Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with Moving Average Disturbance Term

In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. I provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters

GMM Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

We consider a spatial econometric model containing a spatial lag in the dependent variable and the disturbance term with an unknown form of heteroskedasticity in innovations. We first prove that the maximum likelihood (ML) estimator for spatial autoregressive models is generally inconsistent when heteroskedasticity is not taken into account in the estimation. We show that the necessary condition for the consistency of the ML estimator of spatial autoregressive parameters depends on the structure of the spatial weight matrices. Then, we extend the robust generalized method of moment (GMM) estimation approach in Lin and Lee (2010) for the spatial model allowing for a spatial lag not only in the dependent variable but also in the disturbance term. We show the consistency of the robust GMM estimator and determine its asymptotic distribution. Finally, through a comprehensive Monte Carlo simulation, we compare finite sample properties of the robust GMM estimator with other estimators proposed in the literature

Teaching Size and Power Properties of Hypothesis Tests Through Simulations

In this study, we review the graphical methods suggested in Davidson and MacKinnon (Davidson, Russell, and James G. MacKinnon. 1998. “Graphical Methods for Investigating the Size and Power of Hypothesis Tests.” The Manchester School 66 (1): 1–26.) that can be used to investigate size and power properties of hypothesis tests for undergraduate and graduate econometrics courses. These methods can be used to assess finite sample properties of various hypothesis tests through simulation studies. In addition, these methods can be effectively used in classrooms to reinforce students’ understanding of basic hypothesis testing concepts such as Type I error, Type II error, size, power, p-values and under-or-over-sized tests. We illustrate the procedural aspects of these graphical methods through Monte Carlo experiments, and provide the implementation codes written in Matlab and R for the classroom applications

Essays On Spatial Econometrics: Estimation Methods And Applications

This dissertation consists of four essays on the estimation methods and applications of spatial econometrics models. In the first essay, we consider a spatial econometric model containing spatial lags in the dependent variable and the disturbance terms with an unknown form of heteroskedasticity in the innovations. We first prove that the maximum likelihood estimator (MLE) is generally inconsistent when heteroskedasticity is not taken into account in the estimation. We show that the necessary condition for consistency of the MLE depends on the specification of the spatial weight matrices. Then, we extend the robust generalized method of moment (GMM) estimation approach in Lin and Lee (2010) for the spatial models allowing for a spatial lag not only in the dependent variable but also in the disturbance term. We show the consistency of the robust GMM estimator and determine its asymptotic distribution. Finally, through a comprehensive Monte Carlo simulation, we compare the finite sample properties of the robust GMM estimator with other estimators proposed in the literature. In the second essay, the finite sample properties of heteroskedasticity robust estimators suggested for the spatial autoregressive models are compared through simulation studies. Most of the estimators suggested for the estimation of spatial autoregressive models are inconsistent in the presence of an unknown form of heteroskedasticy. The estimators formulated from the GMM and the Bayesian Markov Chain Monte Carlo (MCMC) frameworks can be robust to an unknown form of heterokedasticity. In this essay, the finite sample properties of the robust GMM estimators and the Bayesian estimators based on MCMC approach are compared for the spatial autoregressive models. To this end, a comprehensive Monte Carlo simulation is designed for the spatial models containing a spatial lag in the dependent variable and/or disturbance term. In the second part of the study, two empirical applications are provided to show how heteroskedasticity robust estimators are performing in applied research. In the third essay, we investigate the properties of spatial autoregressive models that have a spatial moving average process in the disturbance term. The spatial moving average process introduces a different interaction structure among observations. In the first part of this essay, we describe the transmission and the effect of shocks under a spatial moving average process. In the second part, we investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. We show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. We also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. We provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters. In the fourth essay, we analyze the effect of foreign direct investment (FDI) on economic activity through a spatially augmented Solow growth model that takes technological interdependence into account. The technological interdependence manifests itself through spatial externalities which allow technology level of a country to depend on technology levels of its neighbors. Based on this modified growth model, we derive regression specifications and study the impact of FDI on economic growth. The spatial autocorrelation, often cited in the empirical growth literature, is properly accounted for through these new specifications. Estimations are carried out with the tools from spatial econometrics. Our findings indicate that FDI inflows have a significant positive effect on the growth rate of host countries

A Review of Cross-Sectional Matrix Exponential Spatial Models

The matrix exponential spatial models exhibit similarities to the conventional spatial autoregressive model in spatial econometrics but offer analytical, computational, and interpretive advantages. This paper provides a comprehensive review of the literature on the estimation, inference, and model selection approaches for the cross-sectional matrix exponential spatial models. We discuss summary measures for the marginal effects of regressors and detail the matrix-vector product method for efficient estimation. Our aim is not only to summarize the main findings from the spatial econometric literature but also to make them more accessible to applied researchers. Additionally, we contribute to the literature by introducing some new results. We propose an M-estimation approach for models with heteroskedastic error terms and demonstrate that the resulting M-estimator is consistent and has an asymptotic normal distribution. We also consider some new results for model selection exercises. In a Monte Carlo study, we examine the finite sample properties of various estimators from the literature alongside the M-estimator.Comment: 60 pages, 4 table

Comparison of uterine, endometrial and ovarian blood flow by transvaginal color Doppler ultrasound in ovulatory and anovulatory cycles

Objectives: Blood flow to uterus and ovaries is demonstrated to be altered during mensturation. Studies has been published stating that blood flow differs also in ovulatory and anovulatory cycles. In this study, using color Doppler ultrasound, we aim to compare uterine, endometrial and ovarian blood flow during ovulatory and anovulatory cycles. Material and methods: Women volunteers who are aged between 18–40 had no endocrinological problem and not recieving exogenous hormone therapy were included to study. Blood levels of FSH, LH, E2, prolactine, DHEAS, free T4 were collected in early follicular phase. Uterina, subendometrial and intraovarian artery blood flow pulsatility and resistance indexes were analysed using Doppler USG technique. Patients were called out to control on 21st of cycle and progesterone levels were analysed. Patients who has ovulation signs in USG and progesterone level above 5 ng/mL were included to ovulatory cycle group. Patient who has no signs of ovulation in ultrasound and has not enough progesterone level were included to anovulatory cycle group. Results: LH and E2 levels were significantly higher in anovulatory patients. No correlation was found between endometrial blood flow resistance and basal E2, prolactine, testosterone levels. However, DHEAS levels were related to endometrial blood flow resistance in anovulatory cycles. No correlation was found between ovarian blood flow resistance/uterine blood flow resistance and basal E2, prolactine, testosterone, DHEAS levels. Conclusions: There is statistically significant difference between endometrial, ovarian, uterine artery blood flow resistance in ovulatory and anovulatory cycles. Blood flow resistance was found to be increased in anovulatory patients. Increased E2 levels in anovulatory cycles were related to endometrial linethickness and endometrial volum

Assessing The Relationship Between Liberalization, Ownership And Performance: The Case Of Turkish Banks

This paper employs a DEA-type Malmquist index approach to evaluate the impact of financial liberalization on the productivity changes of public, private and foreign banks in Turkey during the period between 1981 and 1990. The results indicate that all forms of banks have benefited from financial liberalization. However, foreign banks were found to be the most productive, followed by private banks and public banks respectively. The major source of productivity gains is scale changes for public and private banks and technical progress for foreign banks. It also seems that productivity growth indices of all banks converge towards the end of liberalization period

Bayesian Inference in Spatial Sample Selection Models

In this study, we consider Bayesian methods for the estimation of a sample selection model with spatially correlated disturbance terms. We design a set of Markov chain Monte Carlo (MCMC) algorithms based on the method of data augmentation. The natural parameterization for the covariance structure of our model involves an unidentified parameter that complicates posterior analysis. The unidentified parameter -- the variance of the disturbance term in the selection equation -- is handled in different ways in these algorithms to achieve identification for other parameters. The Bayesian estimator based on these algorithms can account for the selection bias and the full covariance structure implied by the spatial correlation. We illustrate the implementation of these algorithms through a simulation study

Bayesian Inference in Spatial Sample Selection Models

In this study, we consider Bayesian methods for the estimation of a sample selection model with spatially correlated disturbance terms. We design a set of Markov chain Monte Carlo (MCMC) algorithms based on the method of data augmentation. The natural parameterization for the covariance structure of our model involves an unidentified parameter that complicates posterior analysis. The unidentified parameter -- the variance of the disturbance term in the selection equation -- is handled in different ways in these algorithms to achieve identification for other parameters. The Bayesian estimator based on these algorithms can account for the selection bias and the full covariance structure implied by the spatial correlation. We illustrate the implementation of these algorithms through a simulation study