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中級(jí)計(jì)量經(jīng)濟(jì)學(xué)作業(yè)三參考答案

Forδ≠β,

y–δz=y–βz+(β–δ)z,

t t t t t

whichisanI(0)sequence(y–βz)plusanI(1)sequence.SinceanI(1)sequencehasa

t t

growingvariance,itdominatestheI(0)part,andtheresultingsumisanI(1)sequence.

IfunemfollowsastableAR(1)process,thenthisisthenullmodelusedtotestfor

t

Grangercausality:underthenullthatgMdoesnotGrangercauseunem,wecanwrite

t t

unem=β+βunem +u

t 0 1 t-1 t

E(u|unem,gM,unem,gM,K)=0

t t-1 t-1 t-2 t-2

and|β|<1.Now,itisuptoustochoosehowmanylagsofgMtoaddtothisequation.

1

ThesimplestapproachistoaddgM andtodoattest.Butwecouldaddasecondor

t-1

thirdlag(andprobablynotbeyondthiswithannualdata),andcomputeanFtestfor

jointsignificanceofalllagsofgM.

t

3.(a)

RestrictedmodelA:Yt=α1+α2X3t+α3X4t+α4X6t+ut

RestrictedmodelB:Yt=β1+β2X2t+β3X5t+β4X6t+ut

構(gòu)造ModelC：Yt=γ1+γ2X2t+γ3X3t+γ4X4t+γ5X5t+γ6X6t+ut

這時(shí)modelC嵌套或包含了modelA和B

利用F檢驗(yàn)Ho：γ??γ??γ?,根據(jù)檢驗(yàn)結(jié)果作出相應(yīng)判斷

再利用F檢驗(yàn)Ho’：γ??γ??γ?，根據(jù)檢驗(yàn)結(jié)果作出相應(yīng)判斷

(b)Jtest:

4.

(a)

.regLFPLWW1KL6K618WAWEUNCITPRIN

Source|

SS

df

MS

Numberofobs=

753

+

F(8, 744)=

17.28

Model|28. 83.

Prob>F =

0.0000

Residual|155.781861 744.

R-squared =

0.1567

+

AdjR-squared=

0.1476

Total|184.727756 752.

RootMSE =

.45759

LFP| Coef. Std.Err. t P>|t| [95%Conf.Interval]

+

LWW1|

. . 2.92

0.004

.

.

KL6|

-. . -8.14

0.000

-.

-.

K618|

-. . -0.60

0.548

-.

.019037

WA|

-. . -4.55

0.000

-.

-.

WE|

. . 4.87

0.000

.025116

.

UN|

-.003487

.

-0.64

0.525

-. .

CIT|

-.004477

.

-0.12

0.903

-. .

PRIN|

-6.77e-06

1.54e-06

-4.40

0.000

-9.79e-06 -3.75e-06

_cons|

.

.162686

4.26

0.000

. 1.01167

(b)

.logitLFPLWW1KL6K618WAWEUNCITPRIN

Ition0:loglikelihood=-514.8732Ition1:loglikelihood=-449.998Ition2:loglikelihood=-449.4765Ition3:loglikelihood=-449.47564Ition4:loglikelihood=-449.47564

Logisticregression

Numberofobs

=

753

LRchi2(8)

=

130.80

Prob>chi2

=

0.0000

Loglikelihood=-449.47564

PseudoR2

=

0.1270

LFP| Coef. Std.Err. z P>|z| [95%Conf.Interval]

+LWW1| . . 2.95 0.003 . .

KL6

|

-1.469201 . -7.40

0.000

-1.858291

-1.080112

K618

|

-. . -0.75

0.454

-.

.

WA

|

-.

.

-4.51

0.000 -.083554 -.

WE

|

.

.

4.81

0.000

. .

UN

|

-.

.

-0.70

0.483

-. .

CIT

|

.

.

0.07

0.943

-. .361949

PRIN

|

-.

8.11e-06

-4.36

0.000

-. -.

_cons

|

.

.

1.18

0.237

-. 2.527319

(c)

.probitLFPLWW1KL6K618WAWEUNCITPRIN

Ition0:loglikelihood=-514.8732Ition1:loglikelihood=-449.69111Ition2:loglikelihood=-449.39704Ition3:loglikelihood=-449.39696Ition4:loglikelihood=-449.39696

Probitregression

Numberofobs

=

753

LRchi2(8)

=

130.95

Prob>chi2

=

0.0000

Loglikelihood=-449.39696

PseudoR2

=

0.1272

LFP| Coef. Std.Err. z P>|z| [95%Conf.Interval]

+

LWW1| . .092771 3.04

0.002 .

.

KL6| -.880823 . -7.68

0.000 -1.105544

-.

K618|

-.

.

-0.73

0.466

-. .

WA|

-.

.

-4.55

0.000

-. -.

WE|

.

.

4.92

0.000

. .

UN|

-.

.

-0.69

0.489

-. .

CIT|

.

.

0.09

0.926

-. .

PRIN|

-.

4.71e-06

-4.51

0.000

-. -.000012

_cons|

.

.

1.18

0.239

-. 1.51277

(d)

Logit

ForP=0.568

P??1?P??β?LWW??0.568??1?0.568??0. ?0.113958P??1?P??β?KL??0.568??1?0.568????1.469201???0.36051

…….

…….

ForP=0.9

P??1?P??β?LWW??0.9??1?0.9??0. ?0.041798P??1?P??β?KL??0.9??1?0.9????1.469201???0.13222

…….

…….

Probit

ForP=0.568

f?P??β?LWW??0.393?0. ?0.110843f?P??β?KL??0.393???0.880823???0.34616

…………

…………

ForP=0.9

f?P??β?LWW??0.175?0. ?0.049357f?P??β?KL??0.175???0.880823???0.154144

…….

…….

5.

19500

19600

19700

19800

DATE

19500

19600

19700

19800

DATE

IS100000

120000

140000

IE

150000200000250000

(a)

0

5

10

15

Lag

Bartlett'sformulaforMA(q)95%confidencebands

0

5

10

15

Lag

Bartlett'sformulaforMA(q)95%confidencebands

AutocorrelationsofIE

-0.50 0.00 0.50

1.00

60000

80000

AutocorrelationsofIS

-0.50 0.00 0.50

50000

100000

1.00

PlotsofIE PlotsofIS

0

10

20

Lag

30

40

Bartlett'sformulaforMA(q)95%confidencebands

0

10

20

Lag

30

40

Bartlett'sformulaforMA(q)95%confidencebands

AutocorrelationsofD.IE

-0.40-0.200.000.200.40

AutocorrelationsofD.IS

-0.-200.100.000.00.20

ACFofIE ACFofIS

ACFofD.IE ACFofD.IS

0

10

20

Lag

30

40

95%Confidencebands[se1/sqrt(n)]

0

10

20

Lag

30

40

95%Confidencebands[se1/sqrt(n)]

PartialautocorrelationsofD.IE

-0.200.000.200.40

PartialautocorrelationsofD.IS

-0.-200.100.000.00.200.30

(b)

PACFofD.IE PACFofD.IS

IE:ARIMA(2,1,0),ARIMA(6,1,0)****,ARIMA(8,1,0)

IS:ARIMA(2,1,0)****,ARIMA(6,1,0),ARIMA(8,1,0)

(c)

ForIEseries:ARIMA(6,1,0)ForISseries:ARIMA(2,1,0)

IE:ARIMA(2,1,0)

.arimaIEifDATE>19554&DATE<19801,arima(2,1,0)

ARIMAregression

Sample:19562-19794,butwithgaps

Numberofobs

=

72

Waldchi2(2)

=

7.01

Loglikelihood=-698.0455

Prob>chi2

=

0.0301

|D.IE|

Coef.

OPG

Std.Err.

z

P>|z|

[95%Conf.Interval]

+

IE |

_cons| 1772.009 690.9798 2.56 0.010 417.7138 3126.305

ARMA

|

L1.| . .

1.07

0.287

-.

.

L2.| .

.176798

1.89

0.059

-.

.

+

ar|

+

/sigma| 3731.725 411.8912 9.06 0.000 2924.433 4539.017

Note:Thetestofthevarianceagainstzeroisonesided,andthetwo-sidedconfidenceintervalistruncatedatzero.

.estatic

Model| Obs ll(null) ll(model) df AIC BIC

+

.| 72 . -698.0455 4 1404.091 1413.198

Note:N=ObsusedincalculatingBIC;see[R]BICnote

IE:ARIMA(6,1,0)*******

.arimaIEifDATE>19554&DATE<19801,arima(6,1,0)

ARIMAregression

Sample:19562-19794,butwithgaps

Numberofobs

=

72

Waldchi2(6)

=

546.38

Loglikelihood=-689.423

Prob>chi2

=

0.0000

|D.IE|

Coef.

OPG

Std.Err.

z

P>|z|

[95%Conf.Interval]

+

IE |

_cons| 1786.862 437.2394 4.09 0.000 929.8882 2643.835

+

ARMA

|

ar|

L1.|

. . 1.12

0.265

-.

.

L2.|

. . 0.26

0.793

-.

.

L3.|

-. . -7.68

0.000

-.

-.

L4.|

-. . -4.28

0.000

-.622839

-.

L5.|

. . 1.38

0.169

-.

.

L6.|

-. . -2.54

0.011

-.

-.

+

/sigma| 2066.684 317.2699 6.51 0.000 1444.847 2688.522

Note:Thetestofthevarianceagainstzeroisonesided,andthetwo-sidedconfidenceintervalistruncatedatzero.

.estatic

Model| Obs ll(null) ll(model) df AIC BIC

+

.| 72 . -689.423 8 1394.846 1413.059

Note:N=ObsusedincalculatingBIC;see[R]BICnote

IE:ARIMA(8,1,0)

.arimaIEifDATE>19554&DATE<19801,arima(8,1,0)

ARIMAregression

Sample:19562-19794,butwithgaps

Numberofobs

=

72

Waldchi2(8)

=

229.19

Loglikelihood=-687.7048

Prob>chi2

=

0.0000

|D.IE|

Coef.

OPG

Std.Err.

z

P>|z|

[95%Conf.Interval]

+

IE |

_cons| 1758.374 616.0702 2.85 0.004 550.8987 2965.849

+

ARMA

|

ar

|

L1.

|

.357607 . 1.85

0.065

-.

.

L2.

|

. . 0.38

0.702

-.

.

L3.

|

-. . -0.89

0.373

-.

.

L4.

|

-. . -1.01

0.314

-.

.

L5.

|

. . 0.60

0.547

-.

.

L6.

|

-. . -3.22

0.001

-.

-.

L7.

|

. . 5.91

0.000

.

.

L8.

|

. . 0.12

0.906

-.

.

+

/sigma| 2434.234 318.2673 7.65 0.000 1810.441 3058.026

.estatic

Model| Obs ll(null) ll(model) df AIC BIC

+

.| 72 . -687.7048 10 1395.41 1418.176

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10

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NUMPAGES

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IS:ARIMA(2,1,0)******

.arimaISifDATE>19554&DATE<19801,arima(2,1,0)

ARIMAregression

Sample:19562-19794,butwithgaps

Numberofobs

=

72

Waldchi2(2)

=

9.77

Loglikelihood=-664.715

Prob>chi2

=

0.0076

|D.IS|

Coef.

OPG

Std.Err.

z

P>|z|

[95%Conf.Interval]

+

IS |

_cons| 838.0285 398.873 2.10 0.036 56.25176 1619.805

ARMA

|

L1.| .199456 . 1.38

0.169

-.

.

L2.| . . 1.74

0.083

-.

.

+

ar|

+

/sigma| 2363.697 212.9106 11.10 0.000 1946.4 2780.994

Note:Thetestofthevarianceagainstzeroisonesided,andthetwo-sidedconfidenceintervalistruncatedatzero.

.estatic

Model| Obs ll(null) ll(model) df AIC BIC

+

.| 72 . -664.715 4 1337.43 1346.537

Note:N=ObsusedincalculatingBIC;see[R]BICnote

IS:ARIMA(6,1,0)

.arimaISifDATE>19554&DATE<19801,arima(6,1,0)

ARIMAregression

Sample:19562-19794,butwithgaps

Numberofobs

=

72

Waldchi2(6)

=

46.59

Loglikelihood=-662.5394

Prob>chi2

=

0.0000

|D.IS|

Coef.

OPG

Std.Err.

z

P>|z|

[95%Conf.Interval]

+

IS |

_cons| 876.4501 540.3708 1.62 0.105 -182.6573 1935.557

+

ARMA |

ar|

L1.| . . 1.72 0.086 -. .

L2.| . . 1.63 0.103 -.104214 1.134455

L3.| -.605642 . -2.54 0.011 -1.073006 -.

L4.|-. . -1.00 0.316 -. .

L5.| .304689 . 1.14 0.253 -. .

L6.|-. . -0.69 0.490 -. .

+

/sigma| 1811.938 335.1136 5.41 0.000 1155.128 2468.749

Note:Thetestofthevarianceagainstzeroisonesided,andthetwo-sidedconfidenceintervalistruncatedatzero.

.estatic

Model| Obs ll(null) ll(model) df AIC BIC

+

.| 72 . -662.5394 8 1341.079 1359.292

Note:N=ObsusedincalculatingBIC;see[R]BICnote

IS:ARIMA(8,1,0)

.arimaISifDATE>19554&DATE<19801,arima(8,1,0)

ARIMAregression

Sample:19562-19794,butwithgaps

Numberofobs

=

72

Waldchi2(8)

=

63.64

Loglikelihood=-660.4983

Prob>chi2

=

0.0000

|D.IS|

Coef.

OPG

Std.Err.

z

P>|z|

[95%Conf.Interval]

+

IS |

_cons| 911.686 605.7722 1.50 0.132 -2