Modeling and Estimation Issues in Spatial Simultaneous Equations Models

Spatial dependence is one of the main problems in stochastic processes and can be caused by a variety of measurement problems that are associated with the arbitrary delineation of spatial units of observation (such as counties boundaries, census tracts), problems of spatial aggregation, and the presence of spatial externalities and spillover effects. The existence of spatial dependence would then mean that the observations contain less information than if there had been spatial independence. Consequently, hypothesis tests and the statistical properties for estimators in the standard econometric approach will not hold. Thus, in order to obtain approximately the same information as in the case of spatial independence, the spatial dependence needs to be explicitly quantified and modeled. Although advances in spatial econometrics provide researchers with new avenues to address regression problems that are associated with the existence of spatial dependence in regional data sets, most of the applications have, however, been in single-equation frame-works. Yet, for many economic problems there are both multiple endogenous variables and data on observations that interact across space. Therefore, researchers have been in the undesirable position of having to choose between modeling spatial interactions in a single equation frame-work, or using multiple equations but losing the advantage of a spatial econometric approach. In an attempt to address this undesirable position, this research work deals with the modeling and estimation issues in spatial simultaneous equations models. The first part discusses modeling issues in multi-equation Spatial Lag, Spatial Error, and Spatial Autoregressive Models in both cross sectional and panel data sets. Whereas, the second part deals with estimation issues in spatial simultaneous equations models in both cross sectional and panel data sets. Finally, issues related specification tests in spatial simultaneous equations models are discussed

Modeling Small Business Growth, Migration Behavior, Local Public Services and Household Income in Appalachia: A Spatial Simultaneous Equations Approach

In this paper, a spatial simultaneous growth equilibrium model of small business growth, migration behavior, median household income and local public expenditures is developed. The model is empirically estimated by Generalized Spatial Three-Stage Least Squares estimator using count-level data from Appalachia for 1990-2000. The results suggest the existence of interdependence among the growth rates of small business, gross in-and out-migration, median household income and local public services in the form of feedback simultaneities, spatial autoregressive lag and spatial cross-regressive lag simultaneities. The findings also suggest the existence of conditional convergence with respect to endogenous variables of the model. The speeds of adjustment towards the steady states, however, are very slow which would cover many generations. The growth rate of median household income with a half–life time of about 9 years is the fastest and the growth rate of gross in-migration with a half-life time of about 180 years is the slowest to adjust. The findings also indicate the clustering of counties on the bases of their growth rates of median household incomes which would require the need for development policy coordination at the regional level, a region being defined as a group of counties, or the whole Appalachia. Another key finding of the study is also that Appalachian counties with higher initial population sizes were both destinations and sources of migrants during the study period

County-Level Determinants of Local Public Services in Appalachia: A Multivariate Spatial Autoregressive Model Approach

In this paper, multivariate spatial autoregressive model of local public expenditure determination is developed. The empirical model is developed based on maximization of community utility function. The model is estimate by efficient GMM using Appalachian counties and the results indicate significant spatial spillover effects with respect to local public expenditures.Public Economics,

THE ROLE OF SMALL BUSINESS IN ECONOMIC GROWTH AND POVERTY ALLEVIATION IN WEST VIRGINIA: AN EMPIRICAL ANALYSIS

In OLS and 2SLS regression analysis a positive relationship exists between small business and economic growth. A strong inverse relationship also exists between the incidence of poverty and small business and economic growth. Thus, the empirical result establishes the linkage between small business, economic growth and the incidence of povertyResearch Methods/ Statistical Methods,

A SPATIAL MODEL OF REGIONAL VARIATIONS IN EMPLOYMENT GROWTH IN APPALACHIA

In this study, a spatial equilibrium model of employment growth is developed and empirically estimated by Generalized Spatial Two-Stage Least Squares (GS2SLS) estimator using cross-sectional data from Appalachian counties for 1990-2000. Besides the existence of spatial spillover effects, the results suggest that agglomerative effects that arise from the demand and the supply side contribute to employment growth in the study area during the study period. The policy implications of the findings are: (1) Regional cooperation of counties and communities is advisable and may in fact be necessary to design effective policies to encourage employment growth; and (2) Policy makers at the county level may need to design policies that can attract people with high endowments of human capital and higher income into their respective counties.APPALACHIA, EMPLOYMENT GROWTH, SPATIAL MODEL

A Spatial Panel Simultaneous-Equations Model of Business Growth, Migration Behavior, Local Public Services and Household Income in Appalachia

In this paper we develop a spatial panel simultaneous-equations model of business growth, migration behavior, local public services and median household income in a partial lag-adjustment growth-equilibrium framework and utilizing a one-way error component model for the disturbances. This model is an extension of the jobs follow people or people follow jobs literature and it improved previous models in the growth-equilibrium tradition by: (1) explicitly modeling local government and regional income in the growth process; (2) explicitly modeling gross in-migration and gross out-migration separately in order to spell out the differential effects, which used to be glossed over under net population change in previous studies; (3) explicitly incorporating both spatially lagged dependent variables and spatially lagged error terms to account for spatial spillover effects in the data set; and (4) extending and generalizing the modeling and estimation of simultaneous systems of spatially interrelated cross sectional equations into a panel data setting. To estimate the model, we develop a five-step new estimation strategy by generalizing the Generalized Spatial Three-Stage Least Squares (GS3SLS) approach outlined in Kelejian and Prucha (2004) into a panel data setting. The empirical implementation of the model uses county-level data from the 418 Appalachian counties for 1980-2000. Generally, the results from these model estimations are consistent with the theoretical expectations and empirical findings in the equilibrium growth literature and provide support to the basic hypotheses of this study. First, the estimates show the existence of feedback simultaneities among the endogenous variables of the model. Second, the results also show the existence of conditional convergence with respect to the respective endogenous variable of each equation of the model and the speed of adjustment parameters are generally comparable to those in literature. Third, the results from the parameter estimation of the model indicate the existence of spatial autoregressive lag effects and spatial cross-regressive lag effects with respect to the endogenous variables of the model. One of the key conclusions is that sector specific policies should be integrated and harmonized in order to give the desirable outcome. Besides, regionally focusing resources for development policy may yield greater returns than treating all locations the same.Community/Rural/Urban Development,

A Spatial Panel Simultaneous-Equations Model of Business Growth, Migration Behavior, Local Public Services and Household Income in Appalachia

In this paper we develop a spatial panel simultaneous-equations model of business growth, migration behavior, local public services and median household income in a partial lag-adjustment growth-equilibrium framework and utilizing a one-way error component model for the disturbances. This model is an extension of the “jobs follow people or people follow jobs” literature and it improved previous models in the growth-equilibrium tradition by: (1) explicitly modeling local government and regional income in the growth process; (2) explicitly modeling gross in-migration and gross out-migration separately in order to spell out the differential effects, which used to be glossed over under net population change in previous studies; (3) explicitly incorporating both spatially lagged dependent variables and spatially lagged error terms to account for spatial spillover effects in the data set; and (4) extending and generalizing the modeling and estimation of simultaneous systems of spatially interrelated cross sectional equations into a panel data setting. To estimate the model, we develop a five-step new estimation strategy by generalizing the Generalized Spatial Three-Stage Least Squares (GS3SLS) approach outlined in Kelejian and Prucha (2004) into a panel data setting. The empirical implementation of the model uses county-level data from the 418 Appalachian counties for 1980-2000. Generally, the results from these model estimations are consistent with the theoretical expectations and empirical findings in the equilibrium growth literature and provide support to the basic hypotheses of this study. First, the estimates show the existence of feedback simultaneities among the endogenous variables of the model. Second, the results also show the existence of conditional convergence with respect to the respective endogenous variable of each equation of the model and the speed of adjustment parameters are generally comparable to those in literature. Third, the results from the parameter estimation of the model indicate the existence of spatial autoregressive lag effects and spatial cross-regressive lag effects with respect to the endogenous variables of the model. One of the key conclusions is that sector specific policies should be integrated and harmonized in order to give the desirable outcome. Besides, regionally focusing resources for development policy may yield greater returns than treating all locations the same

An Empirical Analysis of Employment, Migration, Local Public Services and Regional Income Growth in Appalachia

This study develops a five-equation simultaneous system in a partial lagadjustment growth-equilibrium framework. It improved previous models in the growthequilibrium tradition by explicitly modeling local government and regional income in the growth process. It also explicitly modeled gross in-migration and gross out-migration separately in order to spell out the differential effects. The results show the existence of feedback simultaneities among the endogenous variables of the model. This finding is important from economic policy perspective because it indicates that sector specific policies should be integrated and harmonized in order to achieve the desirable outcome. Under this circumstance, looking at the direct plus indirect impacts of a change in a given policy is important

A Spatial Model of Regional Variations in Business Growth in Appalachian States

In this study, a spatial growth equilibrium model of business growth is developed and empirically estimated by Generalized Spatial Two-Stage Least Squares (GS2SLS) estimator using cross-sectional data from Appalachian States counties for 1990-2000. Beside the existence of spatial spillover effects, the results suggest that agglomerative effects that arise from both the demand and the supply sides were active in contributing to business growth in the study area during the study period. The policy implications of these findings are: (1) Regional cooperation of counties and communities is advisable and may even in fact be necessary to design appropriate policies that encourage business growth; and (2) Policy makers at the county level may need to design policies that can attract people with high endowment of human capital and higher income into their respective counties

Anemia prevalence in women of reproductive age in low- and middle-income countries between 2000 and 2018

Anemia is a globally widespread condition in women and is associated with reduced economic productivity and increased mortality worldwide. Here we map annual 2000–2018 geospatial estimates of anemia prevalence in women of reproductive age (15–49 years) across 82 low- and middle-income countries (LMICs), stratify anemia by severity and aggregate results to policy-relevant administrative and national levels. Additionally, we provide subnational disparity analyses to provide a comprehensive overview of anemia prevalence inequalities within these countries and predict progress toward the World Health Organization’s Global Nutrition Target (WHO GNT) to reduce anemia by half by 2030. Our results demonstrate widespread moderate improvements in overall anemia prevalence but identify only three LMICs with a high probability of achieving the WHO GNT by 2030 at a national scale, and no LMIC is expected to achieve the target in all their subnational administrative units. Our maps show where large within-country disparities occur, as well as areas likely to fall short of the WHO GNT, offering precision public health tools so that adequate resource allocation and subsequent interventions can be targeted to the most vulnerable populations