Mass appraisal of farmland using classical econometrics and spatial modeling

Mass appraisals of properties traditionally use classical linear regression models (CLRMs); however, there has been the need to model the data spatially. Such modeling of the geographic effects has been used mainly in appraisals of urban areas, but the values of the properties in rural areas are also affected by the geographic location. This paper aims to use spatial regression econometric models in a sample of rural properties to elaborate the plan of values for an area of the North Fluminense Region – RJ, Brazil. The proposed methodology is to investigate and model the effects caused by the spatial autocorrelation on the CLRMs, evaluate their performance comparing them with the spatial models and produce the plan of values through ordinary kriging. The utilized sample consisted of 113 observations and 25 samples of verification. The performance of the obtained surfaces of values was evaluated through the Root Mean Squared Error (RMSE). The results showed that the spatial autocorrelation can have its effects controlled by Spatial Regression Models, because the Spatial Error Model (CAR) allowed to model the spatial dependence present in the residuals. Using the metrics of Akaike information criterion (AIC), R2 and likelihood function (LIK), the CAR model showed better fit in comparison to the CLRM. The results showed that the surface generated by the CAR model showed the best performance with the lowest RMSE. The combination of the methodologies of classical and spatial regressions and the use of geostatistical techniques were adequate to elaborate and obtain the plan of values for rural areas, to be used for various purposes, such as taxation, financing, expropriations, indemnities (in case of creation of conservation units or even in environmental disasters), among others.