﻿ 含有潜变量的Cobb-Douglas生产函数模型及其实证分析 Cobb-Douglas Production Function with a Latent Variable and Its Empirical Study

Statistics and Application
Vol.05 No.03(2016), Article ID:18647,7 pages
10.12677/SA.2016.53031

Cobb-Douglas Production Function with a Latent Variable and Its Empirical Study

Feng Gao*, Xuqing Liu

Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an Jiangsu

Received: Sep. 8th, 2016; accepted: Sep. 23rd, 2016; published: Sep. 29th, 2016

ABSTRACT

Cobb-Douglas production function represents the input-output relationship among the labor force, the invested fund, and the GDP in economics. Considering that the regional soft power (RSP) measures the realistic or underlying competitiveness of a region, it may be theoretically appropriate to integrate RSP as a production factor into the production function. However, RSP is a latent variable, and thus needs a reasonable method of assigning its values. In this paper, we construct a new production function by introducing RSP to the Cobb-Douglas production function. The method of assigning values to RSP is discussed by virtue of factor analysis method L. The empirical study is made by applying the theoretical result to the thirteen cities of Jiangsu province.

Keywords:Cobb-Douglas Production Function, Regional Soft Power, Factor Analysis Method L

Cobb-Douglas生产函数描述了劳动力投入、资金投入与生产总值之间的投入产出关系。区域软实力衡量了一个地区具有的现实的和潜在的竞争优势，因此区域软实力可以作为一种生产要素介入生产函数中，但是区域软实力是“潜变量”，需要一个合理的赋值方法。本文在Cobb-Douglas生产函数中引入区域软实力指标，得到了一个新的生产函数，应用因子分析模型L，给区域软实力进行赋值，最后对江苏省13个城市进行了实证分析。

1. 引言

(1.1)

(1.2)

2. 模型的建立与求解

2.1. 模型的建立

(2.1)

(2.2)

(2.3)

，其协方差阵可以表示为

(2.4)

2.2. 模型的估计

1) 测量模型的估计

(2.5)

(2.6)

(2.7)

(2.8)

(2.9)

2) 对于区域软实力评价模型(2.3)，权重的估计值为

(2.10)

3) 对于回归模型(2.1)，应用最小二乘法进行估计。

3. 实证分析

Table 1. Regional soft power index evaluation system

(3.1)

(3.3)

Table 2. Score of grade two

Table 3. Two level index weight

Table 4. Evaluation results of regional soft power in 13 cities of Jiangsu Province in 2013

(3.4)

(3.5)

4. 结论

Cobb-Douglas Production Function with a Latent Variable and Its Empirical Study[J]. 统计学与应用, 2016, 05(03): 305-311. http://dx.doi.org/10.12677/SA.2016.53031

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