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Essays in microeconometrics

Dong, Hao (2018) Essays in microeconometrics. PhD thesis, The London School of Economics and Political Science (LSE).

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Identification Number: 10.21953/lse.b7k49xprwz15

Abstract

This thesis consists of three chapters, which are works during my PhD study. In the first two chapters, I investigate the estimation of nonparametric and semiparametric econometric models widely used in empirical studies when the data is mismeasured. In the last chapter, my attention moves to the estimation of the effects of the social interactions. In Chapter 1, I study the estimation of the nonparametric additive model in the presence of a mismeasured covariate. In such a situation, the conventional method may cause severe bias. Therefore, I propose a new estimator. The estimation procedure is divided into two stages. In the first stage, to adept to the additive structure, I use a series method. And to deal with the ill-posedness brought by the mismeasurement, I introduce a ridge parameter. The convergence rate is then derived for the first stage estimator. For the distributional results required for inference, based on the first stage estimator, I implement the one-step back-fitting with a deconvolution kernel. Asymptotic normality is derived for the second stage estimator. Chapter 2 investigates the sharp regression-discontinuity (SRD) design when there is a continuously distributed measurement error in the running variable. In such a situation, the discontinuity at the cut-off disappear completely, and using the conventional SRD method cause severe bias. To overcome this, I develop a new estimator of the average treatment effect at the cut-off. Two separate cases characterized by the observability of the treatment status are considered. In the case of observed treatment status, the proposed estimator is the difference between the deconvolution local linear estimators based on treated and control groups. In the case of unobserved treatment status, the observed running variable cannot be used to divide the sample due to the presence of measurement errors. So, the one-sided kernel functions are implemented, and an additional ridging parameter is introduced for regularization. Asymptotic properties of proposed estimators are derived for both cases. Chapter 3 develops a new method to estimate the spillover effects using the factor structure of the variables generating the spillovers. Specifically, we find that such a factor structure implies constraints on the spillovers, which can be utilized to improve the performance of the existing estimator, like LASSO, by adding the factor-induced constraints. The L2 error bound is derived for the proposed estimator. Compared with the unconstrained case, the proposed estimator is more accurate in the sense that it has approximately sharper error bound. Simulation results demonstrate our findings.

Item Type: Thesis (PhD)
Additional Information: © 2018 Hao Dong
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Sets: Departments > Economics
Supervisor: Otsu, Taisuke and Yao, Qiwei
URI: http://etheses.lse.ac.uk/id/eprint/3756

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