Three Essays On Spatial Econometrics With An Emphasis On Testing

This dissertation is a combination of three essays on spatial econometrics and labor economics. Essays 1 and 2 developed double length regression (DLR) tests for testing functional form and spatial dependence, which includes spatial error dependence and spatial lag dependence. More specifically, these essays derive the DLR joint, DLR one-direction, and DLR conditional tests for testing functional forms and spatial dependence. The essays also provide empirical examples and Monte Carlo simulations to examine how the DLR tests perform in the empirical work and how the power of the DLR test depends on changes in functional form and spatial dependence. The results suggested that DLR tests work similarly to its Lagrangian Multiplier (LM) counterpart for testing functional form and spatial dependence in the empirical example and simulations. The DLR tests do not require the second-order derivatives of the log-likelihood function, so they provide practitioners an easy-to-use method to test for functional forms and spatial dependence. Essay 3 investigates the effects of fertility on parental labor force participation and labor supply in Vietnam. The essay uses instrumental variable (IV) probit models to estimate the effects of fertility on parental labor force participation and the IV models to estimate the effects of fertility on parental labor supply. Using the gender of the first child and the same gender of the first two children as two instrumental variables, this essay found negative effects of fertility on maternal labor force participation and labor supply. It also found positive effects of fertility on paternal labor force participation and labor supply. The results suggest that fertility had the specialization effect on parental labor force participation and labor supply in Vietnam. The homogeneity test results indicate that the magnitude of the effects of fertility on parental labor force participation and labor supply is different among parents and locations.

Chapter Two focuses on three classical tests, namely, Wald, LM, and LR, of spatial interactions in the simultaneous SAR Tobit model. We derive the asymptotic distributions of those three tests under both the null and the local alternative hypotheses, establish their asymptotic equivalence and local efficiency, and study finite sample properties using the Monte Carlo simulation. The tests are applied to an empirical example involving the school district income tax in Iowa in 2009. Among 361 school districts, 18.3 percent had rates of zero, so it fits the Tobit setting. Testing results indicate the existence of tax competition among neighboring school districts.

Abstract: The first essay explores the consequences of misspecified spatial interdependence structure in SAR models with a row-normalized weight matrix. I provide the analytical formulae for the asymptotic biases of the OLS estimator when a spatial weight matrix is over-specified, under-specified, or omitted in a simple linear regression model. I then design Monte Carlo experiments to study how a misspecified spatial weight matrix in the SAR model might impact the finite sample properties of the 2SLSE and MLE. The major finding is that an "over-specification" of the weight matrix causes less bias in 2SLSE and MLE as well as lower RMSE than an "under-specification." The results also strongly suggest that goodness of fit measures such as adjusted R-square and log-likelihood can serve as selection criteria for the choice of a spatial weight matrix. In the second essay, I consider the effectiveness of Wald, distance difference, minimum Chi-square, and gradient tests within GMM framework in selecting different specifications of spatial weights in SAR models. The two major results I obtain are (1) that for each of the five tests, GMM framework significantly improves the empirical power of the tests over 2SLS framework, and (2) that when performed in GMM framework, all five tests have suitable empirical size and power with similar performance outcomes. Finally, the third essay investigates the nature of competition in the retail gasoline market using a two year panel data of weekly prices for gas stations in San Diego County. I use IV methods to estimate several spatial autoregressive (SAR) models of stations' price reaction functions after specifying spatial weights based on distance between stations. By using the SAR model, I am able to identify that the brand of competing stations and their relative geographic proximity to the original station are important factors in explaining price variation across gasoline stations, as opposed to just the number of competing stations.

This Advanced Introduction provides a critical review and discussion of research concerning spatial statistics, differentiating between it and spatial econometrics, to answer a set of core questions covering the geographic-tagging-of-data origins of the concept and its theoretical underpinnings, conceptual advances, and challenges for future scholarly work. It offers a vital tool for understanding spatial statistics and surveys how concerns about violating the independent observations assumption of statistical analysis developed into this discipline.

The purpose of models is not to fit the data but to sharpen the questions. S. Karlin, 11th R. A. Fisher Memorial Lecture, Royal Society, 20 April 1983 We are proud to offer this volume in honour of the remarkable career of the Father of Spatial Econometrics, Professor Jean Paelinck, presently of the Tinbergen Institute, Rotterdam. Not one to model solely for the sake of modelling, the above quotation nicely captures Professor Paelinck's unceasing quest for the best question for which an answer is needed. His FLEUR model has sharpened many spatial economics and spatial econometrics questions! Jean Paelinck, arguably, is the founder of modem spatial econometrics, penning the seminal introductory monograph on this topic, Spatial Econometrics, with Klaassen in 1979. In the General Address to the Dutch Statistical Association, on May 2, 1974, in Tilburg, "he coined the term [spatial econometrics] to designate a growing body of the regional science literature that dealt primarily with estimation and testing problems encountered in the implementation of multiregional econometric models" (Anselin, 1988, p. 7); he already had introduced this idea in his introductory report to the 1966 Annual Meeting of the Association de Science Regionale de Langue Fran~aise.

My job market paper, "Bayesian Estimation of a Spatial Autoregressive Model with an Unobserved Endogenous Spatial Weight Matrix and Unobserved Factors", examines the specification and estimation of the SAR model with new features. Motivated by the spillover effects of state medicaid spending on welfare programs, we combine all these new features together for the first time in the SAR model. Specifically, we focus on two ways of defining neighborliness (a source of unobserved spatial weight matrix W): one based on geographical distance and the other on "economic" distance. In this particular application, endogeneity of W comes from the correlation of economic distance and the disturbances in the SAR equation. Unobserved factors are introduced to control for common shocks to all states. For the estimation of the model, the Bayesian MCMC method is employed, which is also supported by simulation results. We find that a dollar increase in a state's neighbors' Medicaid related spending will increase its own Medicaid related spending by about 52 cents. Both geographical and economic distances are shown to have significant effects on the interaction strength of state Medicaid related spending. Our results suggest that in the context of Medicaid spending, welfare motivated move and yardstick competition are both sources of strategic interactions among state governments.

Abstract: This dissertation consists of three chapters covering the following topics in spatial econometrics: estimation, specification and the bootstrap.

World-renowned experts in spatial statistics and spatial econometrics present the latest advances in specification and estimation of spatial econometric models. This includes information on the development of tools and software, and various applications. The text introduces new tests and estimators for spatial regression models, including discrete choice and simultaneous equation models. The performance of techniques is demonstrated through simulation results and a wide array of applications related to economic growth, international trade, knowledge externalities, population-employment dynamics, urban crime, land use, and environmental issues. An exciting new text for academics with a theoretical interest in spatial statistics and econometrics, and for practitioners looking for modern and up-to-date techniques.