考慮到近些年來的全球氣候變暖問題，以及各主要國家之間有關永續發展的討論，很多學者對國民收入與當地環境污染之關聯做了很多研究，關於國民收入對環境污染的影響機制的研究也有長足發展。目前大部分的研究認爲環境污染與國民收入之間的關係服從一個倒U 型的曲線，稱作環境庫茲涅茨曲線（Environmental Kuznets Curve）。工業技術的進步與國際間的污染轉移被認作是影響這個機制的幾個主要驅動因子之二。而在傳統的面板模型（Panel Model）和時間序列模型（Time Series Model）之外，應用灰色系統理論（Grey System Theory）來預測碳排放和環境衰退的研究近年來也在逐漸增加。在此基礎上，爲驗證環境污染的轉移理論，並提高模型的精度，本文拓展了原始的灰色模型（Grey Model），使之適用於面板數據（Panel Data），以建立面板灰色模型（Panel Grey Model），並在拓展後的模型中納入空間加權矩陣（Spatial Weight Matrix），建立了一個新的一階多變量空間面板灰色模型（Spatial Panel Grey Model）來模擬環境的衰退狀況。

鑑於工業發展對環境衰退進程的關鍵性影響，並綜合考慮各種污染物對生態環境的影響，本文採用40 個工業國家自2008 年至2018 年的人均生產總值（Gross Domestic Product），人均生態足跡（Ecological Footprint）以及各個國家的空間位置資料來建立模型。在空間權重矩陣的選擇問題上，本文比較了人均生態足跡在相鄰（Neighbourhood）空間權重矩陣和距離（Distance）空間權重矩陣上的全局莫蘭指數（Global Moran’s I），最終選擇使用相鄰空間權重矩陣建模。

與最原始的灰色模型相比，本文所採用的一階多變量空間灰色模型拓展了灰色模型的用途，使其不僅可以應用于單個的時間序列，也可應用于面板數據，此外本模型還將空間信息納入考量，進一步提高了模型的精度。

建模結果顯示，本文採納的空間面板灰色模型與面板灰色模型相比較，普通的面板模型以及空間面板模型在模型精度上均有提高。模型模擬結果顯示，某國家或者地區的人均生態足跡受到鄰近國家或地區的人均生態足跡的正向影響。這一結果也與全局莫蘭指數所反映的結果一致。若僅以空間灰色模型的結果來看，各地人均生態足跡受到經濟的影響較不顯著。

There has been considerable development in the study of the mechanism of national income effects on environmental pollution. The majority of current research suggests that the relationship between environmental pollution and national income follows an inverted U-shaped curve, which is named after Kuznets as the Environmental Kuznets Curve (EKC). Advancements in industrial technology and international pollution transfer are considered to be two of the main drivers of this mechanism. Except for panel models and time series models, the application of grey system theory to simulate carbon emissions or environmental degradation has been more and more popular. On this basis, to verify the hypothesis of pollution transferring and improve the accuracy of the existing models, this research extended the original Grey Model (GM(1,P)), making it available for panel data to build a panel grey model (PGM(1,P)). In order to take international pollution transferring into consideration, this research involved a spatial weight matrix in PGM(1,P), having created a new spatial panel grey model (SPGM(1,P)) to simulate the degradation of the environment.

This research works on a data set of 40 industrial countries from 2008 to 2018. The independent variable is Gross Domestic Product (GDP) per capita, and the dependent variable is Ecological Footprint (EF) per capita. After a comparison of the neighbourhoodbased spatial weight matrix and distance-based spatial weight matrix, this research found the neighbourhood-based one more suitable by the Global Moran’s I, and a significant positive spatial correlation is observed in this data set.

Compared to other grey models, SPGM(1,P) extended the usage of the grey model, making it available for panel data instead of simply individual time series. Furthermore, it involved a spatial matrix in the model and improved accuracy as well.

The calculation results show that SPGM(1,P) is more accurate than the other three models. It can also prove that spatial transferring of pollution among neighbourhoods really exists. The local region’s pollution level is positively affected by neighbours, which is the same as the conclusion drawn by the Global Moran’ Is. On the result of SPGM(1,P) only, the effect of economic growth on environmental degradation is not significant.

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