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かずひろよしなが
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1 y i = Z i δ i +ε i ε i δ

2 X y i = X Z i δ i + X ε i [ ] 1 δ ˆ i = Z i X( X X) 1 X Z i [ ] 1 σ ˆ 2 Z i X( X X) 1 X Z i Z i X( X X) 1 X y i σ ˆ 2 ˆ σ 2 = [ ] y i Z ˆ [ i δ i ] 1 y N p i Z i δ ˆ i i RSTAT N K p i

3 _2SLS C PLAG P WGWP (WG T G TIME PLAG KLAG XLAG) / DN RSTAT TWO STAGE LEAST SQUARES - DEPENDENT VARIABLE = C 7 EXOGENOUS VARIABLES 3 POSSIBLE ENDOGENOUS VARIABLES 21 OBSERVATIONS DN OPTION IN EFFECT - DIVISOR IS N R-SQUARE =.9767 R-SQUARE ADJUSTED =.9726 VARIANCE OF THE ESTIMATE-SIGMA**2 =

4 STANDARD ERROR OF THE ESTIMATE-SIGMA = SUM OF SQUARED ERRORS-SSE= MEAN OF DEPENDENT VARIABLE = ASYMPTOTIC VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME PLAG COEFFICIENT ERROR ***** DF P-VALUE CORR. COEFFICIENT AT MEANS P.17302E WGWP E CONSTANT DURBIN-WATSON = VON NEUMANN RATIO = RHO = RESIDUAL SUM = E-12 RESIDUAL VARIANCE = SUM OF ABSOLUTE ERRORS= R-SQUARE BETWEEN OBSERVED AND PREDICTED =.9768 RUNS TEST: 9 RUNS, 9 POSITIVE, 12 NEGATIVE, NORMAL STATISTIC = y 1 = Z 1 δ 1 +ε 1 y 2 = Z 2 δ 2 +ε 2... y M = Z M δ M +ε M y = Zδ +ε y = y 1 y 2. y M Z = Z Z Z M P = p 1 + p p M δ = [ δ 1 δ 2... δ M ]

5 ε = [ ε 1 ε 2... ε M ] E[ ε ε ] = σ 11 I σ 12 I. σ 1M I σ 21 I σ 22 I. σ 2M I.... σ M1 I σ M2 I. σ MM I = Σ I N σ ij ˆ σ ij ( ) ( y j Z jˆ δ OLS,j ) = 1 τ y i Z iˆ δ OLS,i δ ˆ OLS,i = ( Z i Z i ) 1 Z i y i τ τ 1 = N or τ 2 = MN P M ττ τ=τ σ Σ ˆ ˆ ij δ ˆ SUR = [ Ζ ( Σ ˆ 1 I N )Z] 1 Z ( Σ ˆ 1 I N )y [ Z ( Σ ˆ 1 I N )Z ] 1 L = MN 2 ln (2π) N 2 ln Σ 1 (y Zδ 2 ) (Σ 1 I N )( y Zδ)

6 δ= δ ˆ R = δ ˆ OLS + ( Z Z) 1 R (R( Z Z) 1 R ) 1 (r Rˆ δ OLS ) ˆ σ ij ( ) ( y j Z jˆ δ R,j ) = 1 τ y i Z iˆ δ R,i ττ τ=τ τ 1 = N or τ 2 = MN (P q) M δ ˆ ˆ RSUR = δ + C ˆ R (RC ˆ R ) 1 (r Rˆ δ ) ˆ = ˆ C ˆ = [ Z ( Σ ˆ 1 I N )Z] 1 δ C Z ( ˆ Σ 1 I N )y σ ij ˆ σ ij ( ) ( y j Z jˆ δ 2SLS,j ) = 1 τ y i Z iˆ δ 2SLS,i τ { } 1 δ ˆ = Z Σ ˆ [ 1 X( X X) 1 X ]Z Z Σ ˆ [ 1 X( X X) 1 X ]y Z Σ ˆ [ ( 1 X( X X) 1 X )Z ] 1

7 δ ˆ R 2 = 1 E E / Y * Y * Y* CHI-SQUARE χ R ˆ 2 σ 2 ij r ij = σ ˆ ii σ ˆ jj BREUSCH-PAGAN LM TEST FOR DIAGONAL COVARIANCE MATRIX

8 M i 1 λ = N i=2 j=1 2 r ij 2 χ (M (M 1)/ 2 ) LIKELIHOOD RATIO TEST OF DIAGONAL COVARIANCE MATRIX M 2 N ln(ˆ σ ii ) ln Σ ˆ i=1 with τ=n 2 χ (M (M 1)/ 2 )

11 ( X X) 1

12 ˆ Σ

13 ln Σ ˆ SYSTEM 3 WG T G TIME1 PLAG KLAG XLAG / DN OLS C PLAG P WGWP OLS I PLAG KLAG P OLS WP TIME1 XLAG X TEST P:1=P:2 _SYSTEM 3 WG T G TIME1 PLAG KLAG XLAG / DN _OLS C PLAG P WGWP _OLS I PLAG KLAG P _OLS WP TIME1 XLAG X THREE STAGE LEAST SQUARES-- 3 EQUATIONS 7 EXOGENOUS VARIABLES 9 RIGHT-HAND SIDE VARIABLES IN SYSTEM MAX ITERATIONS = 1 CONVERGENCE TOLERANCE = OBSERVATIONS DN OPTION IN EFFECT - DIVISOR IS N ITERATION 0 COEFFICIENTS E ITERATION SIGMA BREUSCH-PAGAN LM TEST FOR DIAGONAL COVARIANCE MATRIX CHI-SQUARE = WITH 3 DEGREES OF FREEDOM LOG OF DETERMINANT OF SIGMA= ITERATION 1 SIGMA INVERSE

14 ITERATION 1 COEFFICIENTS ITERATION SIGMA LOG OF DETERMINANT OF SIGMA= SYSTEM R-SQUARE = CHI-SQUARE = WITH 9 D.F. VARIABLE COEFFICIENT ST.ERROR T-RATIO PLAG P WGWP E PLAG KLAG E P E E-01 TIME E XLAG E X E EQUATION 1 OF 3 EQUATIONS DEPENDENT VARIABLE = C 21 OBSERVATIONS R-SQUARE =.9801 VARIANCE OF THE ESTIMATE-SIGMA**2 = STANDARD ERROR OF THE ESTIMATE-SIGMA = SUM OF SQUARED ERRORS-SSE= MEAN OF DEPENDENT VARIABLE = ASYMPTOTIC VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR ***** DF P-VALUE CORR. COEFFICIENT AT MEANS PLAG P WGWP E CONSTANT EQUATION 2 OF 3 EQUATIONS DEPENDENT VARIABLE = I R-SQUARE = OBSERVATIONS VARIANCE OF THE ESTIMATE-SIGMA**2 = STANDARD ERROR OF THE ESTIMATE-SIGMA = SUM OF SQUARED ERRORS-SSE= MEAN OF DEPENDENT VARIABLE = ASYMPTOTIC VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR ***** DF P-VALUE CORR. COEFFICIENT AT MEANS PLAG KLAG E P E E CONSTANT EQUATION 3 OF 3 EQUATIONS DEPENDENT VARIABLE = WP 21 OBSERVATIONS R-SQUARE =.9863 VARIANCE OF THE ESTIMATE-SIGMA**2 = STANDARD ERROR OF THE ESTIMATE-SIGMA = SUM OF SQUARED ERRORS-SSE= MEAN OF DEPENDENT VARIABLE =

15 ASYMPTOTIC VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR ***** DF P-VALUE CORR. COEFFICIENT AT MEANS TIME E XLAG E X E CONSTANT _TEST P:1=P:2 TEST VALUE= STD. ERROR OF TEST VALUE = ASYMPTOTIC NORMAL STATISTIC = WALD CHI-SQUARE STATISTIC = WITH 1 D.F. SYSTEM 2 / RESTRICT OLS A B C OLS D E F RESTRICT B:1+E:2=0 END GENR CONST=1 SYSTEM 2 / RESTRICT NOCONSTANT OLS A B C CONST OLS D E F CONST RESTRICT B:1+E:2=0 RESTRICT CONST:1+CONST:2=1 END

4 OLS 4 OLS 4.1 nurseries dual c dual i = c + βnurseries i + ε i (1) 1. OLS Workfile Quick - Estimate Equation OK Equation specification dual c nurser

4 OLS 4 OLS 4.1 nurseries dual c dual i = c + βnurseries i + ε i (1) 1. OLS Workfile Quick - Estimate Equation OK Equation specification dual c nurser 1 EViews 2 2007/5/17 2007/5/21 4 OLS 2 4.1.............................................. 2 4.2................................................ 9 4.3.............................................. 11 4.4