本研究探討收益全要素生產力（revenue total factor productivity，TFPR）相對水準與工商業總家數如何透過固定資產淨額與薪資費用兩個中介變數，連結至臺灣鄉鎮市區的所得中位數。傳統靜態分群（static clustering）與橫斷面迴歸（cross-sectional regression）難以在同一模型內處理群組間的測量結構異質性、縱向資料的時間相依性，以及要素投入與所得之間可能存在的滯後關聯。
本研究以 2011 至 2022 年鄉鎮市區縱向行政資料為基礎，分兩階段進行分析。第一階段採用混合縱向因素分析模型（mixture of longitudinal factor analyzers，MLFA）進行縱向分群，允許各潛在群組擁有獨立因素結構，並萃取潛在因素分數作為控制變數。第二階段建構以線性混合效應模型為基礎的單期滯後中介模型，以 TFPR 與工商業總家數為自變數，以固定資產淨額與薪資費用為中介變數，所得中位數為結果變數。
實證結果顯示，TFPR 與固定資產淨額呈顯著負向關聯，但其透過固定資產或薪資費用形成的間接效應於主要 Lag-1 設定下未達顯著。此結果反映區域收益生產力差異與資本配置之間未能一致。相較之下，工商業總家數與所得中位數之間存在明顯正向直接關聯，但其透過薪資費用形成的間接效應為負，顯示廠商端薪資費用增加未必同步反映於家戶端所得中位數。逐年估計進一步顯示，部分中介路徑的估計值隨年份改變，呈現時間異質性。
本研究發現工商業總家數與所得中位數之間的關聯較 TFPR 中介路徑更為明顯，TFPR 相關結果則提示區域收益生產力差異與資本配置之間可能未能一致。薪資費用路徑的負向間接效應顯示產業聚集導向的政策若僅著重工商業總家數，未必能保證其利益反映於一般家戶所得。

This study examines how the relative level of revenue total factor productivity (TFPR) and the number of commercial and industrial establishments are linked to median income across Taiwan’s townships through two mediators: fixed assets and wage expenditure. Conventional static clustering and cross-sectional regressions cannot jointly accommodate measurement-structure heterogeneity across groups, temporal dependence in longitudinal data, and possible lagged associations between factor inputs and income.
Using longitudinal administrative data for Taiwan’s townships from 2011 to 2022, this study proceeds in two stages. The first stage applies the mixture of longitudinal factor analyzers (MLFA) to perform longitudinal clustering, allowing each latent group to have a distinct factor structure and extracting latent factor scores as control variables. The second stage constructs a one-period lagged mediation model based on linear mixed-effects models. Revenue total factor productivity (TFPR) and the number of commercial and industrial establishments serve as independent variables, while fixed assets and wage expenditure serve as mediators and median income as the outcome.
The empirical results show that TFPR is significantly and negatively associated with fixed assets, but its indirect effects through fixed assets or wage expenditure are not significant under the main Lag-1 specification. This finding suggests that regional differences in revenue productivity are not fully aligned with capital allocation. In contrast, the number of commercial and industrial establishments has a clear positive direct association with median income, whereas its indirect effect through wage expenditure is negative, suggesting that increases in firm-side wage expenditure do not necessarily translate into higher household-side median income. Wave-by-wave estimation further indicates that some mediation-path estimates vary across years, revealing temporal heterogeneity.
Overall, this study finds that local commercial and industrial activity is more strongly associated with median income than the TFPR-mediated pathways. The TFPR-related results suggest a possible misalignment between regional revenue productivity and capital allocation. The negative wage-mediated indirect effect indicates that agglomeration-oriented policies focusing solely on the scale of local business activity may not guarantee that agglomeration gains are reflected in ordinary household income.

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