構造方程式の作成と応用

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

Identification

事例3Klein’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 1921-41, which is widely known as Klein’s Model I.

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

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

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

for example, identification of the Equation C For example identificationof the equation C

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

Estimates of Klein’s Model I(Estimated Asymptotic Standard Errors in Parentheses) I3SLS（iterative three-stage least squares）

References: • W. Greene (2000), Econometric Analysis, 4th edition, Prentice-Hall. • L. Klein (1950), Economic Fluctuations in the United States 1921-1941, (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, 605-609. • 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

構造方程式の作成と応用

構造方程式の作成と応用

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