中国全要素生产率和估算和分析
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or
Divisia input index
应用实例：技术进步与总量生产函数 (Solow, 1957)
增长核算公式
Technical change is a shift in the production function
(3) 管理（技术）效率与全要素生产率
Farrell (1957)技术效率度量 一般化的Farrell技术效率度量 (Førsund & Hjalmarsson, 1979) 数据包络分析(DEA)模型
TFP=y/X
Differentiating both sides logarithmically
with respect to time gives
•
TFP
d ln y d ln X
••
y X
dt
dt
以成本份额加权平均
If define Notice
•
TFP
d
ln
y
dt
j
•
(wj x j / c) x j
中国全要素生产率估算与分析ຫໍສະໝຸດ Baidu
内容提要
1. 生产率概念的由来 2. 全要素生产率的估算与拆分 3. 全要素生产率与企业改革 4. 全要素生产率与可持续经济增长 5. 中国省际全要素生产率增长变化的实证分析 6. 前苏联和亚洲四小龙的案例 7. 影响全要素生产率增长的因素 8. 中国经济增长模式的转变
一、生产率概念的由来: (1) 投入产出率
The linear transformation of the CCR ratio
for a representative solution
The dual to the linear transformation
Envelopment surface for the inputoriented CCR model
Total factor productivity is the average product of all inputs, it is the ratio of the output to an index of inputs. Let the index of inputs be denoted as X. Then total factor productivity (TFP) is
•
TFP T(x,t) under CRS
以成本在产值中的比重加权： Divisia index
(2) 生产函数与技术进步
A stable relationship between output, inputs, and time exists:
Rate of technical change is defined as:
Farrell measure
Technical Efficiency
(1957)
a road map
Technical Progress (1957)
Shephard
Distance Function (1970)
Stochastic frontier
Deterministic
CCR 模型 （Charnes, Cooper, & Rhodes, 1978）
BCC 模型（Banker, Charnes, & Cooper, 1984）
ADD 模型 （Charnes, et al, 1985）
DEA模型与回归模型的比较
The CCR ratio model (input oriented, 1978)
where ft ( X t ,t) and fT ( XT ,T ) need not be the same functional forms and the components of the input XT and X t may be different.
Divisia indexes and rate of technical change
Technical efficiency (Farrell, 1957) Technical progress (Sollow, 1957) Distance function (Shephard, 1970) DEA (Charnes, Cooper, & Rhodes, 1978). TFP decomposition (Nishimizu & Page, 1982) Malmquist index (Caves, et. al, 1982) Malmquist TFP index decomposition (Färe et al, 1994)
CRS, NIRS, and VRS
General statistics about the DEA bibliography database (Tavaresa, 2002).
DEA publications number by type.
DEA publications number by year
Author statistics
二、全要素生产率的估算与拆分
增长核算法 (Devisia Index) 生产函数估算法
平均生产函数法（技术进步） 前沿生产函数法（技术效率）
Malmquist 指数法拆分(panel data)
技术进步 技术效率改善 规模效率变化
技术效率、距离函数、 DEA、和 Malmquist生产率指数之间的关系
Total differentiation of with respect to time yields
Dividing through by y gives
Under profit maximization, output elassticity equals input Shares in total revenue:
The Output-Oriented CCR model
Suporting hyperplane for the outputoriented CCR model
Restrictions on parameters in DEA
CRS: no restrictions VRS:
Nonincreasing returns to scale (NIRS):
Divisia input index
应用实例：技术进步与总量生产函数 (Solow, 1957)
增长核算公式
Technical change is a shift in the production function
(3) 管理（技术）效率与全要素生产率
Farrell (1957)技术效率度量 一般化的Farrell技术效率度量 (Førsund & Hjalmarsson, 1979) 数据包络分析(DEA)模型
TFP=y/X
Differentiating both sides logarithmically
with respect to time gives
•
TFP
d ln y d ln X
••
y X
dt
dt
以成本份额加权平均
If define Notice
•
TFP
d
ln
y
dt
j
•
(wj x j / c) x j
中国全要素生产率估算与分析ຫໍສະໝຸດ Baidu
内容提要
1. 生产率概念的由来 2. 全要素生产率的估算与拆分 3. 全要素生产率与企业改革 4. 全要素生产率与可持续经济增长 5. 中国省际全要素生产率增长变化的实证分析 6. 前苏联和亚洲四小龙的案例 7. 影响全要素生产率增长的因素 8. 中国经济增长模式的转变
一、生产率概念的由来: (1) 投入产出率
The linear transformation of the CCR ratio
for a representative solution
The dual to the linear transformation
Envelopment surface for the inputoriented CCR model
Total factor productivity is the average product of all inputs, it is the ratio of the output to an index of inputs. Let the index of inputs be denoted as X. Then total factor productivity (TFP) is
•
TFP T(x,t) under CRS
以成本在产值中的比重加权： Divisia index
(2) 生产函数与技术进步
A stable relationship between output, inputs, and time exists:
Rate of technical change is defined as:
Farrell measure
Technical Efficiency
(1957)
a road map
Technical Progress (1957)
Shephard
Distance Function (1970)
Stochastic frontier
Deterministic
CCR 模型 （Charnes, Cooper, & Rhodes, 1978）
BCC 模型（Banker, Charnes, & Cooper, 1984）
ADD 模型 （Charnes, et al, 1985）
DEA模型与回归模型的比较
The CCR ratio model (input oriented, 1978)
where ft ( X t ,t) and fT ( XT ,T ) need not be the same functional forms and the components of the input XT and X t may be different.
Divisia indexes and rate of technical change
Technical efficiency (Farrell, 1957) Technical progress (Sollow, 1957) Distance function (Shephard, 1970) DEA (Charnes, Cooper, & Rhodes, 1978). TFP decomposition (Nishimizu & Page, 1982) Malmquist index (Caves, et. al, 1982) Malmquist TFP index decomposition (Färe et al, 1994)
CRS, NIRS, and VRS
General statistics about the DEA bibliography database (Tavaresa, 2002).
DEA publications number by type.
DEA publications number by year
Author statistics
二、全要素生产率的估算与拆分
增长核算法 (Devisia Index) 生产函数估算法
平均生产函数法（技术进步） 前沿生产函数法（技术效率）
Malmquist 指数法拆分(panel data)
技术进步 技术效率改善 规模效率变化
技术效率、距离函数、 DEA、和 Malmquist生产率指数之间的关系
Total differentiation of with respect to time yields
Dividing through by y gives
Under profit maximization, output elassticity equals input Shares in total revenue:
The Output-Oriented CCR model
Suporting hyperplane for the outputoriented CCR model
Restrictions on parameters in DEA
CRS: no restrictions VRS:
Nonincreasing returns to scale (NIRS):