Spatial panel data models: Unbalanced panel, threshold effect and network structure

• Main Author: MENG, Xiaoyu
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2022
• Subjects: Unbalanced panel; Adjusted quasi score; Spatial effects; Time-varying spatial weights; Threshold effects; Social interaction models; Multi-dimensional fixed effects; Econometrics
• Online Access: https://ink.library.smu.edu.sg/etd_coll/425; https://ink.library.smu.edu.sg/context/etd_coll/article/1423/viewcontent/GPEC_AY2017_PhD_Xiaoyu_Meng.pdf
• Institution: Singapore Management University

This thesis studies the estimation and inference problems for spatial panel data models when the panels are unbalanced, when the panels contain threshold effects, or when the panels contain time-varying network structures. These three scenarios divide the thesis naturally into three chapters. The first chapter considers estimation and inferences for fixed effects spatial panel data models based on unbalanced panels that result from randomly missing spatial units. The unbalanced nature of the panel data renders the standard method of estimation inapplicable. In this chapter, we proposed an M-estimation method where the estimating functions are obtained by adjusting the concentrated quasi scores to account for the estimation of fixed effects and/or the presence of unknown spatiotemporal heteroscedasticity. The method allows for general time-varying spatial weight matrices without row-normalization, and is able to give full control of the individual and time specific effects for all the spatial units involved in the data. Consistency and asymptotic normality of the proposed estimators are established. Inference methods are introduced and their consistency is proved. Monte Carlo results show excellent finite sample performance of the proposed methods. An empirical application is presented on commodity tax competition among US states. The second chapter introduces general estimation and inference methods for threshold spatial panel data models with two-way fixed effects (2FE) in a diminishing-threshold-effects framework. A valid objective function is first obtained by a simple adjustment on the concentrated quasi loglikelihood with 2FE being concentrated out, which leads to a consistent estimation of all common parameters including the threshold parameter. We then show that the estimation of threshold parameter has an asymptotically negligible effect on the asymptotic distribution of the other estimators, and thereby lead to valid inference methods for other common parameters after a bias correction. A likelihood ratio test is proposed for statistical inference on the threshold parameter. We also propose a sup-Wald test for the presence of threshold effects, based on an M-estimation method with the estimating functions being obtained by simply adjusting the concentrated quasi-score functions. Monte Carlo results show that the proposed methods perform well in finite samples. An empirical application is presented on age-of-leader effects on political competitions across Chinese cities. The third chapter considers the specification and estimation of a three-dimensional (3-D) spatial panel data model with time-varying network structures. The model allows for endogenous and exogenous interaction effects, correlation of unobservables, and most importantly group-specific effects that are allowed to interact with the individual and time specific effects. The time-varying network structures provide information on the identification of various interaction effects but also yield time-varying sociomatrices whose row sums may not be constant, which renders the transformation-based quasi maximum likelihood inapplicable. In this chapter, we propose an adjusted quasi score method where the estimating functions are obtained by adjusting the concentrated quasi scores (with fixed effects being concentrated out) to account for the effects of concentration. The method is able to give full control of general specifications of three-way fixed effects. Consistency and asymptotic normality of the proposed estimators are established. Monte Carlo results show excellent finite sample performance of the proposed methods.