價格彈性是數位平台與零售市場制定定價策略的重要依據，但其估計本質上是一個因果推論問題。若價格與需求同時受到未觀測因素影響，傳統迴歸或純預測模型便可能將混淆相關誤認為價格效果。雙重機器學習（Double Machine Learning, DML）因能處理高維度可觀測混淆，已逐漸成為估計價格因果效果的重要工具。實務上，Alibaba 旗下天貓超市的促銷定價系統即透過 DML 控制行銷活動、節慶與天氣等混淆因素，以估計價格對銷量的因果效應 (Deng et al. 2023)，這顯示價格彈性估計與 DML 方法已同時具有學術與業界應用價值。然而在真實資料中，商圈群聚、區域消費習慣等未觀測地理背景，往往會同時牽動價格與需求，形成空間混淆（spatial confounding）。若忽略此類共同空間結構，價格彈性估計可能產生偏誤，局部係數模型也可能將殘留空間背景誤讀為真實異質性。
為處理上述問題，本文提出一套結合 DML、莫蘭特徵向量映射（Moran’s eigenvector maps, MEM）與地理加權迴歸（geographically weighted regression, GWR）的兩階段估計流程。第一階段將 MEM 作為由座標資訊建構的空間代理變數，納入 DML 正交化模型，以降低價格殘差與需求殘差中的共同空間結構。第二階段則在正交化後的殘差上估計價格彈性，並依研究目的使用全域 OLS 或 GWR 還原局部價格彈性表面。由於真實資料中無法觀測真實價格彈性與空間混淆樣態，本文進一步貼合真實零售情境設計模擬實驗，比較 MEM 核函數、MEM 保留數量、交叉配適切分方式與第一階段正交化模型，並以偏誤、空間混淆殘留、local coefficient RMSE 與空間相關係數評估方法表現。
模擬結果顯示，在空間共享同一價格彈性且存在空間混淆的情境中，未加入空間代理變數的 Naive DML 與僅控制線性座標的 DML 仍保留明顯偏誤，加入 MEM 後則能將全域價格彈性估計拉回真值附近。進一步在有空間異質性係數情境下的模擬顯示，若直接使用原始價格與需求進行 Naive GWR，局部係數容易受到空間混淆污染。相對地，DML-MEM-GWR 先降低共同空間混淆，再估計局部係數，因而能降低 local coefficient RMSE 並重建真實係數表面的空間起伏。當真實效果接近同質時，GWR 會透過留一交叉驗證（leave-one-out cross-validation, LOO-CV）選擇接近全域的帶寬，使各位置的係數估計趨近同質，並接近 DML-MEM-OLS 的估計結果，未呈現明顯的假異質性。
本文最後將此流程應用於台灣雲端發票瓶裝水品項資料。實證結果顯示，在第一階段同時控制時間、交易行為、供給結構與水品類固定差異後，加入 MEM 仍能使五個水品類的價量殘差共同空間結構下降，五品類價量殘差雙變數莫蘭指數方均根（\mathrm{RMS}\left(I_{PD}\right)）相對 DML baseline 約降低 79.4%。第二階段先以交互 OLS 估計各水品類的全域價格彈性，再以逐品類 GWR 估計各鄉鎮的局部係數。結果顯示，鹼性水與氣泡水的需求對價格較敏感，純水與礦泉水則較不敏感。五個水品類的 GWR 均選擇涵蓋該品類全部鄉鎮的帶寬，逐品類局部係數以各品類的全域水準為中心呈現平緩變化。整體而言，本研究提出的 DML-MEM-GWR 框架提供一套具體的實作流程，可為數位平台、零售市場與區域定價決策提供更具因果可信度的實證基礎。

Price elasticity is a key input for pricing decisions in digital platforms and retail markets, but its estimation is fundamentally a causal inference problem. When price and demand are jointly affected by unobserved factors, conventional regression or purely predictive models may mistake confounded association for a price effect. Double Machine Learning (DML) has become an important tool for estimating causal price effects because it can adjust for high-dimensional observed confounders. In practice, Alibaba’s Tmall Supermarket promotion pricing system uses DML to control for marketing campaigns, holidays, weather, and other confounders when estimating the causal effect of price on sales (Deng et al. 2023), showing that price elasticity estimation with DML has both academic and industrial relevance. However, in real-world data, unobserved geographic backgrounds such as business-district clustering and regional consumption habits may jointly affect price and demand, creating spatial confounding. If such shared spatial structure is ignored, price elasticity estimates may be biased, and local coefficient models may mistake residual spatial background for genuine heterogeneity.
To address this problem, this study proposes a two-stage framework that combines DML, Moran’s eigenvector maps (MEM), and geographically weighted regression (GWR). In the first stage, MEM is used as a coordinate-based spatial proxy in the DML orthogonalization model to reduce shared spatial structure in price and demand residuals. In the second stage, price elasticity is estimated from the orthogonalized residuals using either global OLS or GWR, depending on the research objective. Because true elasticity and spatial confounding patterns are unobservable in real data, this study designs simulation experiments that reflect realistic retail settings and compares MEM kernels, MEM counts, cross-fitting splits, and first-stage orthogonalization learners using bias, spatial confounder leakage, local coefficient RMSE, and spatial correlation.
The simulation results show that, when price elasticity is spatially shared and spatial confounding is present, Naive DML and DML with only linear coordinate controls remain substantially biased, whereas adding MEM brings the global elasticity estimate close to the true value. Further simulations with spatially heterogeneous coefficients show that Naive GWR applied directly to raw price and demand is easily contaminated by spatial confounding. By contrast, DML-MEM-GWR first reduces shared spatial confounding and then estimates local coefficients, thereby lowering local coefficient RMSE and recovering the spatial variation of the true coefficient surface. When the true effect is close to homogeneous, GWR selects a near-global bandwidth through leave-one-out cross-validation (LOO-CV), causing the location-specific coefficient estimates to converge toward a homogeneous pattern and approach the DML-MEM-OLS estimate without exhibiting substantial false heterogeneity.
Finally, the framework is applied to Taiwan cloud invoice data for bottled water products. The empirical results show that, after controlling for time composition, transaction behavior, basic supply structure, and water-type fixed differences in the first stage, adding MEM still reduces the shared spatial structure in price and demand residuals. The root mean square of the five water-type price-demand bivariate Moran’s I values (\mathrm{RMS}\left(I_{PD}\right)) falls by about 79.4% relative to the DML baseline. In the second stage, interaction OLS estimates global elasticities by water type, and water-type-specific GWR estimates township-level local coefficients. The estimates show that alkaline water and sparkling water are more price-sensitive, whereas purified water and mineral water are less price-sensitive. GWR selects a bandwidth covering all available townships within each water type, and the local coefficients vary smoothly around the corresponding water-type-level elasticities. Overall, the proposed DML-MEM-GWR framework provides a concrete workflow for producing more causally credible empirical evidence for digital platforms, retail markets, and regional pricing decisions.

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