應用分量迴歸於大量估價之增進──以新北市高價七區為例

Improvement in Mass Appraisal Using Quantile Regressions for House Prices of Higher-Priced Districts in New Taipei City

房地產具有高度異質性，影響房屋價格的變數對不同價位房價的影響效果可能不同。因此，晚近一些文獻將分量迴歸應用於住宅大量估價，得到較好的預測。然而，利用分量迴歸估測房價有兩個可增進的空間。第一，若是以總價為應變數，因為樓地板面積對總價有正向顯著影響，部分物件地段價值較低（高）但具有大（小）坪數，可能被歸於高（低）總價分量進行估測，導致估測值高（低）於實際總價。本論文檢視新北市高單價七區自民國102年1月到106年11月之實價登錄房價資訊，分別以總價取對數與單價取對數為應變數，進行分量迴歸。結果發現，不論是以平均誤差比絕對值（Mean Absolute Percentage Error, MAPE）或是命中率，各區以單價取對數為應變數的估價精準度都顯著高於以總價取對數為應變數的精準度。第二，縱使以單價對數為應變數進行分量迴歸仍有瑕疵。部分低（高）地段價值的低（高）屋齡物件可能被歸於高（低）單價分量估測，造成估測值大（小）於實際單價。基於進一步增進估測精準度，本文提出調整屋齡效果分量迴歸如下。先就單價對數進行分量迴歸，再就單價對數扣除屋齡效果後對屋齡以外變數進行分量迴歸，最後將預測值加入屋齡效果。結果顯示：除了新店0.50分量外，七區各分量調整屋齡效果分量迴歸的MAPE都比簡單分量迴歸為低，命中率都較大。其中以蘆洲與三重降幅最大，調整效果最好。探究因素發現，如果相近分量公告價值差異越小，以調整屋齡效果降低預測誤差效果越好。

Instead of OLS regressions, several studies use quantile regressions to identify the implicit prices of housing characteristics for different points in the distribution of house prices in order to have precise prediction in terms of mean absolute percentage error (MAPE). Nevertheless, there are two shortcomings. Firstly, taking total prices as the dependent variables, houses of large floor area but in lower-value area may be categorized into higher quantiles and overestimated. Taking total prices and unit prices as the dependent variables, separately, this study uses quantile regressions for house prices of seven higher-priced districts in New Taipei City, between 2013 and 2017. Empirical results show that the MAPE of unit price quantile regression is far lower than the MAPE of total price quantile regression. Secondly, even though we take unit prices as the dependent variables, younger houses located in lower-value areas, may be categorized into higher price quantiles and overestimated, while older houses located in higher-value areas, may be categorized into lower price quantiles and underestimated. We improve on this shortcoming by deducting the effects of age from house unit prices as the dependent variables, conducting quantile regressions for variables other than age variables, and adding back the effects of age to predicted prices. Empirical results show that the MAPEs of modified quantile regressions are much lower than the MAPEs of simple quantile regressions. Furthermore, houses of adjacent quantiles with closer assessed land values, have much lower MAPEs.