Διερεύνηση της συμπεριφοράς των προβλημάτων αυτοσυσχέτισης και ετερογένειας σε γραμμικά υποδείγματα με χωρικά δεδομένα και μελέτη περίπτωσης γονιμότητας του πληθυσμού της Ελλάδας σε επίπεδο δήμου
Investigating the behaviour of autocorrelation and heterogeneity problems in linear models with spatial data and a case study of fertility of the population of Greece at local authority level
Τσιμπάνος, Απόστολος Η.
KeywordsΧωρικά δεδομένα ; Χωρική οικονομετρία ; Οικονομετρικά υποδείγματα ; Χωρική αυτοσυσχέτιση ; Χωρική ανάλυση ; Στοχαστικές διαδικασίες ; Γραμμικός προγραμματισμός ; Ανάλυση παλινδρόμησης ; Χωρική ετερογένεια ; Δημογραφία
The estimation of linear regression models with spatial data, that is cross-sectional data collected and obtained from different geographical regions, carries serious risks due to the appearance of spatial effects which influence the result reliability in case such effects are ignored by the researcher. Spatial effects, which are attributed to the nature of the data, are distinguished from spatial dependence and spatial heterogeneity outcomes. Spatial dependence means that the values of a variable are not independent of each other but correlated according to their geographical positions creating clusters of observations. Spatial heterogeneity means that the relationship between the variables under consideration does not remain constant throughout the study region but varies from point to point. The treatment of spatial effects is achieved by their incorporation in the model using spatial econometric models. This PhD thesis deals with topics relating to the problems of spatial dependence and spatial heterogeneity in the linear regression model. More specifically, the structure of the thesis is organized as follows: Chapter 1 gives a brief introduction to spatial analysis methodology presenting the peculiarities of spatial data and the construction of the spatial weights matrix. In addition, the main spatial processes and spatial econometric models are described. Chapter 2 examines, using simulation techniques, the behavior of the LM spatial dependence and specification tests which are applied for detecting the spatial autocorrelation problem in the errors of a linear model and for selecting the appropriate spatial econometric model. The results obtained through the simulation process confirm the results presented in the literature concerning test behavior in small and medium samples and contribute to further information for their behavior in large samples. Moreover, the spurious regression phenomenon is also presented in the same chapter as another reason leading to spatial autocorrelation in the errors of an econometric model. Using simulation analysis with two independent stationary spatial autoregressive processes of order one, SAR(1), similarities are recognized in the appearance of the phenomenon for spatial data with time series data. However, if the analyst takes into account the suggestions deriving from the LM spatial dependence and specification tests and estimates a spatial econometric model the spurious regression problem will not be revealed. Chapter 3 investigates, employing simulation techniques, the behavior of the geographically weighted regression which is commonly used to remedy the spatial heterogeneity problem through local modeling estimation as well as the performance of the tests which examine its contribution. The findings indicate that, in some cases, despite the good performance and the advantages of this method misleading results can be obtained. Moreover, the concept of spurious local regression is examined for two independent stationary spatial autoregressive processes of order one, SAR(1). The main conclusion of the analysis is that the researcher should be very cautious when estimating local models applying geographically weighted regression as spurious behavior will appear at the local level, a problem that cannot be avoided in contrast to the same problem at the global level which can be treated. Chapter 4 tries empirically to explain spatial variations and patterns in the relationships between the fertility level of the population of Greece and a number of selected socioeconomic indicators at the local authority level taking into account the existence of spatial heterogeneity. The estimation of the model, applying the geographically weighted regression method and mapping the results, reveals that considerable differentials exist at the municipalities level in the direction and intensity of social and economic factors affecting fertility.