英文标题：
《Revisiting Transformation and Directional Technology Distance Functions》
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作者：
Yaryna Kolomiytseva
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最新提交年份：
2018
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英文摘要：
In the first part of the paper, we prove the equivalence of the unsymmetric transformation function and an efficient joint production function (JPF) under strong monotonicity conditions imposed on input and output correspondences. Monotonicity, continuity, and convexity properties sufficient for a symmetric transformation function to be an efficient JPF are also stated. In the second part, we show that the most frequently used functional form for the directional technology distance function (DTDF), the quadratic, does not satisfy homogeneity of degree $-1$ in the direction vector. This implies that the quadratic function is not the directional technology distance function. We provide derivation of the DTDF from a symmetric transformation function and show how this approach can be used to obtain functional forms that satisfy both translation property and homogeneity of degree $-1$ in the direction vector if the optimal solution of an underlying optimization problem can be expressed in closed form.
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中文摘要：
在本文的第一部分中，我们证明了在强单调条件下，非对称变换函数与有效联合生产函数（JPF）的等价性。还说明了对称变换函数是有效JPF的单调性、连续性和凸性。在第二部分中，我们证明了方向技术距离函数（DTDF）最常用的函数形式，即二次函数，在方向向量中不满足度$-1$的齐次性。这意味着二次函数不是方向技术距离函数。我们提供了从对称变换函数推导DTDF的方法，并展示了如果基础优化问题的最优解可以用闭合形式表示，那么如何使用这种方法来获得同时满足平移性质和方向向量上阶数$-1$齐性的函数形式。
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分类信息：

一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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