. We consider two popular classes of estimators for dynamic discrete choice models: K-step maximum likelihood estimators (K-ML) and K-step minimum distance estimators (K-MD), where K denotes the number of policy iterations employed in the estimation problem. These estimator classes include popular estimators such as Rust (1987)’s nested fixed point estimator, Hotz and Miller (1993)’s conditional choice probability estimator, Aguirregabiria and Mira (2002)’s nested algorithm estimator, and Pesendorfer and Schmidt-Dengler (2008)’s least squares estimator. We derive and compare the asymptotic distributions of K- ML and K-MD estimators when the model is arbitrarily locally misspecified and we obtain three main results. In the absence of misspecification, Aguirregabiria and Mira (2002) show that all K-ML estimators are asymptotically equivalent regardless of the choice of K. Our first result shows that this finding extends to a locally misspecified model, regardless of the degree of local misspecification. As a second result, we show that an analogous result holds for all K-MD estimators, i.e., all K- MD estimator are asymptotically equivalent regardless of the choice of K. Our third and final result is to compare K-MD and K-ML estimators in terms of asymptotic mean squared error. Under local misspecification, the optimally weighted K-MD estimator depends on the unknown asymptotic bias and is no longer feasible. In turn, feasible K-MD estimators could have an asymptotic mean squared error that is higher or lower than that of the K-ML estimators. To demonstrate the relevance of our asymptotic analysis, we illustrate our findings using in a simulation exercise based on a misspecified version of Rust (1987) bus engine problem.

The last chapter investigates the causal effect of the Omnibus Budget Reconcil- iation Act of 1993, which caused the biggest change to the EITC in its history, on unemployment and labor force participation among single mothers. Unemployment and labor force participation are difficult to define for a few reasons, for example, be- cause of marginally attached workers. Instead of searching for the unique definition for each of these two concepts, this chapter bounds unemployment and labor force participation by observable variables and, as a result, considers various competing definitions of these two concepts simultaneously. This bounding strategy leads to partial identification of the treatment effect. The inference results depend on the construction of the bounds, but they imply positive effect on labor force participa- tion and negligible effect on unemployment. The results imply that the difference- in-difference result based on the BLS definition of unemployment can be misleading

due to misclassification of unemployment.

Three Essays on Extremal Quantiles

Extremal quantile index is a concept that the quantile index will drift to zero (or one)

as the sample size increases. The three chapters of my dissertation consists of three

applications of this concept in three distinct econometric problems. In Chapter 2, I

use the concept of extremal quantile index to derive new asymptotic properties and

inference method for quantile treatment effect estimators when the quantile index

of interest is close to zero. In Chapter 3, I rely on the concept of extremal quantile

index to achieve identification at infinity of the sample selection models and propose

a new inference method. Last, in Chapter 4, I use the concept of extremal quantile

index to define an asymptotic trimming scheme which can be used to control the

convergence rate of the estimator of the intercept of binary response models.

MRI-Guided Radiation Therapy: Investigating the Accuracy of Treatment Delivery

Purpose: To develop, evaluate and apply a novel high-resolution 3D remote dosimetry protocol for validation of MRI guided radiation therapy treatments (MRIdian® by ViewRay®). We demonstrate the first application of the protocol (including two small but required new correction terms) utilizing radiochromic 3D plastic PRESAGE® with optical-CT readout.

Methods: A detailed study of PRESAGE® dosimeters (2kg) was conducted to investigate the temporal and spatial stability of radiation induced optical density change (ΔOD) over 8 days. Temporal stability was investigated on 3 dosimeters irradiated with four equally-spaced square 6MV fields delivering doses between 10cGy and 300cGy. Doses were imaged (read-out) by optical-CT at multiple intervals. Spatial stability of ΔOD response was investigated on 3 other dosimeters irradiated uniformly with 15MV extended-SSD fields with doses of 15cGy, 30cGy and 60cGy. Temporal and spatial (radial) changes were investigated using CERR and MATLAB’s Curve Fitting Tool-box. A protocol was developed to extrapolate measured ΔOD readings at t=48hr (the typical shipment time in remote dosimetry) to time t=1hr.

Results: All dosimeters were observed to gradually darken with time (<5% per day). Consistent intra-batch sensitivity (0.0930±0.002 ΔOD/cm/Gy) and linearity (R2=0.9996) was observed at t=1hr. A small radial effect (<3%) was observed, attributed to curing thermodynamics during manufacture. The refined remote dosimetry protocol (including polynomial correction terms for temporal and spatial effects, CT and CR) was then applied to independent dosimeters irradiated with MR-IGRT treatments. Excellent line profile agreement and 3D-gamma results for 3%/3mm, 10% threshold were observed, with an average passing rate 96.5%± 3.43%.

Conclusion: A novel 3D remote dosimetry protocol is presented capable of validation of advanced radiation treatments (including MR-IGRT). The protocol uses 2kg radiochromic plastic dosimeters read-out by optical-CT within a week of treatment. The protocol requires small corrections for temporal and spatially-dependent behaviors observed between irradiation and readout.