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計量経済学

課題(1)

 

Ct= a + b Yt    とおくと、

 

Ct= -153.864 + 0.679474 Yt

     (11.4845)  (.240243E-02)      Adjusted R-squared = 0.997383

 

課題(2)

 

一人あたりCt、YtをそれぞれCpYpとすると、回帰式は

 

Cp= a + b Yp

   

Cp= -.133362E-02 + 0.689714 Yp

    (.123071E-03) (.440714E-02)    Adjusted R-squared = 0.991498

 

課題(3)

 

@AR(1)をutに仮定して推定

 

Ct = 2819.48 + 0.467335 Yt

      (514.549) (0.027541)       Adjusted R-squared = 0.999860

 

Aダービン・ワトソン検定(修正の前と後)

 

修正前…Durbin-Watson statistic = 0.080206

修正後…Durbin-Watson statistic = 2.06460

 

修正前は0に近く、強い正の系列相関が見られる。

修正後は2に近く、系列相関はほとんどないと考えられる。修正前と修正後のDurbin-Watson statistic より、修正前は系列相関があったが修正後は有意水準1%でも帰無仮説ρ=0が棄却されず、自己相関がないということがいえる。

 

課題(1)

推定式:lnYiti1lnLit2lnKit+uit

 

 

α

β1

β2

σu2

σε2

Fixed

 effects

0.344484

0.768792

0.026077

0.047034

0.021151

Randam

 effects

1.63392

0.219540

0.782703

0.026077

0.039867

0.088825

0.032801

0.020302

Pool

2.12097

0.275136

0.674654

0.065943

0.089301

0.029162

0.026151

 

課題(2)

F(16,270) = 28.328

有意水準1%で共通の定数項を持つという帰無仮説は棄却される。

よって、各企業の生産関数は異なる定数項をもつ。

 

                       PANEL DATA ESTIMATION

                       =====================

 

 Balanced data:  NI=   17, T=   17, NOB=   289

 

 TOTAL (plain OLS) Estimates:

 

 Dependent variable: LNY

 

  Mean of dependent variable = 6.50638        Std. error of regression = .256794

 Std. dev. of dependent var. = 1.96040                       R-squared = .982961

    Sum of squared residuals = 18.8598              Adjusted R-squared = .982841

       Variance of residuals = .065943

 

            Estimated    Standard

 Variable  Coefficient     Error       t-statistic

 LNL       .275136       .029162       9.43485

 LNK       .674654       .026151       25.7989

 C         2.12097       .089301       23.7507

 

 BETWEEN (OLS on means) Estimates:

 

 Dependent variable: LNY

 

  Mean of dependent variable = 6.50638        Std. error of regression = .184735

 Std. dev. of dependent var. = 1.92556                       R-squared = .991946

    Sum of squared residuals = .477779              Adjusted R-squared = .990796

       Variance of residuals = .034127

 

            Estimated    Standard

 Variable  Coefficient     Error       t-statistic

 LNL       .537680       .144594       3.71855

 LNK       .422608       .134353       3.14550

 C         2.97010       .452037       6.57047

 

 WITHIN (fixed effects) Estimates:

 

 Dependent variable: LNY

 

 Sum of squared residuals = 7.04066                          R-squared = .993639

    Variance of residuals = .026077                 Adjusted R-squared = .993215

 Std. error of regression = .161482

 

            Estimated    Standard

 Variable  Coefficient     Error       t-statistic

 LNL       .344484       .047034       7.32419

 LNK       .768792       .021151       36.3475

 

 F test of A,B=Ai,B:  F(16,270) = 28.328,  P-value = [.0000]

 Critical F value for diffuse prior (Leamer, p.114) =   6.2184   

 

 Variance Components (random effects) Estimates:

 

 VWITH (variance of Uit)   =  0.26077E-01

 VBET  (variance of Ai)    =  0.39867E-01

 (computed from small sample formula)

 THETA (0=WITHIN, 1=TOTAL) =  0.37050E-01

 

 Dependent variable: LNY

 

 Sum of squared residuals = 7.91333                          R-squared = .992850

    Variance of residuals = .029309                 Adjusted R-squared = .992374

 Std. error of regression = .171198

 

            Estimated    Standard

 Variable  Coefficient     Error       t-statistic

 LNL       .219540       .032801       6.69307

 LNK       .782703       .020302       38.5524

 C         1.63392       .088825       18.3948

 

 Hausman test of H0:RE vs. FE:  CHISQ(2) = 21.925,  P-value = [.0000]