Microsoft Word - 計量研修テキスト_第5版）.doc

(1)

Q8-1【テキスト P131】

◆ Engle-Granger 検定

Dependent Variable: RM2 Method: Least Squares Date: 11/04/05 Time: 15:15 Sample: 1967Q1 1999Q1 Included observations: 129

Variable Coefficient Std. Error t-Statistic Prob.

RGDP 0.012792 0.000194 65.92203 0.0000 R -95.45715 11.33648 -8.420349 0.0000 C -443.4312 124.8461 -3.551821 0.0005

R-squared 0.989294 Mean dependent var 3124.543 Adjusted R-squared 0.989124 S.D. dependent var 1529.608 S.E. of regression 159.5169 Akaike info criterion 13.00516 Sum squared resid 3206149. Schwarz criterion 13.07166 Log likelihood -835.8327 F-statistic 5821.739 Durbin-Watson stat 0.677246 Prob(F-statistic) 0.000000

共和分なしが棄却 ⇒ 上記パラメーターの係数推定値は『超一致性』という性質を有する。

（つまり共和分あり）

（上記パラメーターの計数推定値を用いたときの残差系列が定常である（＝共和分あり）

かどうか以下にて確認を行う。）

(2)

τ＝－3.7429 ＋(1/124)×(－8.352) ＋(1/(124×124))×(－13.41）＝－3.81

－3.86＜τ＝－3.81 であり

Null Hypothesis: RESID01 has a unit root Exogenous: None

Lag Length: 4 (Automatic based on SIC, MAXLAG=12)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -3.861180 0.0002 Test critical values: 1% level -2.583744

5% level -1.943427

10% level -1.615011

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID01) Method: Least Squares

Date: 11/04/05 Time: 15:19 Sample (adjusted): 1968Q2 1999Q1

Included observations: 124 after adjustments

RESID01(-1) -0.189323 0.049032 -3.861180 0.0002 D(RESID01(-1)) -0.096813 0.083308 -1.162111 0.2475 D(RESID01(-2)) 0.224583 0.081044 2.771140 0.0065 D(RESID01(-3)) -0.038088 0.083831 -0.454342 0.6504 D(RESID01(-4)) 0.524326 0.080090 6.546694 0.0000

R-squared 0.740254 Mean dependent var 1.251927 Adjusted R-squared 0.731523 S.D. dependent var 132.5547 S.E. of regression 68.68298 Akaike info criterion 11.33637 Sum squared resid 561364.9 Schwarz criterion 11.45009 Log likelihood -697.8548 Durbin-Watson stat 1.857663

有意水準 5 パーセントで H

0

：共和分なしを棄却

この臨界値は利用不可

Mackinnon 表（p6）を用いて

正しい臨界値を算出

(3)

Q8-2【テキストP139】

◆ Johansenタイプの共和分検定

Date: 11/04/05 Time: 17:45 Sample (adjusted): 1967Q3 1999Q1

Included observations: 127 after adjustments Trend assumption: Linear deterministic trend Series: RM2 RGDP R

Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.179662 31.90042 29.79707 0.0282 At most 1 0.047958 6.749453 15.49471 0.6069 At most 2 0.003992 0.507944 3.841466 0.4760

Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level

**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05

None * 0.179662 25.15096 21.13162 0.0128 At most 1 0.047958 6.241509 14.26460 0.5824 At most 2 0.003992 0.507944 3.841466 0.4760

Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level

Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

RM2 RGDP R

0.004483 -5.93E-05 0.788142 0.001070 -2.72E-05 -0.633378 0.005624 -6.86E-05 0.344075

Unrestricted Adjustment Coefficients (alpha):

D(RM2) -23.48677 6.756824 2.457682 D(RGDP) 581.0812 385.6731 146.5167 D(R) -0.008676 0.061241 -0.011492

共和分ベクト

ルは１本

トレース検定

最大固有値検定

(4)

1 Cointegrating Equation(s): Log likelihood -1955.714

Normalized cointegrating coefficients (standard error in parentheses)

RM2 RGDP R

1.000000 -0.013220 175.8026 (0.00061) (36.2769)

Adjustment coefficients (standard error in parentheses) D(RM2) -0.105294 (0.02865) D(RGDP) 2.605050 (1.28488) D(R) -3.89E-05 (0.00014)

RM2 RGDP R

1.000000 0.000000 1007.103 (241.523) 0.000000 1.000000 62883.50

(17959.0)

Adjustment coefficients (standard error in parentheses) D(RM2) -0.098061 0.001208 (0.02932) (0.00041) D(RGDP) 3.017890 -0.044934 (1.31116) (0.01855) D(R) 2.67E-05 -1.15E-06 (0.00014) (1.9E-06)

符号は正負反対

共和分ベクトル

(5)

Q8-3【テキスト P142】

◆ 誤差修正モデルの集計

Model A

Dependent Variable: D(RM2) Method: Least Squares Date: 11/11/05 Time: 12:13 Sample (adjusted): 1967Q3 1999Q1

D(RM2(-1)) -0.766421 0.059619 -12.85523 0.0000 D(RGDP(-1)) 0.003851 0.002078 1.853156 0.0663 D(R(-1)) 10.58822 20.41298 0.518700 0.6049 RESID01(-1) -0.087977 0.048281 -1.822198 0.0709

C 58.21688 8.907505 6.535711 0.0000

R-squared 0.639576 Mean dependent var 39.60394 Adjusted R-squared 0.627759 S.D. dependent var 122.7610 S.E. of regression 74.89842 Akaike info criterion 11.50872 Sum squared resid 684392.3 Schwarz criterion 11.62069 Log likelihood -725.8035 F-statistic 54.12250 Durbin-Watson stat 1.210813 Prob(F-statistic) 0.000000

Model B

Dependent Variable: D(RM2) Method: Least Squares Date: 11/17/05 Time: 18:46 Sample (adjusted): 1967Q3 1999Q1

D(RGDP) 0.007428 0.003139 2.366266 0.0196 D(R) 30.24476 29.81975 1.014253 0.3125 D(RGDP(-1)) -0.000973 0.003150 -0.309038 0.7578 D(R(-1)) 11.86488 31.01801 0.382516 0.7027 RESID01(-1) -0.342852 0.068291 -5.020489 0.0000 C 21.67259 15.36925 1.410127 0.1611

R-squared 0.196848 Mean dependent var 39.60394 Adjusted R-squared 0.163659 S.D. dependent var 122.7610 S.E. of regression 112.2669 Akaike info criterion 12.32573 Sum squared resid 1525068. Schwarz criterion 12.46010 Log likelihood -776.6837 F-statistic 5.931264 Durbin-Watson stat 3.023075 Prob(F-statistic) 0.000061

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Model C Dependent Variable: D(RM2) Method: Least Squares Date: 11/17/05 Time: 18:47 Sample (adjusted): 1967Q3 1999Q1

D(RM2(-1)) -0.762839 0.056712 -13.45114 0.0000 D(RGDP) 0.007324 0.001990 3.679793 0.0004 D(R) 20.14072 18.92361 1.064317 0.2893 D(RGDP(-1)) 0.002569 0.002015 1.275243 0.2047 D(R(-1)) 8.047629 19.67056 0.409120 0.6832 RESID01(-1) -0.114351 0.046516 -2.458315 0.0154 C 41.97706 9.861847 4.256511 0.0000

R-squared 0.679735 Mean dependent var 39.60394 Adjusted R-squared 0.663722 S.D. dependent var 122.7610 S.E. of regression 71.18844 Akaike info criterion 11.42208 Sum squared resid 608135.4 Schwarz criterion 11.57885 Log likelihood -718.3020 F-statistic 42.44834 Durbin-Watson stat 1.243786 Prob(F-statistic) 0.000000

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演習【テキスト P143】

問 2）各変数の単位根検定

・WDOTについてのADF検定～和分次数は１

注）レベル系列では単位根ありの帰無仮説を棄却できず

Null Hypothesis: D(WDOT) has a unit root

Exogenous: None

t-Statistic Prob.*

5% level -1.949609

10% level -1.611593

Augmented Dickey-Fuller Test Equation Dependent Variable: D(WDOT,2)

Method: Least Squares Date: 11/17/05 Time: 14:13 Sample (adjusted): 1962 2000

D(WDOT(-1)) -1.085957 0.158110 -6.868380 0.0000

R-squared 0.553713 Mean dependent var -0.086667 Adjusted R-squared 0.553713 S.D. dependent var 4.868098 S.E. of regression 3.252120 Akaike info criterion 5.221798 Sum squared resid 401.8989 Schwarz criterion 5.264453 Log likelihood -100.8251 Durbin-Watson stat 2.034670

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・CPIDOTについてのADF検定～和分次数は１

注）レベル系列では単位根ありの帰無仮説を棄却できず

Null Hypothesis: D(CPIDOT) has a unit root

Exogenous: None

t-Statistic Prob.*

5% level -1.949609

10% level -1.611593

Augmented Dickey-Fuller Test Equation Dependent Variable: D(CPIDOT,2) Method: Least Squares

Date: 11/17/05 Time: 14:16 Sample (adjusted): 1962 2000

D(CPIDOT(-1)) -1.005614 0.161203 -6.238175 0.0000

R-squared 0.505860 Mean dependent var -0.053590 Adjusted R-squared 0.505860 S.D. dependent var 4.079513 S.E. of regression 2.867699 Akaike info criterion 4.970203 Sum squared resid 312.5004 Schwarz criterion 5.012859 Log likelihood -95.91896 Durbin-Watson stat 2.010199

(9)

・INVRUについてのADF検定～和分次数は１

注）レベル系列では単位根ありの帰無仮説を棄却できず

Null Hypothesis: D(INVRU) has a unit root

Exogenous: None

t-Statistic Prob.*

5% level -1.949609

10% level -1.611593

Augmented Dickey-Fuller Test Equation Dependent Variable: D(INVRU,2) Method: Least Squares

D(INVRU(-1)) -0.663213 0.149292 -4.442401 0.0001

R-squared 0.341306 Mean dependent var -0.001700 Adjusted R-squared 0.341306 S.D. dependent var 0.061669 S.E. of regression 0.050050 Akaike info criterion -3.126265 Sum squared resid 0.095192 Schwarz criterion -3.083610 Log likelihood 61.96217 Durbin-Watson stat 1.869526

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問３）Engle-Granger検定

Engle-Granger検定：帰無仮説（共和分なし）が棄却⇒共和分あり

Mackinnon 表（p132）での有意水準 5％における臨界値を算出

τ＝－3.7429 ＋(1/40)×(－8.352) ＋(1/(40×40))×(－13.41）＝－3.96

－4.79＜τ＝－3.96 であり

帰無仮説は有意水準 5％にて棄却される

Null Hypothesis: RESID01 has a unit root Exogenous: None

t-Statistic Prob.*

5% level -1.949319

10% level -1.611711

Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID01) Method: Least Squares

RESID01(-1) -0.762076 0.158859 -4.797174 0.0000

R-squared 0.370880 Mean dependent var 0.036024 Adjusted R-squared 0.370880 S.D. dependent var 1.960219 S.E. of regression 1.554788 Akaike info criterion 3.745238 Sum squared resid 94.27728 Schwarz criterion 3.787460 Log likelihood -73.90476 Durbin-Watson stat 1.987382

この臨界値は利用不可

Mackinnon 表（p132）を用

いて正しい臨界値を算出

(11)

問４）Error Correction Model の推定

Model A(P142)に相当～RESID01 が有意でない

Model B(P143)に相当～RESID01 が有意

Dependent Variable: D(WDOT)

D(INVRU) 17.08327 5.490076 3.111663 0.0038 D(CPIDOT) 0.876423 0.097327 9.004890 0.0000 D(INVRU(-1)) -6.327187 5.780843 -1.094509 0.2817 D(CPIDOT(-1)) 0.211404 0.097709 2.163624 0.0378 RESID01(-1) -0.758395 0.158484 -4.785316 0.0000 C -0.098060 0.255199 -0.384251 0.7033

R-squared 0.809647 Mean dependent var -0.365641 Adjusted R-squared 0.780805 S.D. dependent var 3.243661 S.E. of regression 1.518625 Akaike info criterion 3.814127 Sum squared resid 76.10537 Schwarz criterion 4.070059 Log likelihood -68.37547 F-statistic 28.07234 Durbin-Watson stat 1.887822 Prob(F-statistic) 0.000000 Dependent Variable: D(WDOT)

D(WDOT(-1)) -0.796663 0.288256 -2.763738 0.0092 D(INVRU(-1)) 36.01574 9.973617 3.611101 0.0010 D(CPIDOT(-1)) 0.646496 0.291678 2.216471 0.0335 RESID01(-1) 0.054406 0.358856 0.151611 0.8804 C -0.100094 0.446824 -0.224012 0.8241

R-squared 0.372055 Mean dependent var -0.365641 Adjusted R-squared 0.298179 S.D. dependent var 3.243661 S.E. of regression 2.717369 Akaike info criterion 4.956414 Sum squared resid 251.0591 Schwarz criterion 5.169691 Log likelihood -91.65008 F-statistic 5.036220 Durbin-Watson stat 1.533185 Prob(F-statistic) 0.002688

(12)

Model C(P143)に相当～RESID01 が有意

Dependent Variable: D(WDOT)

D(WDOT(-1)) -0.075629 0.184465 -0.409990 0.6845 D(INVRU) 16.48883 5.746530 2.869354 0.0072 D(CPIDOT) 0.859512 0.106860 8.043359 0.0000 D(INVRU(-1)) -4.396006 7.514612 -0.584994 0.5627 D(CPIDOT(-1)) 0.268849 0.171537 1.567293 0.1269 RESID01(-1) -0.696040 0.221128 -3.147675 0.0035 C -0.096928 0.258493 -0.374973 0.7102

R-squared 0.810641 Mean dependent var -0.365641 Adjusted R-squared 0.775136 S.D. dependent var 3.243661 S.E. of regression 1.538137 Akaike info criterion 3.860169 Sum squared resid 75.70768 Schwarz criterion 4.158757 Log likelihood -68.27330 F-statistic 22.83189 Durbin-Watson stat 1.842557 Prob(F-statistic) 0.000000

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問５）Johansen タイプの共和分検定

Included observations: 39 after adjustments Trend assumption: No deterministic trend Series: WDOT INVRU CPIDOT

Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05

None 0.317440 22.90871 24.27596 0.0736 At most 1 0.151451 8.014409 12.32090 0.2355 At most 2 0.040430 1.609526 4.129906 0.2401

Trace test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05

None 0.317440 14.89430 17.79730 0.1297 At most 1 0.151451 6.404883 11.22480 0.3059 At most 2 0.040430 1.609526 4.129906 0.2401

Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level

Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

WDOT INVRU CPIDOT

-0.259022 -0.181387 0.561796 0.394924 -3.722120 -0.259232 -0.065622 2.877015 -0.021370

Unrestricted Adjustment Coefficients (alpha):

D(WDOT) -1.229669 -0.354196 0.186531 D(INVRU) -0.015846 -0.001795 -0.006875 D(CPIDOT) -1.106914 0.334827 0.250378

トレース検定

最大固有値検定

次頁に続く

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Johansen タイプの検定では『共和分ベクトルなし』の結果

WDOT INVRU CPIDOT

1.000000 0.700275 -2.168908 (3.13575) (0.32597)

Adjustment coefficients (standard error in parentheses) D(WDOT) 0.318512 (0.09731) D(INVRU) 0.004105 (0.00182) D(CPIDOT) 0.286715 (0.09717)

WDOT INVRU CPIDOT

1.000000 0.000000 -2.064301 (0.16164) 0.000000 1.000000 -0.149380

(0.02490)

Adjustment coefficients (standard error in parentheses) D(WDOT) 0.178631 1.541406 (0.17517) (1.38216) D(INVRU) 0.003396 0.009556 (0.00332) (0.02618) D(CPIDOT) 0.418946 -1.045486 (0.17514) (1.38194)

Microsoft Word - 計量研修テキスト_第5版）.doc

Q8-1【テキスト P131】

◆ Engle-Granger 検定

共和分なしが棄却 ⇒ 上記パラメーターの係数推定値は『超一致性』という性質を有する。

（つまり共和分あり）

（上記パラメーターの計数推定値を用いたときの残差系列が定常である（＝共和分あり）

かどうか以下にて確認を行う。）

τ＝ －3.7429 ＋(1/124)×(－8.352) ＋(1/(124×124))×(－13.41）＝ －3.81

－3.86＜τ＝－3.81 であり

有意水準 5 パーセントで H

：共和分なしを棄却

この臨界値は利用不可

Mackinnon 表（p6）を用いて

正しい臨界値を算出

Q8-2【テキストP139】

◆ Johansenタイプの共和分検定

共和分ベクト

ルは１本

トレース検定

最大固有値検定

符号は正負反対

共和分ベクトル

Q8-3【テキスト P142】

◆ 誤差修正モデルの集計

演習【テキスト P143】

問 2）各変数の単位根検定

・WDOTについてのADF検定 ～ 和分次数は１

注）レベル系列では単位根ありの帰無仮説を棄却できず

・CPIDOTについてのADF検定 ～ 和分次数は１

注）レベル系列では単位根ありの帰無仮説を棄却できず

・INVRUについてのADF検定 ～ 和分次数は１

注）レベル系列では単位根ありの帰無仮説を棄却できず

問３）Engle-Granger検定

Engle-Granger検定：帰無仮説（共和分なし）が棄却⇒共和分あり

Mackinnon 表（p132）での有意水準 5％における臨界値を算出

τ＝ －3.7429 ＋(1/40)×(－8.352) ＋(1/(40×40))×(－13.41）＝ －3.96

－4.79＜τ＝－3.96 であり

帰無仮説は有意水準 5％にて棄却される

この臨界値は利用不可

Mackinnon 表（p132）を用

いて正しい臨界値を算出

問４）Error Correction Model の推定

Model A(P142)に相当～RESID01 が有意でない

Model B(P143)に相当～RESID01 が有意

Model C(P143)に相当～RESID01 が有意

問５）Johansen タイプの共和分検定

トレース検定

最大固有値検定

次頁に続く

Johansen タイプの検定では『共和分ベクトルなし』の結果

τ＝－3.7429 ＋(1/124)×(－8.352) ＋(1/(124×124))×(－13.41）＝－3.81

・WDOTについてのADF検定～和分次数は１

・CPIDOTについてのADF検定～和分次数は１

・INVRUについてのADF検定～和分次数は１

τ＝－3.7429 ＋(1/40)×(－8.352) ＋(1/(40×40))×(－13.41）＝－3.96