龐皓計量經濟學課后規(guī)范標準答案第七章

統(tǒng)計學2班

第六次作業(yè)

1、⑴①模型一：peg=4+&尸

DependentVariable:PCE

Method:LeastSquares

Date:11/12/14Time:21:52

Sample:19701987

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

C-216.426932.69425-6.6197230.0000

PDI1.0081060.01503367.059200.0000

R-squared0.996455Meandependentvar1955.606

AdjustedR-squared0.996233S.D.dependentvar307.7170

S.E.ofregression18.88628Akaikeinfocriterion8.819188

Sumsquaredresid5707.065Schwarzcriterion8.918118

Loglikelihood-77.37269Hannan-Quinncriter.8.832829

F-statistic4496.936Durbin-Watsonstat1.366654

Prob(F-statistic)0.000000

PCEt=-2164269+1.0081

(-6.619723)(67.05920)

R2=0.996455F=4496.936DW=1.366654

美國個人消費支出受個人可支配收入影響，通過回歸可知，個人可支配收入PDI每增加一

個單位,個人消費支出平均增加1.008106個單位。

②模型二：PCEt=g+B2PDIt+BFCEp+u,

DependentVariable:PCE

Method:LeastSquares

Date:11/12/14Time:22:00

Sample(adjusted):19711987

Includedobservations:17afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C-233.273645.55736-5.120436O0002

PDIO9823820.1409286970817ooooo

PCEC-1)O0371580.144026O257997O8002

R-squared0.996542Meandependentvar1982876

AdjustedR-squared0.996048S.D.dependentvar293.9125

S.E.ofregression18.47783Akaikeinfocriterion8.829805

Sumsquaredresid4780.022Schwarzcriterion8.976843

Loglikelihood72.05335HannanQuinncriter.8.84-4^21

F-statistic2017.064Durbin-Watsonstat1.570195

Prot>(F-statistic)0.000000

PCE,=—233273a0.982387〃+0.037158℃￡；,

T(-5.120436)(6.970817)(0.257997)

R2=0.996542F=2017.064DW=1.570l95

美國個人消費支出PCE不僅受當期個人可支配收入PDI影響，還受滯后一期個人消費支出

PCEt.（自身影響。

⑵從模型一得MPC=l.(X)8106

從模型二可得短期MPO0.982382.

從庫伊特模型工=。(1一團+鳳%+乃仁+(4—9I)可得見為尸E工的系數即

2=0.0371f

因為，長期MPC即長期乘數為：￡川，根據庫伊特模型丹=河兄(0<；1<1),。當s-8

1=0

800.\—^/?

時，Z片=6。+/+…=&+4%+鳳+…=4Z元=A)--7=

r=o1=11-41—A

09X23X2

所以長期MPC=MPC=—.........=1.02023

1-0.037158

2、Y：固定資產投資X：銷售額

(1)設定模型為：工*=。+您,+4，Z*為被解釋變量的預期最佳值

運用局部調整假定，模型轉換為：匕="+瓦房+萬；％+“

其中：d=6a、樂=郊,伙=\一6、山=詠：

DependentVariable:Y

Method:LeastSquares

Date:11/14/14Time:20:53

Sample(adjusted):19812001

Includedobservations:21afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C-15.104034.729450-3.1936130.0050

X0.6292730.0978196.4330310.0000

Y(-1)0.2716760.1148582.3653150.0294

R-squared0.987125Meandependentvar109.2167

AdjustedR-squared0.985695S.D.dependentvar51.78550

S.E.ofregression6.193728Akaikeinfocriterion6.616515

Sumsquaredresid690.5208Schwarz:criterion6.765733

Loglikelihood-66.47341Hannan-Quinncriter.6.648899

F-statistic690.0561Durbin-Watsonstat1.518595

Prob(F-statiStic)0.000000

y=-15.104034-0.62927^+0.27167€K,

II(-1

T(-3.193613)(6.433031)(2.365315)

R?=0.987125F=690.0561DW=1.518595

???儲=&,尺=羽/=]_&"=砌,5=1-6=1-0.271676=0.728324

a=9=需黑二20.7381,左條牒2864

局部調整模型估計結果為：匕=-20.7381+0.864X,

經濟意義：該地區(qū)銷售額每增加1億元，未來預期最佳新增固定資產投資為0.846億元

采用德賓h檢驗如下

〃0：夕=(),修：夕工()

d_I〃1.518595I21

T\\-nVar(p；)=(2V1-21*0.1148582

在顯著性水平a=0.05下，查標準正態(tài)分布表得臨界值=%S5=196,因此拒絕原假設

|/^=1.29728<^=1.96,因此接受原假設，說明自回歸模型不存在一階自相關。

⑵設定模型：Y；=aX"\對模型做對數變換：lnH=lna+/lnX,+M

運用局部調整假定，模型轉換為：lnZ=/+4；lnX/+/7；ln21+"

其中：lna*=51na，4；=羽,尸;=1—反“=砌

DependentVariable:LNY

Method:LeastSquares

Date:11/14/14Time:21:35

Sample(adjusted):19812001

Includedobservations:21afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

c-107R046O1R4144-5254256ooooo

LNX0.9045220.1112438.1310390.0000

LNY(-1)0.2600330.0877992.9616840.0084

R-squared0.993725Meandependentvar4.559823

AdjustedR-squared0.993028S.D.dependentvar0.562953

S.E.ofregression0.047007Akaikeinfocriterion-3.145469

Sumsquaredresid0.039774Schwarzcriterion-2.996251

Loglikelihood36.02742Hannan-Quinncriter.-3.113085

F-statistic1425.219Durbin-Watsonstat1.479333

Prob(F-statiStic)0.000000

InV；=-1.078046P0.904522nX,+0.260033^

T(-5.854366)(8.131039)(2.961684)

R2=0.993725F=1425.219DW=1.479333

???In，=Sin名片=印,夕；=I—5,〃；=砌5=l-尸；=l-0.260036.7399

,\na-1.078046一一八°區(qū)0.904522，

\x\a=------=--------------=-1.4569￡=江=------------=1.2224

Z)0.739967d0.739967

經濟意義：該地區(qū)銷化:額每增加1億元，未來預期最佳新增固定資產投資為0.846億元

采用德賓h檢驗如K

:p=0,H、；p豐0

n1.518595、21

=（Z1一一「）=1.29728

21-2P0.1148582

在顯著性水平a=0.05下，查標準正態(tài)分布表得臨界值兒<0s§=196,因此拒絕原假設

|/?|=1.29728<=1.96,因此接受原假設，說明自回歸模型不存在一階自相關。

3、阿爾多蒙多項式變換

DependentVariable:Y

Method:LeastSquares

Date:11/14/14Time:22:07

Sample(adjusted):19842001

Includedobservations:18aleradjustments

VariableCoefficientStd.Errort-StatisticProb.

C-35.492348.192884-4.3320930.0007

PDL01-0.0312280.123416-0.2530310.8039

PDL02-0.2523360.062441-4.0411820.0012

PDL030.1043920.0623111.6753380.1160

R-squared0.984670Meandependentvar121.2322

AdjustedR-squared0.981385S.D.dependentvar45.63348

S.E.ofregression6.226131Akaikeinfocriterion6.688517

Sumsquaredresid542.7059Schwarzcriterion6.886378

Loglikelihood-56.19666Hannan-Quinncriter.6.715800

F-statistic299.7429Durbin-Watsonstat1.130400

Prob(F-statistic)0.000000

LagDistributionofXiCoefficientStd.Errort-Statistic

100.891010.174565.10425

110.325500.089983.61759

X

2-0.031230.12342-0.25303

3-0.179170.08488-2.11094

\?4-0.118330.18034-0.65616

SunofLags0.887780.0300729.5262

匕=-35.49234+0.89101X,+0.32550X,,-0.03123X,--0.17917X,r0.11833V.

4、Y：新增固定資產X：全省工業(yè)總產值

(1)設定模型為：Z*=a+您,+4

運用局部調整假定，模型轉換為：匕=，+瓦%+用工1+“

其中:d=汰、樂=郊6=1-3,山=6內

Dependentvanaoie:丫

Method:LeastSquares

Date:11/16/14Time：14:24

Sample(adjusted):19631995

Includedobservations:33afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C1.8966451.1671271.6250550.1146

X0.1021990.0247824.1239610.0003

Y(-1)0.0147000.1828650.0803890.9365

R-squared0.584750Meandependentvar7.804242

AdjustedRsquared0.557066S.D.dependentvor5.889686

S.E.ofregression3.919779Akaikeinfocriterion5.656455

Sumsquaredresid460.9399Schwarzcriterion5.792502

Loglikelihood-90.33151Hannan-Quinncriter.5.702231

F-statistic21.12278Durbin-Watsonstat1.901308

Prob(F-statistic)0.000002

/=1.89664的0.10219”+0.014%]

T(1.625055)(4.123961)(0.080389)

R2=0.58475CF=2I.I2228DW=l.90l308

可以看出，全省工業(yè)總產值X的回歸系數顯著，而新增固定資產滯后一期Yp的回歸系數

不顯著。R2=().58475C較小，模型上總體對樣本數據以合較差。

???a*=必，聞=郊6=f"=物,^=1-/7；=1-0.0147=0.9853

￡哼二嘿翳川。372

所以最終方程為：^=1.92494+0.1037^

經濟意義：全省工業(yè)總產值每計劃增加1(億元)，則未來預期最佳新增固定資產量為0.1037

億元。

(2)設定模型：Z=a+廬；+4。

采用自適應假定模型變?yōu)椋篩,=儲+區(qū)用+才匕1+"

其中：a*=ya.Pl=加瓜=1-/,//；=“一(1一力〃”

DependentVariable:Y

Method:LeastSquares

Date:11/16/14Time:14:24

Sample(adjusted):19631995

Includedobservations:33afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C1.8966451.1671271.6250550.1146

X0.1021990.0247824.1239610.0003

Y(-1)0.0147000.1828650.0803890.9365

R-squared0.584750Meandependentvar7.804242

AdjustedR-squared0.557066S.D.dependentvar5.889686

S.E.ofregression3.919779Akaikeinfocriterion5.656455

Sumsquaredresid460.9399Schwarzcriterion5.792502

Loglikelihood-90.33151Hannan-Quinncriter.5.702231

F-statistic21.12278Durbin-Watsonstat1.901308

Prob(F-statistic)0.000002

Yr=1.896645b0.10219”+0.014備

T(1.625055)(4.123961)(0.080389)

R2=0.58475(：F=2l.l2228DW=l.90l308

可以看出，全省工業(yè)總產值X的回歸系數顯著，而新增固定資產滯后一期丫皿的回歸系數

不顯著。R2=0.58475c較小，模型上總體對樣本數據與合較差。

,/a—6a,0^=印、氏==p,,—(I—/)//,_)>y=1-隹—1-0.0147=0.9853

a1.896645l=L92494-6號=端翳=°」0372

a=一

0.9853

所以最終方程為：年=1.92494+0.1037%

經濟意義：全省工業(yè)總產值每預期增加增加1（億元），當期新增固定資產量為0.1037（億

元）。

（3）局部調整模型和自適應模型的區(qū)別在于：

局部調整模型是對因變量的局部調整而得到的：解釋變量的現(xiàn)值影響著被解釋變量的預期

值。

自適應模型是由自變量的自適應過程而得到的。預期的解釋變量的變化影響被解釋變量現(xiàn)

值。

由【可歸結果可見，新增固定資產滯后一期丫皿的回歸系數并不顯著，說明兩個模型的設定都

不合理。

5、Y：年末貨幣流通量X,：社會商品零售額X2：城鄉(xiāng)居民儲蓄余額（單位：億元）

⑴模型：Y；=a+^XU+河乂2,+“Y；為長期貨幣流通量

運用局部調整假定，模型轉換為：Yt=a^-/3；XU+^X2l+0；Y,_.+//；

其中：&=8a、B；=B及R=用”隊="認山=甌

DependentVariable:Y

Method:LeastSquares

Date:11/16/14Time:15:03

Sample(adjusted):19541985

Includedobservations:32afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C6596.2284344.0781.5184420.1401

X10.0474510.0396101.1979400.2410

X20.2748380.0905343.0357360.0051

Y(-1)0.4052750.1872202.1646990.0391

R-squared0.967247Meandependentvar55355.97

AdjustedR-squared0.963738S.D.dependentvar40464.90

S.E.ofregression7705.604Akaikeinfocriterion2085375

Sumsquaredresid1.66E*09Schwarzcriterion21.03697

Loglikelihood-329.6600Hannan-Quinncriter.20.91448

F-statistic275.6267Durbin-Watsonstat2.109534

Prob(F-statistic)0.000000

Yf=6596228+0.04745PCk+0.27483%+040527%

T(1.518442)(LI97940)(3.035736)(2.164699)

R2=0.967247F=275.6267DW=2.l09534

=da，6、=用、、&二砌，區(qū)=l-反”=%,

5=1-4；=1—0.405275=0.59472f

/=6596228二10.047451

10912237,A=￡==0.07979

T-0.594725-J0.594725

故局部調整模型估計結果為：^=110912237+0.07979￥?+0.46213￥2/

經濟意義：在其他條件不變的情況下，該地區(qū)社會商品零售額每增加1億元，預期年末貨幣

流通量增加0.07979億元"司樣，在其他條件不變的情況下，該地區(qū)城鄉(xiāng)居民儲蓄余額每增

加1億元，則預期年末貨幣流通量增加0.46213億元。

(2)模型先對模型做對數變化：lnY”=lna+41nx”+/ynX2,+4

運用局部調整假定,模型轉換為：In工=a*+尸；InX,+力；InX2,+〃In+〃；

其中，=51na,/7；=羽4=羽2，鳳=1一反"二加

DependentVariable:LNY

Method:LeastSquares

Date:11/16/14Time:15:26

Sample(adjusted):19541985

Includedobservations:32afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C0.6443331.6778880.3840140.7039

LNX10.2062300.2555570.8069840.4265

LNX20.1801680.1549131.1630310.2546

LNY(-1)0.5314450.1092604.8640490.0000

R-squared0.968959Meandependentvar10.70088

AdjustedR-squared0.965633S.D.dependentvar0.672279

S.E.ofregression0.124629Akaikeinfocriterion-1.210486

Sumsquaredresid0.434905Schwarzcriterion-1.027269

Luylikelihood23.36778Hcirin<dri-Quiririuril&r.-1.149755

F-statistic291.3458Durbin-Watsonstat1.914829

Prob(F-statistic)0.000000

InYt=0.64433務0.206230nXlz+0.l80168nX2z4-0.531445nYt_x

T(0.384014)(0.806984)(L16303D(4.864049)

叱二0.968959F=29l.3458DW=1.914829

"=51na,萬；=羽,氏=羽2，區(qū)=1—氏”=%，

5=1一區(qū)=1—0.531445=0.46855f

a0.6443330：0.206230

lna=——=--------=1.37515,伏=—=---------=0.44014

60.468555B0.468555

反=0.18016內

20.38452

y-0.468555~

故局部調整模型估計結果為：In年=1.3751卦0.44014nX“+0.38452nX2,

經濟意義：在其他條件不變的情況下，該地區(qū)社會商品零售額每增加1%,預期年末貨幣流

通量增加0.44104機同樣，在其他條件不變的情況下，該地區(qū)城鄉(xiāng)居民儲蓄余額每增加1%,

則預期年末貨幣流通量增加0.38452機

即年末貨幣流通量對社會商品零售額的長期彈性為：0.44104；貨幣需求對城鄉(xiāng)居民儲蓄余

額的長期彈性為0.38452。

8、Y:消費總額X：貨后收入總額

⑴假設消費同收入的模型為：工=4+4%+4

作回歸如下：

DependentVariable:Y

Fvlethod:LeastSquares

Date:11/16/14Time:15:44

Sample:19752004

Includedobservations:30

VariableCoefficientStd.Errort-StatisticProb.

C27.765947.9450833.4947330.0016

X0.8077310.02284035.365420.0000

R-squared0.978103Meandependentvar262.1725

AdjustedR-squared0.977321S.D.dependentvar159.3349

S.E.ofregression23.99515Akaikeinfocriterion9.257921

Sumsquaredresid16121.49Schwarzcriterion9.351334

Loglikelihood-136.8688Hannan-Quinncriter.9.287805

F-statistic1250.713Durbin-Watsonstat1.280986

Prob(F-statistic)0.000000

^=27.265944-0.80773^,

T(3.494733)(35.36542)

R2=0.978103F=1250.713DW=1.280986

從回歸結果來看，t檢驗值，F(xiàn)檢驗值均顯著，