Date of Degree
Wim P. Vijverberg
Spatial econometrics, matrix exponential spatial specification
This thesis consists of three essays on the matrix exponential spatial specification. In the first essay, we study the generalized method of moments (GMM) estimation of matrix exponential spatial specification(p,q) (MESS(p,q)). We extend the model to a general higher order case and derive its GMM estimator. The large sample properties are also studied. Under homoskedasticity a best GMM estimator (BGMME) is derived and shown to be consistent and asymptotically normal. Under heteroskedasticity an optimal GMM estimator (OGMME) is derived and shown to be consistent and asymptotically normal as well. Monte Carlo experiments that discuss the large sample properties of quasi-maximum likelihood estimator (QMLE) and different GMM estimators are reported.
The standard error of the second-stage GMM estimator is known to be downward biased compared with the empirical standard deviation. In the second essay we utilize the finite sample correction method in Windmeijer (2005) to the best generalized methods of moment estimator (BGMME) of the matrix exponential spatial specification (MESS) to improve the inference. We first present MESS and discuss its assumptions and BGMME following previous literature (Debarsy et al., 2015). Then we describe how to apply the correction method to the BGMME. The corrected asymptotic standard error of the BGMME (CBGMME) is shown to better approximate the empirical standard deviation than that of the original BGMME in terms of having smaller percentage deviations. The better performance of the corrected standard error thus improves the inference in terms of having better size property, which holds under normal, non-normal and heteroskedastic disturbances. Results of Monte Carlo experiments are reported to show that the proposed CBGMME has excellent performance.
In the third essay, a unified M-estimation method is proposed for the matrix exponential spatial dynamic panel specification (MESDPS) with fixed effects in short panels. The quasi-maximum likelihood (QML) estimation for the dynamic panel data (DPD) model has long been known to have the initial condition specification problem. The MESDPS also suffers from this problem. The initial-condition free M-estimator in this paper solves this problem and is proved to be consistent and asymptotically normal. An outer product of martingale difference (OPMD) estimator for the variance-covariance (VC) matrix of the M-estimator is also derived and proved to be consistent. The finite sample properties of the M-estimator is studied through an extensive Monte Carlo study. The method is applied to US outward FDI data to show its validity.
Yang, Ye, "Three Essays on Spatial Econometrics: the Matrix Exponential Spatial Specification" (2021). CUNY Academic Works.