經濟實證模型函數型態之選擇－－以臺灣稻作生產函數為例

Selecting Functional Form for Empirical Economic Model-- The Case of Taiwan Rice Production Function

經濟學者在設立實證模型時，多會面臨函數型態選取的問題。實證函數型態對研究結果影響極大，因為當所選用的函數型態不符合樣本資料特性時，將會導衍出不當的實證推估結果。函數型態不斷地推陳出新，雖提供研究者更多的選擇，但亦使選擇更加複雜化。近年來，學者一致以伸縮性為函數型態選取的基本要件。雖然許多文獻已提出各種數學上、統計上及理論上的選取實證模型函數型態之準則，但缺乏整合而令人難以適從。本研究由歷年相關文獻中歸納出選取函數型態應具備的實證及理論準則，前者包括：(1)蒙地卡羅實驗、(2)巢狀檢定、(3)非巢狀檢定；後者為(4)先驗假說檢定。為具體說明應用上述準則選取函數的實際過程與方法，本文特以臺灣稻作生產函數為例，以十二種常見的傳統及具有伸縮性的生產函數型態為對象，首先以實際樣本資料自行配適函數型態的實證選取準則，再輔以理論選取準則為本研究的選取方法。經實證準則篩選之結果，以modified resistance, translog及generalized Cobb-Douglas三種函數型態最能符合臺灣稻作生產資料所配適之生產函數。若輔以先驗假說評判，當考量生產函數具有齊質性條件時，generalized Cobb-Douglas與translog函數皆符合臺灣稻作生產技術行為；但在線性齊次性條件要求下，僅generalized Cobb-Douglas函數符合此生產條件。

Choosing appropriate functional forms is a crucial task for empirical economists in model building. Unfavorable estimation results are usually generated from functions which are not suitable for the characteristics implied by sampling data. The growing number of available functional forms provide model builders not only a wider set to choose from but also complication in selection. Recently, the notion of flexibilty has become the principle of explicitly choosing for functional forms. Although selection criteria based on mathematical, statistical, and theoretical properties have been proposed by numerous studies, they are very difficult to implement for lack of integration. This study provided a sequential selection process for empirical model building in which three empirical criteria: (1) Monte Carlo experiments; (2) nested hypothesis testing; (3) nonnested hypothesis testing, as well as a theoretical criterion, (4) maintained hypothesis test are combined. An empirical example of choosing production functional form for Taiwan's rice industry was also provided in this paper. Twelve functions consisting the most traditional and locally flexible forms were compared based on the criteria suggested above. The modified resistance, translog, and generalized Cobb-Douglas forms were found to fit the rice production data better than others as judged by emprical selection criteria. To determine which form is superior, theoretical properties of production were then taken into consideration. The test results showed that both generalized Cobb-Douglas and translog were consistent with the homothetic hypothesis, while only the generalized Cobb-Douglas met the conditions of homogeneity.