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The Ohio State University

1. Xu, Xingbai, Xu. Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models.

Degree: PhD, Economics, 2016, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529

Spatial econometrics has been obtained more and more
attention in the recent years. The spatial autoregressive (SAR)
model is one of the most widely used and studied models in spatial
econometrics. So far, most studies have been focused on linear SAR
models. However, some types of spatial or network data, for
example, censored data or discrete choice data, are very common and
useful, but not suitable to study by a linear SAR model. That is
why I study an SAR Tobit model and an SAR binary choice model in
this dissertation. Chapter 1 studies a Tobit model with spatial
autoregressive interactions. We consider the maximum likelihood
estimation (MLE) for this model and analyze asymptotic properties
of the estimator based on the spatial near-epoch dependence (NED)
of the dependent variable process generated from the model
structure. We show that the MLE is consistent and asymptotically
normally distributed. Monte Carlo experiments are performed to
verify finite sample properties of the estimator.Chapter 2 extends
the MLE estimation of the SAR Tobit model studied in Chapter 1 to
distribution-free estimation. We examine the sieve MLE of the
model, where the disturbances are i.i.d. with an unknown
distribution. This model can be applied to spatial econometrics and
social networks when data are censored. We show that related
variables are spatial NED. An important contribution of this
chapter is that I develop some exponential inequalities for spatial
NED random fields, which are also useful in other semiparametric
studies when spatial correlation exists. With these inequalities,
we establish the consistency of the estimator. Asymptotic
distributions of structural parameters of the model are derived
from a functional central limit theorem and projection. Simulations
show that the sieve MLE can improve the finite sample performance
upon misspecified normal MLEs, in terms of reduction in the bias
and standard deviation. As an empirical application, we examine the
school district income surtax rates in Iowa. Our results show that
the spatial spillover effects are significant, but they may be
overestimated if disturbances are restricted to be normally
distributed.Chapter 3 studies the method of simulated moments (MSM)
estimation of a binary choice game model with network links, where
the network peer effects are non-negative, and there might be only
one or few networks in the sample. The proposed estimation method
can be applied to studies with binary dependent variables in the
fields of empirical IO, social network and spatial econometrics.
The model might have multiple Nash equilibria. We assume that the
maximum Nash equilibrium, which always exists and is strongly
coalition-proof and Pareto optimal, is selected. The challenging
econometric issues are the possible correlation among all dependent
variables and the discontinuous functional form of our simulated
moments. We overcome these challenges via the empirical process
theory and derive the spatial NED of the dependent variable. We
establish a criterion for an NED random…
*Advisors/Committee Members: Lee, Lung-fei (Advisor).*

Subjects/Keywords: Economics; spatial econometrics, near-epoch dependence, maximum likelihood, method of simulated moments, large sample properties, Monte Carlo, sieve estimation, Tobit model, binary choice model

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Xu, Xingbai, X. (2016). Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529

Chicago Manual of Style (16^{th} Edition):

Xu, Xingbai, Xu. “Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models.” 2016. Doctoral Dissertation, The Ohio State University. Accessed November 28, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529.

MLA Handbook (7^{th} Edition):

Xu, Xingbai, Xu. “Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models.” 2016. Web. 28 Nov 2020.

Vancouver:

Xu, Xingbai X. Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models. [Internet] [Doctoral dissertation]. The Ohio State University; 2016. [cited 2020 Nov 28]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529.

Council of Science Editors:

Xu, Xingbai X. Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models. [Doctoral Dissertation]. The Ohio State University; 2016. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529

2. Liu, Tuo. Model Selection and Adaptive Lasso Estimation of Spatial Models.

Degree: PhD, Economics, 2017, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1500379101560737

Various spatial econometrics models have been proposed
to characterize spatially correlated data. As economic theories
provide little guidance on constructing a true model, we are often
faced with the problem to choose among spatial econometrics models.
My dissertation develops a Vuong-type test and an adaptive Lasso
procedure that complement existing spatial model selection methods
in several aspects. Chapter 1 develops a likelihood-ratio test for
model selection between two spatial econometrics models. It
generalizes Vuong (1989) to models with spatial near-epoch
dependent (NED) data. We measure the distance from a model to a
data generating process by Kullback-Leibler Information Criterion
and test the null hypothesis that two models are equally close to
the data generating process. We make no assumption on the model
specification of the truth and allow for the cases where both,
either or neither of the two competing models is mis-specified.As a
prerequisite of the test, we first show that the quasi-maximum
likelihood estimators (QMLE) of spatial econometrics models are
consistent estimators of their pseudo-true values and are
asymptotically normal under regularity conditions. In particular,
we study spatial autoregressive models with spatial autoregressive
errors (SARAR) and matrix exponential spatial specification (MESS)
models. With asymptotic properties of QMLEs and limit theorems for
NED random fields, we then derive the limiting null distribution of
the test statistic. A spatial heteroskedastic and autoregressive
consistent estimator of asymptotic variance of the test statistic
under the null, which is necessary to implement the test, is
constructed. Monte Carlo experiments are designed to investigate
finite sample performance of QMLEs for SARAR and MESS models, as
well as the size and power of the proposed test. Chapter 2 proposes
a penalized maximum likelihood approach with adaptive Lasso penalty
to estimate SARAR models. It allows for simultaneous model
selection and parameter estimation. With appropriately chosen
tuning parameter, the resulting estimators enjoy the oracle
properties, in other words, zero parameters are estimated as zeros
with probability approaching one and nonzero parameters possess the
same asymptotic distribution as if the true model is known. We
extend Zhu, Huang and Ryes (2010)’s work to account for models with
spatial lags. We also allow the number of parameters to grow with
sample size at a relatively slow rate. As maximum likelihood
estimation is computationally demanding, we generalize the least
squares approximation (LSA) algorithm (Wang and Leng, 2010) to
spatial linear models and prove that the LSA estimators perform as
efficiently as the oracle as long as a consistent initial estimator
with proper convergence rate is adopted in the algorithm. By using
the LSA algorithm with a computationally simple initial estimator,
we can perform penalized maximum likelihood estimation of SARAR
models much faster than Zhu, Huang and Ryes (2010) without
sacrificing efficiency.
*Advisors/Committee Members: Lee, Lung-fei (Advisor).*

Subjects/Keywords: Economics; likelihood ratio; near-epoch dependence; spatial autoregressive model; matrix exponential spatial specification, model selection; adaptive lasso; oracle property; least square approximation; selection consistency

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Liu, T. (2017). Model Selection and Adaptive Lasso Estimation of Spatial Models. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1500379101560737

Chicago Manual of Style (16^{th} Edition):

Liu, Tuo. “Model Selection and Adaptive Lasso Estimation of Spatial Models.” 2017. Doctoral Dissertation, The Ohio State University. Accessed November 28, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500379101560737.

MLA Handbook (7^{th} Edition):

Liu, Tuo. “Model Selection and Adaptive Lasso Estimation of Spatial Models.” 2017. Web. 28 Nov 2020.

Vancouver:

Liu T. Model Selection and Adaptive Lasso Estimation of Spatial Models. [Internet] [Doctoral dissertation]. The Ohio State University; 2017. [cited 2020 Nov 28]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1500379101560737.

Council of Science Editors:

Liu T. Model Selection and Adaptive Lasso Estimation of Spatial Models. [Doctoral Dissertation]. The Ohio State University; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1500379101560737

Penn State University

3. Zhu, Shengbo. Essays on Financial Economics and Econometrics.

Degree: 2020, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/18113szz126

In a recent seminal paper, Steve Ross proposed an attractive strategy to extract the physical distribution and risk aversion from just state prices. However, empirical papers that try to use his Recovery Theorem almost all lead to a depressing conclusion: the recovery theorem does not work. Both the state-price matrix and the recovered physical transition matrix are unreasonable and highly sensitive to subjective specifications and constraints. Borovička, Hansen and Scheinkman (2016) proposes a widely-accepted explanation for the empirical failure: according to the Hansen-Scheinkman decomposition established in Hansen and Scheinkman (2009), the assumption about the stochastic discount factor in Ross (2015) is equivalent to arbitrarily setting the martingale component to be 1, which is quite unlikely in reality. In Chapter 1, I argue that in contrast to Borovička, Hansen and Scheinkman (2016), the assumption about the stochastic discount factor in Ross (2015) actually does not set the martingale component in the Hansen-Scheinkman decomposition to be 1. What causes the empirical failure is actually a time-homogeneous state-price matrix, which induces quite restrictive implications on the underlying price process and those restrictions are easily violated in reality. In particular, when the underlying price is used as the state variable or as one component
of the state vector, this restriction becomes an eigenvalue equation that contradicts the important eigenvalue equation in Ross (2015), which in this case makes the Recovery Theorem not just empirically implausible, but also logically inconsistent.
Chapter 2 studies the following conceptual question: in what sense is the Fundamental Theorem of Asset Pricing similar to the two-period no-arbitrage theorem (a.k.a., Farkas lemma)? The purpose of studying this question is (1) to study the information that can be extracted from prices of derivatives in a multi-period context, generalizing the result in a two-period case in Breeden and Litzenberger (1978); (2) to find a way
to write down explicitly a multi-period arbitrage process, just as a two-period arbitrage can be written down as a vector. To answer the above conceptual question, I break it down into three more specific questions: (1) How to generalize the concept of states to a multi-period model? (2) How to generalize the concept of state price to a multi-period model? (3) In what sense is a multi-period arbitrage process similar to a two-period arbitrage strategy which is just a vector? The key to answering those questions is to explicitly describe the probability space on which price processes are defined, especially what “information flow” means. I adopt
the canonical probability space (i.e., the space of all possible paths of some price process) and propose to consider the whole path of as the state variable and the “path prices”(i.e., the equivalent martingale measure) as the analogue of state prices. This chapter discusses how we can recover prices of paths using prices of associated derivative securities and…
*Advisors/Committee Members: Andrew Ronald Gallant, Dissertation Advisor/Co-Advisor, Andrew Ronald Gallant, Committee Chair/Co-Chair, Patrik Guggenberger, Committee Member, Keisuke Hirano, Committee Member, Jingzhi Huang, Outside Member, Shouyong Shi, Committee Member, Marc Albert Henry, Program Head/Chair.*

Subjects/Keywords: Ross recovery theorem; equivalent martingale measure; stochastic discount factor; martingale condition; state price; path price; intrinsic inconsistency; implied process; fundamental theorem of asset pricing; canonical probability space; Markovian quasi-MLE; conditional asymptotic independence; mixing condition; near-epoch dependence

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Zhu, S. (2020). Essays on Financial Economics and Econometrics. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/18113szz126

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Zhu, Shengbo. “Essays on Financial Economics and Econometrics.” 2020. Thesis, Penn State University. Accessed November 28, 2020. https://submit-etda.libraries.psu.edu/catalog/18113szz126.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Zhu, Shengbo. “Essays on Financial Economics and Econometrics.” 2020. Web. 28 Nov 2020.

Vancouver:

Zhu S. Essays on Financial Economics and Econometrics. [Internet] [Thesis]. Penn State University; 2020. [cited 2020 Nov 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/18113szz126.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhu S. Essays on Financial Economics and Econometrics. [Thesis]. Penn State University; 2020. Available from: https://submit-etda.libraries.psu.edu/catalog/18113szz126

Not specified: Masters Thesis or Doctoral Dissertation