Sieve Maximum Likelihood Estimation of the Spatial Autoregressive Tobit Model
(with Lung-fei Lee, Job Market Paper 1, submitted to Journal of Econometrics)
This paper extends the ML estimation of a spatial autoregressive Tobit model under normal disturbances in Xu and Lee (2015, Journal of Econometrics) 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 weakly dependent, or more precisely, spatial near-epoch dependent (NED). An important contribution of this paper is that we develop some exponential inequalities for spatial NED random fields, which are also useful in other (e.g., 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.
(with Lung-fei Lee, Job Market Paper 1, submitted to Journal of Econometrics)
This paper extends the ML estimation of a spatial autoregressive Tobit model under normal disturbances in Xu and Lee (2015, Journal of Econometrics) 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 weakly dependent, or more precisely, spatial near-epoch dependent (NED). An important contribution of this paper is that we develop some exponential inequalities for spatial NED random fields, which are also useful in other (e.g., 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.
Estimation of a Binary Choice Game Model with Network Links
(with Lung-fei Lee, Job market paper 2)
This paper studies the simulated moment 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 in a network setting 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 simulated moment method by some Monte Carlo experiments.
(with Lung-fei Lee, Job market paper 2)
This paper studies the simulated moment 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 in a network setting 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 simulated moment method by some Monte Carlo experiments.
Maximum Likelihood Estimation of a Spatial Autoregressive Tobit Model
(with Lung-fei Lee, Journal of Econometrics, 188 (1), September 2015, pp.264-280)
This paper studies the MLE for a spatial autoregressive model with censored dependent variables. One challenging issue in this paper is how to handle a binary-valued function that appears in the log-likelihood function. We develop spatial NED properties of the dependent variable and related variables. Then we establish the consistency and asymptotic normality of the estimator by properties of spatial NED. We design some Monte Carlo experiments based on an empirical application studying the school district income tax rates in Iowa. These experiments show that the estimator has satisfactory finite-sample performance, if the distribution of the disturbance is not too far from a normal one.
(with Lung-fei Lee, Journal of Econometrics, 188 (1), September 2015, pp.264-280)
This paper studies the MLE for a spatial autoregressive model with censored dependent variables. One challenging issue in this paper is how to handle a binary-valued function that appears in the log-likelihood function. We develop spatial NED properties of the dependent variable and related variables. Then we establish the consistency and asymptotic normality of the estimator by properties of spatial NED. We design some Monte Carlo experiments based on an empirical application studying the school district income tax rates in Iowa. These experiments show that the estimator has satisfactory finite-sample performance, if the distribution of the disturbance is not too far from a normal one.
A Spatial Autoregressive Model with a Nonlinear Transformation of the Dependent Variable
(with Lung-fei Lee, Journal of Econometrics, 186(1), May 2015, pp.1-18)
This paper develops a spatial autoregressive model with a strictly increasing transformation on the dependent variable. Of particular interest is a structural interaction model for share data. We consider possible IV estimation and MLE for this model and analyze their consistency and asymptotic distributions based on spatial NED. We also design a statistical test to compare the nonlinear transformation against alternatives. Monte Carlo experiments are designed to investigate the finite-sample performance of the proposed estimator, and the size and power of the test.
(with Lung-fei Lee, Journal of Econometrics, 186(1), May 2015, pp.1-18)
This paper develops a spatial autoregressive model with a strictly increasing transformation on the dependent variable. Of particular interest is a structural interaction model for share data. We consider possible IV estimation and MLE for this model and analyze their consistency and asymptotic distributions based on spatial NED. We also design a statistical test to compare the nonlinear transformation against alternatives. Monte Carlo experiments are designed to investigate the finite-sample performance of the proposed estimator, and the size and power of the test.