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.

Plate-specific gain map correction for the improvement of detective quantum efficiency in computed radiography.

PURPOSE: The purpose of this work is to improve the noise power spectrum (NPS), and thus the detective quantum efficiency (DQE), of computed radiography (CR) images by correcting for spatial gain variations specific to individual imaging plates. CR devices have not traditionally employed gain-map corrections, unlike the case with flat-panel detectors, because of the multiplicity of plates used with each reader. The lack of gain-map correction has limited the DQE(f) at higher exposures with CR. This current work describes a feasible solution to generating plate-specific gain maps. METHODS: Ten high-exposure open field images were taken with an RQA5 spectrum, using a sixth generation CR plate suspended in air without a cassette. Image values were converted to exposure, the plates registered using fiducial dots on the plate, the ten images averaged, and then high-pass filtered to remove low frequency contributions from field inhomogeneity. A gain-map was then produced by converting all pixel values in the average into fractions with mean of one. The resultant gain-map of the plate was used to normalize subsequent single images to correct for spatial gain fluctuation. To validate performance, the normalized NPS (NNPS) for all images was calculated both with and without the gain-map correction. Variations in the quality of correction due to exposure levels, beam voltage/spectrum, CR reader used, and registration were investigated. RESULTS: The NNPS with plate-specific gain-map correction showed improvement over the noncorrected case over the range of frequencies from 0.15 to 2.5 mm(-1). At high exposure (40 mR), NNPS was 50%-90% better with gain-map correction than without. A small further improvement in NNPS was seen from carefully registering the gain-map with subsequent images using small fiducial dots, because of slight misregistration during scanning. Further improvement was seen in the NNPS from scaling the gain map about the mean to account for different beam spectra. CONCLUSIONS: This study demonstrates that a simple gain-map can be used to correct for the fixed-pattern noise in a given plate and thus improve the DQE of CR imaging. Such a method could easily be implemented by manufacturers because each plate has a unique bar code and the gain-map for all plates associated with a reader could be stored for future retrieval. These experiments indicated that an improvement in NPS (and hence, DQE) is possible, depending on exposure level, over a wide range of frequencies with this technique.