Taylor, Luke
(2017)
Essays in nonparametric estimation and inference.
PhD thesis, London School of Economics and Political Science.
Abstract
This thesis consists of three chapters which represent my journey as a researcher during this PhD. The uniting theme is nonparametric estimation and inference in the presence of data problems. The first chapter begins with nonparametric estimation in the presence of a censored dependent variable and endogenous regressors. For Chapters 2 and 3 my attention moves to problems of inference in the presence of mismeasured data.
In Chapter 1 we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalise the identification argument put forward in Altonji, Ichimura and Otsu (2012), construct a nonparametric estimator, characterise its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. We show that the estimator is consistent and asymptotically normally distributed.
Chapter 2 considers specification testing for regression models with errors-in-variables. In contrast to the method proposed by Hall and Ma (2007), our test allows general nonlinear regression models. Since our test employs the smoothing approach, it complements the nonsmoothing one by Hall and Ma in terms of local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities and develop a bootstrap method to approximate the critical value. We apply the test to the specification of Engel curves in the US. Finally, some simulation results endorse our theoretical findings: our test has advantages in detecting high frequency alternatives and dominates the existing tests under certain specifications.
Chapter 3 develops a nonparametric significance test for regression models with measurement error in the regressors. To the best of our knowledge, this is the first test of its kind. We use a ‘semi-smoothing’ approach with nonparametric deconvolution estimators and show that our test is able to overcome the slow rates of convergence associated with such estimators. In particular, our test is able to detect local alternatives at the √n rate. We derive the asymptotic distribution under i.i.d. and weakly dependent data, and provide bootstrap procedures for both data types. We also highlight the finite sample performance of the test through a Monte Carlo study. Finally, we discuss two empirical applications. The first considers the effect of cognitive ability on a range of socio-economic variables. The second uses time series data - and a novel approach to estimate the measurement error without repeated measurements - to investigate whether future inflation expectations are able to stimulate current consumption.
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