空間計量模型應用於汽車保險之研究

臺灣關於車險的研究很多，大多數著重在出險因素、消費者特性與通路等等，較少討論與空間因素對理賠金額的影響。因此本研究將空間因素納入傳統迴歸模型之中，建立空間落遲模型(SLM)、空間誤差模型(SEM)與空間杜賓模型(SDM)，進而在三個模型之中，找出配適能力最佳的模型。本研究針對2015年任意車體損失險資料進行分析。研究發現，不同地區平均賠款金額具有空間自相關，並以由下而上的方法(Bottom-Up Approach)，使用Robust-LM檢定與LM檢定來比較SLM和SEM兩個模型，檢定結果發現，SEM優於SLM。最後透過Wald檢定來比較SDM模型與SEM模型，結果發現SDM優於SEM。本研究透過SDM模型的分析結果發現， 30歲到60歲比例、平均排氣量與自付額比例與鄰近地區的平均賠款金額呈現顯著的正相關，而男性比例、平均車齡、甲式車體險比例、已婚比例、直接通路比例與出險次數與鄰近地區的平均賠款金額呈現顯著負相關。

關鍵字

汽車保險；空間計量模型；空間杜賓模型

並列摘要

There have been numerous studies in the literature focusing on the analysis of Taiwan automobile insurance data. However, most of these studies primarily investigate the relationships between claim amounts and non-spatial determinants such as personal factors, consumer characteristics, or insurance channels. The influence of spatial factors on automobile insurance claims has received limited attention. Therefore, this study aims to address such research gap by incorporating a spatial perspective. Specifically, we explore the application of three spatial regression techniques, namely the Spatial Lag Model (SLM), Spatial Error Model (SEM), and Spatial Durbin Model (SDM), in analyzing vehicle body damage insurance data from year 2015. Our objective is to determine the most suitable model among these three approaches. This study identifies the presence of spatial autocorrelation in claim amounts across different regions, highlighting the need for employing spatial models (SLM, SEM, SDM). We utilize a Bottom-Up Approach based on the Robust-LM test and LM test to compare the SLM and SEM models, and our results indicate the superiority of SEM over SLM. Furthermore, through the Wald test, we find that the SDM model outperforms SEM. The findings from the SDM model demonstrate significant positive associations between the proportion of individuals aged 30 to 60, average engine displacement, and the proportion of deductibles with the average claim amount in neighboring areas. Conversely, the proportion of males, average age of vehicles, proportion of Type A auto body insurance, proportion of married individuals, proportion of direct channels, and number of claims have significant negative impacts on the mean claim amount in neighboring areas.