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Author: Abhimanyu Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Abhimanyu Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Abhimanyu Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Kai Yang
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Databases with cross-sectional interdependent variables have highlighted the need for new data analysis techniques to model interdependence patterns cross-sectional units. Among various models to describe the interdependence, spatial autoregressive models (SAR) have attracted much attention. The theory and practice of single dependent variable SAR have been well established. Although a large number of economic theories may concern about interrelations among several economic variables, econometric studies regarding multivariate and simultaneous equations SAR models are limited. This dissertation is filling in this gap. This dissertation is composed of two chapters, the first chapter focuses on models with cross-sectional data, while the second chapter is on models in panel data which incorporates both intertemporal dynamics and spatial interdependence. The first chapter investigates a simultaneous equations spatial autoregressive model which incorporates simultaneity effects, own-variable spatial lags and cross-variable spatial lags as explanatory variables, and allows for correlation between disturbances across equations. In exposition, this chapter also discusses a multivariate spatial autoregressive model that can be treated as a reduced form of the simultaneous equations model. For a multivariate model, we provide identification conditions in terms of the existence of instruments for spatial lags and regularities of the weight matrix structure. Rank conditions and order conditions are provided for identification of structural parameters in the simultaneous equations model. In this chapter we study parameter spaces, the parameter identification, asymptotic properties of the quasi-maximum likelihood estimation, and computational issues. Monte Carlo experiments illustrate the advantages of the QML, broader applicability and efficiency, compared to instrumental variables based estimation methods in the existing literature. The second chapter introduces multivariate and simultaneous equations dynamic panel spatial autoregressive models in the cases of stability and spatial cointegration. A spatial unit is assumed to depend on its lagged term, and to respond to its neighbours' or peers' behaviour in the current period (spatial lags), and in the previous period (space-time lags). The disturbances in the model are specified with time fixed effects and individual fixed effects in addition to idiosyncratic disturbances. This chapter investigates identification for the model with simultaneous effects, time dynamic effects, and spatial effects. In the estimation of stable and spatially cointegrated models, we investigate QMLE and establish asymptotic properties of the estimator. Convergence rates of parameters may change depending on variables being stable or unstable. We analyze asymptotic biases and suggest bias-corrected estimates. We also study a robust estimation method which can be applied to stable case, spatial cointergration case and some spatial explosion cases. We apply the model to study the grain market integration using a unique historical dataset of rice and wheat prices of 65 cities in 49 years in Yangtze River Basin. The empirical result shows that rice and wheat prices are spatially cointegrated across cities. These results provide evidences of interregional and intertemporal grain market integration and trading network in the eighteenth-century Yangtze River basin.
Author: Yang Yang (Econometrics researcher)
Publisher:
ISBN:
Category : Econometrics
Languages : en
Pages : 0
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Spatial econometrics models, especially the spatial autoregressive (SAR) model and its extension to panel settings had been used widely in empirical research in several different fields, especially when we need to capture the effects from networks. However, more empirical researchers are focusing on new questions where the linear spatial econometrics models could not handle. My dissertation tries to extend traditional models to capture two types of effect: risk spillover through financial networks and heterogeneous peer effect through social networks, and develops likelihood approach to estimate these models. Chapter 1 tries to incorporate risk spillover effect with GARCH type models. By introducing both intra-temporal and inter-temporal risk spillover through network, we propose a new multivariate conditional volatility model. For stationary case, the model can capture the dynamic of conditional heteroskedasticity structure when there are long-run stable links among multiple markets, and it is easy to be estimated consistently by QMLE approach. By Monte Carlo simulations, we show good finite sample performance when n/T → 0. When applying the model to monthly stock return innovations of 11 eurozone countries from March 1999 to April 2021, by using geographical and institutional links to capture the network between the countries, the performance of our model dominates single variate GARCH(1,1), EGARCH(1,1) and multivariate GARCH with both constant correlation and dynamic conditional correlation settings by likelihood values and AIC criteria. ii Chapter 2 considers social interaction models with group fixed effects and observed heterogeneity among agents. By likelihood approach, with the control of group-level confounding effects of the common variables, both heterogeneous endogenous peer effects and exogenous contextual effects can be identified and estimated consistently. Under some regularity assumptions, we prove the consistency and asymptotic normality of the QMLE. Monte Carlo simulation results show that our QMLE has good finite sample performance. For an application, we investigate the China Education Panel Survey (CEPS) and focus on gender heterogeneity on academic achievement of Grade 8 students in junior high school. We capture significant gender disparities in peer effects from gender subgroups in a classroom. Besides, female students’ test scores are more subject to both female and male peers’ average achievement.
Author: Wei Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 147
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Abstract: This dissertation is composed of three essays on spatial econometric models with missing data. Spatial models that have a long history in regional science and geography have received substantial attention in various areas of economics recently. Applications of spatial econometric models prevail in urban, developmental and labor economics among others. In practice, an issue that researchers often face is the missing data problem. Although many solutions such as list-wise deletion and EM algorithm can be found in literature, most of them are either not suited for spatial models or hard to apply due to technical difficulties. My research focuses on the estimation of the spatial econometric models in the presence of missing data problems. The first chapter develops a GMM method based on linear moments for the estimation of mixed regressive, spatial autoregressive (MRSAR) models with missing observations in the dependent variables. The estimation method uses the expectation of the missing data, as a function of the observed independent variables and the parameters to be estimated, to replace the missing data themselves in the estimation. The proposed GMM estimators are shown to be consistent and asymptotically normal. Feasible optimal weighting matrix for the GMM estimation is given. We extend our estimation method to MRSAR models with heteroskedastic disturbances, high order MRSAR models and unbalanced spatial panel data models with random effects as well. From these extensions, we see that the proposed GMM method has more compatibility, compared with the conventional EM algorithm. The second chapter considers a group interaction model first proposed by Lee (2006); this model is a special case of the spatial autoregressive (SAR) models. It is a first attempt to estimate the model in a more general random sample setting, i.e. a framework in which only a random sample rather than the whole population in a group is available. We incorporate group heteroskedasticity along with the endogenous, exogenous and group fixed effects in the model. We prove that, under some basic assumptions and certain identification conditions, the quasi maximum likelihood (QML) estimators are consistent and asymptotically normal when the functional form of the group heteroskedasticity is known. Two types of misspecifications are considered, and, under each, the estimators are inconsistent. We also propose IV estimation in the case that the group heteroskedasticity is unknown. A LM test of group heteroskedasticity is given at the end. The third chapter considers the same group interaction model as that in the second chapter, but focuses on the large group interaction case and uses a random effects setting for the group specific characters. A GMM estimation framework using moment conditions from both within and between equations is applied to the model. We prove that under some basic assumptions and certain identification conditions, the GMM estimators are consistent and asymptotically normal, and the convergence rates of the estimators are higher than those of the estimators derived from the within equations only. Feasible optimal GMM estimators are proposed.
Author: Sang-Yeob Lee
Publisher:
ISBN:
Category : Econometrics
Languages : en
Pages : 117
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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.
Author: Qu, Xi
Publisher:
ISBN:
Category :
Languages : en
Pages : 158
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Book Description
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.
Author: Baris M. Kazar
Publisher: Springer Science & Business Media
ISBN: 1461418429
Category : Computers
Languages : en
Pages : 81
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Book Description
Explosive growth in the size of spatial databases has highlighted the need for spatial data mining techniques to mine the interesting but implicit spatial patterns within these large databases. This book explores computational structure of the exact and approximate spatial autoregression (SAR) model solutions. Estimation of the parameters of the SAR model using Maximum Likelihood (ML) theory is computationally very expensive because of the need to compute the logarithm of the determinant (log-det) of a large matrix in the log-likelihood function. The second part of the book introduces theory on SAR model solutions. The third part of the book applies parallel processing techniques to the exact SAR model solutions. Parallel formulations of the SAR model parameter estimation procedure based on ML theory are probed using data parallelism with load-balancing techniques. Although this parallel implementation showed scalability up to eight processors, the exact SAR model solution still suffers from high computational complexity and memory requirements. These limitations have led the book to investigate serial and parallel approximate solutions for SAR model parameter estimation. In the fourth and fifth parts of the book, two candidate approximate-semi-sparse solutions of the SAR model based on Taylor's Series expansion and Chebyshev Polynomials are presented. Experiments show that the differences between exact and approximate SAR parameter estimates have no significant effect on the prediction accuracy. In the last part of the book, we developed a new ML based approximate SAR model solution and its variants in the next part of the thesis. The new approximate SAR model solution is called the Gauss-Lanczos approximated SAR model solution. We algebraically rank the error of the Chebyshev Polynomial approximation, Taylor's Series approximation and the Gauss-Lanczos approximation to the solution of the SAR model and its variants. In other words, we established a novel relationship between the error in the log-det term, which is the approximated term in the concentrated log-likelihood function and the error in estimating the SAR parameter for all of the approximate SAR model solutions.
Author: Xu Lin
Publisher:
ISBN:
Category : Autoregression (Statistics)
Languages : en
Pages : 119
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Abstract: As an effective method in analyzing interdependence among the observations, the spatial autoregressive (SAR) models have witnessed ever-increasing applications. This dissertation intends to enrich both the spatial econometrics theory and the social interaction estimations. In the first essay, a SAR model with group unobservables is applied to analyze peer effects in student academic achievement. Unlike the linear-in-means model in Manski (1993), the SAR model can identify both endogenous and contextual social effects due to variations in the peer measurements, thus resolving the "reflection problem". The group fixed effects term captures the confounding effects of the common variables faced by the same group members. I use datasets from the National Longitudinal Study of Adolescent Health (Add Health) survey and specify peer groups as friendship networks. I find evidence for both endogenous and contextual effects, even after controlling for school-grade fixed effects. The result indicates that students benefit from the presence of high quality peers, and that associating with peers living with both parents helps improve a student's GPA, while associating with peers whose mothers receive welfare has a negative effect. The second essay considers the GMM estimation of SAR models with unknown heteroskedasticity. We show that MLE is inconsistent whereas GMM estimators obtained from certain moment conditions are robust. Asymptotically valid inferences can be drawn from the consistent covariance matrix estimator. And efficiency can be improved by constructing the optimal weighted GMM estimation. We also propose some general tests for heteroskedasticity. In the Monte Carlo study, 2SLS estimators have large variances and biases in finite samples for cases where regressors do not have strong effects. The robust GMM estimator has desirable properties while the biases associated with MLE and non-robust GMM estimator may remain in large sample, especially, for the spatial effect coefficient and the intercept term. However, the magnitudes of biases are only moderate and those biases may be statistically insignificant with moderate large sample sizes. The various approaches are applied to the study of county teenage pregnancy rates. The results suggest a strong spatial convergence among county teenage pregnancy rates with a significant spatial effect.
Author: Aman Ullah
Publisher: CRC Press
ISBN: 1482269902
Category : Business & Economics
Languages : en
Pages : 646
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Book Description
This work examines theoretical issues, as well as practical developments in statistical inference related to econometric models and analysis. This work offers discussions on such areas as the function of statistics in aggregation, income inequality, poverty, health, spatial econometrics, panel and survey data, bootstrapping and time series.
