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This book provides an overview of three generations of spatial econometric models: models based on cross-sectional data, static models based on spatial panels and dynamic spatial panel data models. The book not only presents different model specifications and their corresponding estimators, but also critically discusses the purposes for which these models can be used and how their results should be interpreted.
In this paper, we study the spatial dynamic panel data models with high-order time-varying endogenous weights matrices. The quasi-maximum likelihood (QML) estimator is inconsistent under heteroskedastic errors and would be computationally complicated due to the evaluation of the Jacobian determinants in the likelihood function. To overcome these two issues, we propose the generalized method of moments (GMM) estimator and establish its asymptotic property under two scenarios: (i) finite T with large n, (ii) T can be large but small relative to n. We prove the consistency and asymptotic normality of these GMM estimators with finite or many moments. Furthermore, under homoskedastic errors, by designing appropriate moment conditions, the GMM estimator can be more efficient than the QML estimator. Monte Carlo simulations confirm that our proposed GMM estimators have satisfactory finite sample performances. We then apply our model to study multi-dimensional spillover effects of research and development (R&D) activities in China's listed firms. Empirical results show that market spillover dominates in the strategic interaction of R&D investments, while the technological spillover dominates in the innovation performance.
This paper develops a nonlinear spatial dynamic panel data model, with one particularly interesting application to a structural interaction model for share data. To account for effects from popular units, the spatial weights matrices in our model can allow for dominant units, with unbounded column sums. To account for heterogeneity, our model includes individual fixed effects and heteroskedastic errors. We further consider the potential time-varying endogeneity in spatial weights when weights are constructed by socioeconomic distances. For parameter estimation, we propose the quasi-maximum likelihood estimator (QMLE), generalized methods of moments estimator (GMME) and root estimator (RTE), and establish their consistency and asymptotic normality based on the near epoch dependence (NED) framework. We show that the RTE is asymptotically as efficient as the QMLE in the homoskedastic case, and is asymptotically as efficient as the GMME in the heteroskedastic case. For the panel data setting, we cover both $n,T rightarrow infty$ and large $n$ with finite $T$, and the strength of the dominant units equals to 1 as long as $T rightarrow infty$. In the empirical application, we apply our model to China's prefectural city-level data and find significant spillover effects of the employment share of tertiary industry, indicating that the development of tertiary industry in large cities can promote the tertiary industry in small cities.
This paper considers a class of GMM estimators for general dynamic panel models, allowing for cross sectional dependence due to spatial lags and due to unspecified common shocks. We significantly expand the scope of the existing literature by allowing for endogenous spatial weight matrices, time-varying interactive effects, as well as weakly exogenous covariates. The model is expected to be useful for empirical work in both macro and microeconomics. An important area of application is in social interaction and network models where our specification can accommodate data dependent network formation. We discuss explicit examples from the recent social interaction literature. Identification of spatial interaction parameters is achieved through a combination of linear and quadratic moment conditions. We develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions. This is an important ingredient to a tractable asymptotic distribution of our estimators. In the social interactions example, orthogonal forward differencing amounts to controlling for unobserved correlated effects by combining multiple outcome measures.
My dissertation research addresses issues in spatial panel data models, which study the interactions of economic units across space and time. Individuals interact with their neighbors and the outcomes are interdependent. The strength of the interaction depends on the distance between the individuals, which can be based on geography or constructed from economic theory. Accounting for spatial interactions allows one to quantify both the direct effect of a variable and its indirect effect through impacting neighbors. However, two issues often arise. First, spatial dependence can be alternatively generated from common unobserved factors (e.g. economy-wide shocks) where neighbors have similar responses. Second, the distance between economic units can be endogenous, and this will in fact be the case if the distance is constructed from variables that correlate with disturbances in the outcomes. The first chapter studies the estimation of a dynamic spatial panel data model with interactive individual and time effects with large n and T. The model has a rich spatial structure including contemporaneous spatial interaction and spatial heterogeneity. Dynamic features include individual time lag and spatial diffusion. In a standard two way fixed effects panel regression model, the unobservables contain an individual specific but time invariant component, and a component that is time variant but common across individuals. We generalize this model by allowing the interaction between time effects and individual effects. This chapter provides a tool for empirical researchers to guard against attributing correlated responses to common time effects as spatial effects. The interactive effects are treated as parameters, so as to allow correlations between the interactive effects and the regressors. We consider a quasi-maximum likelihood estimation and show estimator consistency and characterize its asymptotic distribution. The Monte Carlo experiment shows that the estimator performs well and the proposed bias correction is effective. The second chapter proposes a unified approach to model endogenous spatial dependences while accounting for common factors. The spatial weights matrices are constructed from variables that may correlate with the disturbances in the outcomes. We make minimal assumptions on the distributions of the factors and follow a fixed effects approach. We provide conditions under which the quasi-maximum likelihood estimator is consistent and asymptotically normal, under the asymptotics where both the cross section and time dimensions become large. The limiting distribution is normal but may not be centered for the estimates of the spatial interaction coefficient and the variances. An analytical bias correction is proposed to improve the inference. The Monte Carlo simulations demonstrate good finite sample properties of the bias corrected estimator. We illustrate the empirical relevance of the theory by applying the method to analyze the effect of house price dynamics on reverse mortgage origination rates.
The second edition of a comprehensive state-of-the-art graduate level text on microeconometric methods, substantially revised and updated. The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.
The Oxford Handbook of Panel Data examines new developments in the theory and applications of panel data. It includes basic topics like non-stationary panels, co-integration in panels, multifactor panel models, panel unit roots, measurement error in panels, incidental parameters and dynamic panels, spatial panels, nonparametric panel data, random coefficients, treatment effects, sample selection, count panel data, limited dependent variable panel models, unbalanced panel models with interactive effects and influential observations in panel data. Contributors to the Handbook explore applications of panel data to a wide range of topics in economics, including health, labor, marketing, trade, productivity, and macro applications in panels. This Handbook is an informative and comprehensive guide for both those who are relatively new to the field and for those wishing to extend their knowledge to the frontier. It is a trusted and definitive source on panel data, having been edited by Professor Badi Baltagi-widely recognized as one of the foremost econometricians in the area of panel data econometrics. Professor Baltagi has successfully recruited an all-star cast of experts for each of the well-chosen topics in the Handbook.