Essays On Nonparametric And High Dimensional Econometrics

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Essays On Nonparametric And High Dimensional Econometrics

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Author : Jesper Riis-Vestergaard Soerensen
language : en
Publisher:
Release Date : 2018

Essays On Nonparametric And High Dimensional Econometrics written by Jesper Riis-Vestergaard Soerensen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

This dissertation studies questions related to identification, estimation, and specification testing of nonparametric and high-dimensional econometric models. The thesis is composed by two chapters. In Chapter 1, I propose specification tests for two formally distinct but related classes of econometric models: (1) semiparametric conditional moment restriction models dependent on conditional expectation functions, and (2) a class of high-dimensional unconditional moment restriction models dependent on high-dimensional best linear predictors. These classes may be motivated by economic models in which agents make choices under uncertainty and therefore have to predict payoff-relevant variables such as the behavior of other agents. The proposed tests are shown to be both asymptotically correctly sized and consistent. Moreover, I establish a bound on the rate of local alternatives for which the test for high-dimensional unconditional moment restriction models is consistent. These results allow researchers to test the specification of their models without introducing additional parametric, typically ad hoc, assumptions on expectations. In Chapter 2, I show that it is possible to identify and estimate a generalized panel regression model (GPRM) without imposing any parametric structure on (1) the function of observable explanatory variables, (2) the systematic function through which the function of observable explanatory variables, fixed effect, and disturbance term generate the outcome variable, or (3) the distribution of unobservables. I proceed with estimation using a series maximum rank correlation estimator (SMRCE) of the function of observable explanatory variables and provide conditions under which L2-consistency is achieved. I also provide conditions under which both L2 and uniform convergence rates of the SMRCE may be derived.

Essays On Non Parametric And High Dimensional Econometrics

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Author : Zhenting Sun
language : en
Publisher:
Release Date : 2018

Essays On Non Parametric And High Dimensional Econometrics written by Zhenting Sun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

Chapter 1 studies the instrument validity for local average treatment effects. we provide a testable implication for instrument validity in the local average treatment effect (LATE) framework with multivalued treatments. Based on this testable implication, we construct a nonparametric test of instrument validity in the multivalued treatment LATE framework. The test is asymptotically consistent. The size of the test can be promoted to the nominal significance level over much of the null, indicating a good power property. Simulation evidence is provided to show the good performance of the test in finite samples. Chapter 2 constructs improved nonparametric bootstrap tests of Lorenz dominance based on preliminary estimation of a contact set. Our tests achieve the nominal rejection rate asymptotically on the boundary of the null; that is, when Lorenz dominance is satisfied, and the Lorenz curves coincide on some interval. Numerical simulations indicate that our tests enjoy substantially improved power compared to existing procedures at relevant sample sizes. Chapter 3 proposes a sieve focused GMM (SFGMM) estimator for general high-dimensional semiparametric conditional moment models in the presence of endogeneity. Under certain conditions, the SFGMM estimator has oracle consistency properties and converges at a desirable rate. We then establish the asymptotic normality of the plug-in SFGMM estimator for possibly irregular functionals. Simulation evidence illustrates the performance of the proposed estimator.

Essays On High Dimensional Econometrics

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Author : Guan Yun Kenwin Maung
language : en
Publisher:
Release Date : 2023

Essays On High Dimensional Econometrics written by Guan Yun Kenwin Maung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Big data categories.

"This dissertation consists of three chapters on high-dimensional econometrics. These chapters introduce novel methods to deal with econometric models where the number of unknown parameters is large relative to the available sample size. The first chapter introduces a dimension-reducing estimator for economic and financial networks. Many network econometric models rely on known adjacency matrices. This becomes a problem for investigations when the network structure is not readily accessed or constructed. Furthermore, direct estimation may be cumbersome or infeasible if the number of units in the network is large. To deal with this, I propose a Structural Vector Autoregression (SVAR) data-driven approach to recover the network structure via matrix regression under a large N and T asymptotic framework. The high-dimensionality of the problem is dealt with by focusing on low-rank representations of the network. I show, both theoretically and through simulations, that the reduced-form estimator is consistent and asymptotically normal, and suggest an identification strategy for the SVAR as implied by its network structure. In the empirical study, I extract volatility connectedness between major US financial institutions and find a greater degree of interconnectedness compared to the literature. I further demonstrate the utility of the estimated network for systemic risk analysis by identifying key propagators of volatility spillovers in the financial sector. The second chapter deals with maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs). This problem might be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or exceeds the sample size, I adopt a sparse framework and propose two penalized maximum likelihood estimators with either the Lasso or the smoothly clipped absolute deviation (SCAD) penalty. I show that both estimators are estimation consistent, while the SCAD estimator also selects relevant parameters with probability approaching one. A modified EM-algorithm is developed for the case of Gaussian errors and simulations show that the algorithm exhibits desirable finite sample performance. In an application to short-horizon return predictability in the US, I estimate a 15 variable 2-state MS-VAR(1) and obtain the often reported counter-cyclicality in predictability. The variable selection property of the proposed estimators helps to identify predictors that contribute strongly to predictability during economic contractions but are otherwise irrelevant in expansions. Furthermore, out-of-sample analyses indicate that large MS-VARs can significantly outperform "hard-to-beat" predictors like the historical average. In the final chapter, I propose a new nonparametric estimator of time-varying forecast combination weights. When the number of individual forecasts is small, I study the asymptotic properties of the local linear estimator. When the number of candidate forecasts exceeds or diverges with the sample size, I consider penalized local linear estimation with the group SCAD penalty. I show that the estimator exhibits the oracle property and correctly selects relevant forecasts with probability approaching one. Simulations indicate that the proposed estimators outperform existing combination schemes when structural changes exist. An empirical application on inflation and unemployment forecasting highlights the merits of the approach relative to other popular methods in the literature."--Pages ix-x.

Endogenous Econometric Models And Multi Stage Estimation In High Dimensional Settings

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Author : Ying Zhu
language : en
Publisher:
Release Date : 2015

Endogenous Econometric Models And Multi Stage Estimation In High Dimensional Settings written by Ying Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

Econometric models based on observational data are often endogenous due to measurement error, autocorrelated errors, simultaneity and omitted variables, non-random sampling, self-selection, etc. Parameter estimates of these models without corrective measures may be inconsistent. The potential high-dimensional feature of these models (where the dimension of the parameters of interests is comparable to or even larger than the sample size) further complicates the statistical estimation and inference. My dissertation studies two different types of high-dimensional endogenous econometrics problems in depth and develops statistical tools together with their theoretical guarantees. The first essay in this dissertation explores the validity of the two-stage regularized least squares estimation procedure for sparse linear models in high-dimensional settings with possibly many endogenous regressors. The second essay is focused on the semiparametric sample selection model in high-dimensional settings under a weak nonparametric restriction on the form of the selection correction, for which a multi-stage projection-based regularized procedure is proposed. The number of regressors in the main equation, p, and the number of regressors in the first-stage equation, d, can grow with and exceed the sample size n in the respective models. The analysis considers the sparsity case where the number of non-zero components in the vectors of coefficients is bounded above by some integer which is allowed to grow with n but slowly compared to n, or the vectors of coefficients can be approximated by exactly sparse vectors. Simulations are conducted to gain insight on the small-sample performance of these high-dimensional multi-stage estimators. The proposed estimators in the second essay are also applied to study the pricing decisions of the gasoline retailers in the Greater Saint Louis area. The main theoretical results of both essays are finite-sample bounds from which sufficient scaling conditions on the sample size for estimation consistency and variable selection consistency (i.e., the multi-stage high-dimensional estimation procedures correctly select the non-zero coefficients in the main equation with high probability) are established. A technical issue regarding the so-called "restricted eigenvalue (RE) condition" for estimation consistency and the "mutual incoherence (MI) condition" for selection consistency arises in these multi-stage estimation procedures from allowing the number of regressors in the main equation to exceed n and this paper provides analysis to verify these RE and MI conditions. In particular, for the semiparametric sample selection model, these verifications also provide a finite-sample guarantee of the population identification condition required by the semiparametric sample selection models. In the second essay, statistical efficiency of the proposed estimators is studied via lower bounds on minimax risks and the result shows that, for a family of models with exactly sparse structure on the coefficient vector in the main equation, one of the proposed estimators attains the smallest estimation error up to the (n, d, p)-scaling among a class of procedures in worst-case scenarios. Inference procedures for the coefficients of the main equation, one based on a pivotal Dantzig selector to construct non-asymptotic confidence sets and one based on a post-selection strategy (when perfect or near-perfect selection of the high-dimensional coefficients is achieved), are discussed. Other theoretical contributions of this essay include establishing the non-asymptotic counterpart of the familiar asymptotic "oracle" type of results from previous literature: the estimator of the coefficients in the main equation behaves as if the unknown nonparametric component were known, provided the nonparametric component is sufficiently smooth.

Essays On Nonparametric Econometrics

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Author : Young Jun Lee
language : en
Publisher:
Release Date : 2019

Essays On Nonparametric Econometrics written by Young Jun Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

This dissertation consists of three chapters that focus on the nonparametric method on time-varying parameter models and optimal transport problem. // The first chapter, which is jointly authored with Dennis Kristensen, develops a novel asymptotic theory for local polynomial (quasi-) maximum-likelihood estimators of time-varying parameters in a broad class of nonlinear time series models. Under weak regularity conditions, we show the proposed estimators are consistent and follow normal distributions in large samples. We demonstrate the usefulness of our general results by applying our theory to local (quasi-) maximum-likelihood estimators of a time-varying VAR's, ARCH and GARCH, and Poisson autogressions. // The second chapter proposes a sieve M-estimation of the solution to the optimal transport problem. Many problems in economics, including matching models and quantile methods, have the structure of an optimal transport problem. The sieve M-estimator is consistent under very little structure on the underlying optimal transport problem being solved. I then derive convergence rates for the estimator and its derivative when the surplus function Φ(X, Y) = X"2Y. The derived convergence rates are the same as the optimal rate in the context of regression and density estimations. The results can be extended to the conditional optimal transport problem having the conditional vector quantiles as an application. // In the third chapter, I consider the multidimensional matching as one of the primary applications of the optimal transport problem. We employ the sieve simultaneous minimum distance estimation method to estimate the parameters in the equilibrium wage and assignment functions. Our estimation results show that worker-job complementarities in manual skills strongly decreased, whereas complementarities in cognitive skills increased. This phenomenon is consistent with the one of Lindenlaub (2017).

Essays On Nonparametric And Semiparametric Econometrics

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Author : Eduardo García Echeverri
language : en
Publisher:
Release Date : 2022

Essays On Nonparametric And Semiparametric Econometrics written by Eduardo García Echeverri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Social mobility categories.

"This dissertation consists of three chapters on nonparametric and semiparametric econometrics. Chapter 1 introduces the estimators used in the empirical applications of Chapter 2 and therefore should be read first. Chapter 3 is independent from the first two. The first chapter introduces a measure of intergenerational social mobility based on [phi]-divergences. The measure can be decomposed to study mobility in population subgroups of interest and can be used to describe mobility of multiple outcome variables across an arbitrary number of generations, unlike most indicators in the literature. The measure also fully controls for marginal distributions, meaning it is not affected by income growth or changes in income inequality. I propose two estimators for the measure: a non-parametric estimator and an estimator based on the mobility matrix. I provide conditions under which these estimators are n-consistent and asymptotically normal. In the second chapter, I use a specific [phi]-divergence (the Hellinger distance) to measure multidimensional social mobility in the USA and Germany. For this purpose, I use the Panel Study of Income Dynamics (PSID), the German Socio-Economic Panel (SOEP), and US administrative tax data. The measure reveals lower income and health mobility in the USA than Germany, but the opposite for educational mobility. It also shows income mobility for both countries is lowest in the tails of the parental income distribution and greatest in the centre. This inverted U-pattern is more pronounced in the USA. Most of these empirical findings for population subgroups are hidden to the existing indicators in the literature. Chapter 3 introduces a Low CPU Cost Semiparametric (LCS) estimator for linear single index models. The LCS estimator significantly reduces estimation time when compared to the standard semiparametric estimator in Ichimura (1993). It does so by more than 90% in medium sample sizes. Moreover, it makes estimation feasible in a regular PC when the sample size exceeds 10,000 observations. We provide conditions for consistency and asymptotic normality of the LCS estimator based on spline function theory. In our empirical application, we study determinants of expenditures in vocational rehabilitation (VR) programs using the RSA-911 data, containing information on more than 900,000 workers with disabilities. We find that minorities such as African Americans, Hispanic or females have lower expenditures in VR programs. On the other hand, expenditure is greater for more educated workers."--Pages viii-ix.

Essays In Nonlinear Time Series Econometrics

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Author : Niels Haldrup
language : en
Publisher: OUP Oxford
Release Date : 2014-06-26

Essays In Nonlinear Time Series Econometrics written by Niels Haldrup and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Business & Economics categories.

This edited collection concerns nonlinear economic relations that involve time. It is divided into four broad themes that all reflect the work and methodology of Professor Timo Teräsvirta, one of the leading scholars in the field of nonlinear time series econometrics. The themes are: Testing for linearity and functional form, specification testing and estimation of nonlinear time series models in the form of smooth transition models, model selection and econometric methodology, and finally applications within the area of financial econometrics. All these research fields include contributions that represent state of the art in econometrics such as testing for neglected nonlinearity in neural network models, time-varying GARCH and smooth transition models, STAR models and common factors in volatility modeling, semi-automatic general to specific model selection for nonlinear dynamic models, high-dimensional data analysis for parametric and semi-parametric regression models with dependent data, commodity price modeling, financial analysts earnings forecasts based on asymmetric loss function, local Gaussian correlation and dependence for asymmetric return dependence, and the use of bootstrap aggregation to improve forecast accuracy. Each chapter represents original scholarly work, and reflects the intellectual impact that Timo Teräsvirta has had and will continue to have, on the profession.

Essays In Nonparametric Econometrics

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Author : Tomasz Olma
language : en
Publisher:
Release Date : 2021*

Essays In Nonparametric Econometrics written by Tomasz Olma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021* with categories.

Three Essays On Nonparametric Econometrics With Applications To Financial Economics And Insurance

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Author : Kuangyu Wen
language : en
Publisher:
Release Date : 2015

Three Essays On Nonparametric Econometrics With Applications To Financial Economics And Insurance written by Kuangyu Wen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

This dissertation includes three essays. The first essay concerns nonparametric kernel density estimation on the unit interval. The Kernel Density Estimator (KDE) suffers boundary biases when applied to densities on bounded supports, which are assumed to be the unit interval. Transformations mapping the unit interval to the real line can be used to remove boundary biases. However, this approach may induce erratic tail behaviors when the estimated density of transformed data is transformed back to its original scale. I propose a modified transformation based KDE that employs a tapered and tilted back-transformation. I derive the theoretical properties of the new estimator and show that it asymptotically dominates the naive transformation based estimator while maintains its simplicity. I then propose three automatic methods of smoothing parameter selection. Monte Carlo simulations demonstrate the good finite sample performance of the proposed estimator, especially for densities with poles near the boundaries. An example with real data is provided. The second essay proposes a new kernel estimator of copula densities. The standard kernel estimator suffers boundary biases since copula densities are defined on a bounded support and often tend to infinity on the boundaries. A transformation based estimator aptly remedies both boundary biases and inconsistencies due to unbounded densities. This method, however, might entail undesirable boundary behaviors due to an unbounded multiplicative factor associated with the transformation. I propose a modified transformation-based estimator that employs an infinitesimal tapering device to mitigate the influence of the unbounded multiplier. I establish the asymptotic properties of our estimator and show that it dominates the original transformation estimator in terms of mean squared error due to bias correction. I present two practically simple methods of smoothing parameter selection. I further show that the proposed estimator admits higher order bias reduction for Gaussian copulas and provides outstanding performance for Gaussian and near Gaussian copulas. This appealing feature makes our estimator particularly suitable for financial data analyses. Extensive simulations corroborate our theoretical analysis and demonstrate outstanding performance of the proposed method relative to competing estimators. Three empirical applications are provided. The third essay studies nonparametric estimation of crop yield distributions and crop insurance premium rates. Since U.S. crop yield data are typically available at county level for only a few decades, nonparametric estimation of yield distribution for individual counties suffers from small sample sizes. The fact that nearby counties share similarities in their yield distributions suggests possible efficiency gains through information pooling. I propose a weighted kernel density estimator subject to selected spatial moment restrictions. The weights are calculated using the method of empirical likelihood and the spatial moments are specified based on the consideration of flexibility and robustness. I further extend the proposed method to the adaptive kernel density estimation. My simulations demonstrate the outstanding performance of the proposed methods in the estimation of crop yield distributions and that of crop insurance premium rates. I apply these methods to estimate corn yield distributions and crop insurance premium rates for the ninety-nine counties in Iowa. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155094

Essays On Econometrics

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Author :
language : en
Publisher:
Release Date : 2015

Essays On Econometrics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

This dissertation consists of three chapters on semiparametric/nonparametric econometric models with endogeneity. The first chapter considers conditional moment models where the parameters of interest include both finite-dimensional parameters and unknown functions. First, we provide new methods of pointwise and uniform inference for the estimates of both finite- and infinite-dimensional components of the parameters and functionals of the parameters. Second, under partial identification, we show how to construct pointwise confidence regions by inverting a quasi-likelihood ratio (QLR) statistic. We provide a consistent bootstrap procedure for obtaining critical values corresponding to the QLR. Furthermore, we generalize the uniform confidence bands from point identified case to uniform confidence sets over the domain of the unknown functions by inverting a sup-QLR statistic. The new methods are applied to construct pointwise confidence intervals and uniform confidence bands for shape-invariant Engel curves. The second chapter considers the problem of choosing the regularization parameter and the smoothing parameter in nonparametric instrumental variables estimation. We propose a Mallows' C p -type criterion to select these two parameters simultaneously. We show that the proposed selection criterion is optimal in the sense that the selected estimate asymptotically achieves the lowest possible mean squared error among all candidates. To account for model uncertainty, we introduce a new model averaging estimator for nonparametric instrumental variables regressions. We propose a Mallows criterion for the weight selection and demonstrate its asymptotic optimality. The third chapter develops empirical likelihood ratio tests for conditional moment models in which the unknown parameter can contain infinite-dimensional components. We obtain (1) the limiting distribution of the sieve conditional empirical likelihood ratio (SCELR) test statistic for functionals of parameters under the null hypothesis and local alternatives, and (2) the limiting distribution of the SCELR test statistics for conditional moment restrictions (a consistent specification test) under null hypothesis and local alternatives.