1. 構造方程式ゼミナール
2012年11月21日
構造方程式の作成と応用

2. Identification

3. 事例3　Klein’s Model(1950)
1950 年のクラインのモデル1 は僅か8 本の方程式で構成され、1921 年から40 年にかけて大不況の経緯を見事にトレースし、これを持って、経済学は一人前の科学として船出を遂げたと言われる。
In a book published in 1950, Lawrence Klein reported a model of the U.S. economy for the period , which is widely known as Klein’s Model I.

4. Klein’s Model(1950) ①Consumption ②Investment ③Private wages
④Equilibrium demand 　　
⑤Private profits
⑥Capital stock

5. Data for Klein’s Model, 22 yearly Observations, 1920-1941
Year=date
C=consumption,
P=corporate profits,
Wp=private wage bill,
Wg=government wage bill,
I=investment,
Kt-1=previous year’s capital stock,
X=GNP,
G=government nonwage spending,
T=indirect business taxes plus net exports,
A=time trend measured as years from 1931

6. Exogenous variables G : government nonwage spending
T : indirect business taxes plus net exports
Wg : government wage bill
A : time trend measured as years from 1931
Predetermined variables Kt-1 : previous year’s capital stock
Pt-1 : corporate profits
Xt-1 : gross demand
The endogenous variables are each on the left-hand side of an equation
Put all the endogenous variable to the left-hand side of an equation
If the structural equation is expressed by a matrix

7. For example identification of the equation C

8. Estimates of Klein’s Model I
Estimation
Klein’s model by 2SLS;
Klein’s model by 3SLS
Evaluation;

9. Estimates of Klein’s Model I (Estimated Asymptotic Standard Errors in Parentheses)
2SLS
3SLS C
16.6
0.017
0.216
0.810
16.4
0.125
0.163
0.79
(1.32)
(0.118)
(0.107)
(0.04)
(1.3)
(0.108)
(0.1)
(0.033) I
20.3
0.150
0.616
-0.158
28.2
-0.013
0.756
-0.195
(7.54)
(0.173)
(0.162)
(0.036)
(6.79)
(0.153)
(0.038) Wp
1.5
0.439
0.157
0.13
1.8
0.4
0.181
0.15
(1.15)
(0.039)
(0.029)
(1.12)
(0.032)
(0.034)
(0.028)
OLS
I3SLS
16.2
0.193
0.09
0.796
0.165
0.177
0.766
(0.091)
(1.22)
(0.096)
(0.09)
(0.035)
10.1
0.48
0.333
-0.112
42.9
-0.356
1.01
-0.26
(5.47)
(0.097)
(0.101)
(0.027)
(10.6)
(0.26)
(0.249)
(0.051)
1.48
0.146
2.62
0.375
0.194
0.168
(1.27)
(0.037)
(1.2)
(0.031)
I3SLS（iterative three-stage least squares）

10. References:
W. Greene (2000), Econometric Analysis, 4th edition, Prentice-Hall.
L. Klein (1950), Economic Fluctuations in the United States , (preface), Cowles Foundation Monograph
Robert Dixon, Simulation with Klein's Model I Using TSP, Department of Economics at the University of Melbourne
L. Klein, The dynamics of Price Flexibility: Comment, AER, Vol.40,
No.4,
L. Klein (1947), The Use of Econometric Models as a Guide to conomic
Policy, Econometrica, Vol.15, No.2.
David A. Freedman (2005). Statistical Models: Theory and Practice,
Cambridge University press.
David R. Brillinger(2001). Time Series-Data Analysis and Theory,
　　 　Society for Industrial and Applied Mathematics Philadelphia
N. Zhang (2012) A Statistical Model for Global-Flow-of-Funds Analysis
Social Systems Solutions Applied by Economic Sciences and Mathematical Solutions , Vol.3, No.1, 77-97