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Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models

Xu, Xingbai, Xu
http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Economics.
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 field to be stochastically equicontinuous and we apply it to develop the consistency and asymptotic normality of the estimator. We examine computational issues and finite sample properties of the MSM by some Monte Carlo experiments.
Lung-fei Lee (Advisor)
Jason Blevins (Committee Member)
Robert de Jong (Committee Member)
194 p.
Economics
spatial econometrics, near-epoch dependence, maximum likelihood, method of simulated moments, large sample properties, Monte Carlo, sieve estimation, Tobit model, binary choice model

Recommended Citations

Citations

  • Xu, Xu, X. (2016). Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529

    APA Style (7th edition)

  • Xu, Xu, Xingbai. Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529.

    MLA Style (8th edition)

  • Xu, Xu, Xingbai. "Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529

    Chicago Manual of Style (17th edition)

osu1461249529
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This open access ETD is published by The Ohio State University and OhioLINK.