第七章練習(xí)題及參考解答(第四版)計量經(jīng)濟(jì)學(xué)

第七章練習(xí)題及參考解答

7.1表7.4中給出了1981-2015年中國城鎮(zhèn)居民人:勻年消費支出(PCE)和城鎮(zhèn)居民人均

可支配收入(PDI)數(shù)據(jù)。

表7.41981-2015年中國城鎮(zhèn)居民消費支出(PCE)和可支配收入(PDI)數(shù)據(jù)(單位：元)

年度城鎮(zhèn)居民人均城鎮(zhèn)居民人均可支年度城鎮(zhèn)居民人均城鎮(zhèn)居民人均可支

消費支出PCE配收入PDI消費支出PCE配收入PDI

1981456.80500.4019991615.915854.02

1982471.00535.3020004998.006280.00

1983505.90564.6020015309.016859.60

1984559.40652.1020026029.887702.80

1985673.20739.1020036510.948472.20

1986799.00900.9020047182.109421.60

1987884.401002.1020057942.8810493.00

19881104.001180.2020068696.5511759.50

1989121LOO1373.9320079997.4713785.80

19901278.901510.20200811242.8515780.76

19911453.801700.60200912264.5517174.65

19921671.702026.60201013471.4519109.44

19932110.802577.40201115160.8921809.78

19942851.303496.20201216674.3224564.72

19953537.574283.00201318022.6426955.10

19963919.474838.90201419968.0829381.00

19974185.645160.30201521392.3631790.31

19984331.615425.10

估計卜列模型:

PCE,=4+A2PDI,+從

PCE,=B]+B2PDI,+B3PCE.1+ur

(1)解釋這兩個回歸模型的結(jié)果。

(2)短期和長期邊際消費傾向(MPC)是多少？分析該地區(qū)消費同收入的關(guān)系。

(3)建立適當(dāng)?shù)姆植紲竽Ｐ?，用庫伊克變換轉(zhuǎn)換為庫伊克模型后進(jìn)行估計，并對估計

結(jié)果進(jìn)行分析判斷。

【練習(xí)題7.1參考解答】

(1)解釋這兩個回歸模型的結(jié)果。

DependentVariable:PCE

Method:LeastSquares

Date:03/10/18Time:09:12

Sample;19812005

Includedobservations:25

VariableCoefficientStd.Errort-StatisticProb.

C149.097524,567346.0689330.0000

PDI0.7575270.005085148.98400.0000

R-squared0.998965Meandependentvar2983.768

AdjustedR-squared0.998920S.D.dependentvar2364.412

S.E.ofregression77.70773Akaikeinfocriterion11.62040

Sumsquaredresid138885.3Schwarzcriterion11.71791

Loglikelihood-143.2551F-statistic22196.24

Durbin-Watsonstat0.531721Prob(F-statistic)0.000000

——_-

收入跟消費間有顯著關(guān)系。收入每增加1元，消費增加0.76元。

DependentVariable:PCE

Method:LeastSquares

Date:03/10/18Time:09:13

Sample(adjusted):19822005

Includedobservations:24afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C147.688626.735795.5240010.0000

PDI0.6791230.0699599.7073850.0000

PCE(-1)0.1110350.1001861.1082870.2803

R-squared0.999012Meandependentvar3089.059

AdjustedR-squared0.998918S.D.dependentvar2354.635

S.E.ofregression77.44504Akaikeinfocriterion11.65348

Sumsquaredresid-25952.4Schwarzcriterion11.80074

Loglikelihood-136.8418F-statistic10620.10

Durbin-Watsonstat_0.688430_Prob(F-statistic)0.000000

(2)短期和長期邊際消費傾向(MPC)是多少？分析該地區(qū)消費同收入的關(guān)系。

短期MPC=0.68,長期MPC=0.679/(l-0.l11)=0.764

(3)建立適當(dāng)?shù)姆植紲竽Ｐ?，用庫伊克變換轉(zhuǎn)換為庫伊克模型后進(jìn)行估計，并對估計

結(jié)果進(jìn)行分析判斷。

在滯后1-5期內(nèi)，根據(jù)AIC最小，選擇滯后5期，其回歸結(jié)果如下：

DependentVariable:PCE

Method:LeastSquares

Date:03/10/18Time:09:25

Sample(adjusted):19862005

Includedobservations:20afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C167.959033.277935.0471580.0002

PDI0.7079330.1248785.6689810.0001

PDI(-1)0.2252720.2742930.8212830.4263

PDI(-2)-0.1789110.316743-0.5648470.5818

PDI(-3)-0.0695250.328725-0.2114980.8358

PDI(-4)0.2648740.3004700.8815320.3940

PDI(-5)-0.2269660.145557-1.5592920.1429

R-squared0.999382Meandependentvar3596.396

AdjustedR-squared0.999096S.D.dependentvar2254.922

S.E.ofregression67.79561Akaikeinfocriterion11.54009

Sumsquaredresid59751.18Schwarzcriterion11.88860

Loglikelihood-108.4009F-statistic3501.011

Durbin-Watsonstat1.471380Prob(F-statistic)0.000000

當(dāng)期收入對消費有顯著影響，但各滯后期影響并不顯著。不顯著可能是分布滯后模型

直接估計時共線性造成的，也可能是真沒顯著影響。庫力克模型估計結(jié)果見上表，PCE(-1)

部分?可ri結(jié)果t檢驗不顯著八

7.2表7.5中給出了中國1980-20I6年固定資產(chǎn)投資Y與社會消費品零售總額X的資

料。取阿爾蒙多項式的次數(shù)m=2,運(yùn)用阿爾蒙多項式變換法估計以下分布滯后模型：

Y產(chǎn)a+0°X戶優(yōu)X-+p2X,_2+用X_+dXf+u,

表7.5中國1980-2016年固定資產(chǎn)投資Y與社會零售總額X數(shù)據(jù)(單位：億元)

年份固定資產(chǎn)投資社會消費品零售總額年份固定資產(chǎn)投資社會消費品零售總

YXY額X

1980910.92140.0199929854.735647.9

1981961.02350.02(XM)32917.739105.7

19821230.42570.0200137213.543055.4

19831430.12849.4200243499.948135.9

19841832.93376.4200355566.652516.3

19852543.24305.0200470477.459501.0

19863120.64950.0200588773.667176.6

19873791.75820.02006109998.276410.0

19884753.87440.0200/137323.989210.0

19894410.48101.42008172828.4114830.1

19904517.08300.12009224598.8132678.4

19915594.59415.62010251683.8156998.4

19928080.110993.72011311485.1183918.6

199313072.314270.42012374694.7210307.0

199417042.118622.92013446294.1237809.9

199520019.323613.82014512020.7271896.1

199622913.528360.22015561999.8300930.8

199724941.131252.92016606465.7332316.3

199828406.233378.1

【練習(xí)題7.2參考解答】

直接估計結(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:09:32

Sample(adjusted):19842016

Includedobservations:33afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-23633.423701.825-6.3842600.0000

X0.4619270.9181980.5030800.6190

X(-1)2.0865661.6859581.2376140.2265

X(-2)-0.5432541.708205-0.3180260.7529

X(-3)1.1505771.8438080.6240220.5379

X(-4)-1.3173211.283331-1.0264860.3138

R-squared0.993755Meandependentvar128264.7

AdjustedR-squared0.992598S.D.dependentvar180131.0

S.E.ofregression■5497.23Akaikeinfocriterion22.29768

Sumsquaredresid6.48E+09Schwarzcriterion22.56977

Loglikelihood-361.9117F-statistic859.2660

Durbin-Watsonstat0.229807Prob(F-statistic)0.000000

使用阿爾蒙變換估計結(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:09:37

Sample(adjusted):19842016

Includedobservations:33afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-23683.133619.054-6.5440100.0000

ZO0.8016780.6237781.2851980.2089

Z10.4823171.3667070.3529050.7267

Z2-0.2333220.358793-0.6502980.5206

R-squared0.993572Meandependentvar128264.7

AdjustedR-squared0.992907S.D.dependentvar180131.0

S.E.ofregression15170.17Akaikeinfocriterion22.20526

Sumsquaredresid6.67E+09Schwarzcriterion22.38666

Loglikelihood-362.3868F-statistic1494.254

Durbin-Watsonstat0.287072Prob(F-statistic)0.000000

根據(jù)力++a1可計算出

Bo-4)-0.802

=a{}+a]+?2=1.051

=a()+2al+4a2=0.833

py=a()+3。]+9a2=0.149

8=%+4%+16a2=-1.002

直接使用軟件結(jié)果：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:09:39

Sample(adjusted):19842016

Includedobservations:33afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-23683.133619.054-6.5440100.0000

PDL010.8330240.7026451.1855550.2454

PDL02-0.4509710.144976-3.1106620.0042

PDL03-0.2333220.358793-0.6502980.5206

R-squared0.993572Meandependentvar128264.7

AdjustedR-squared0.992907S.D.dependentvar180131.0

S.E.ofregression15170.17Akaikeinfocriterion22.20526

Sumsquaredresid6.67E+09Schwarzcriterion22.38666

Loglikelihood-362.3868F-statistic1494.254

Durbin-Watsonstat0.287072Prob(F-statistic)0.000000

LagjCoefficienStd.ErrorT-Statistic

DistributionofXt

*|00.801680.623781.28520

*|11.050670.427232.45927

*|20.833020.702641.18555

.*|30.148730.311660.47722

A|4-1.002210.92567-1.08269

Sumof1.831900.185629.86901

Lags_一一

7.3利用表7.5的數(shù)據(jù)，運(yùn)用局部調(diào)整假定或自適應(yīng)預(yù)期假定估計以下模型參數(shù)，并解稱

模型的經(jīng)濟(jì)意義，探測模型擾動項的一階自相關(guān)性：

1）設(shè)定模型

Y；=a+flX,

其中匕'為預(yù)期最佳值。

2)設(shè)定模型

Y；=aX^e11'

其中匕?為預(yù)期最佳值。

3)設(shè)定模型

匕=a+外：+/

其中X；為預(yù)期最佳值。

【練習(xí)題7.3參考解答】

1)設(shè)定模型

y：=a+px,+wz

其中匕"為預(yù)期最佳值。

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:10:09

Sample(adjusted):19812016

Includedobservations:36afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

0-5669.5052498.919-2.2687830.0299

X0.6649820.1301835.1080430.0000

Y(-1)0.7335440.0778119.4272690.0000

R-squared0.997893Meandependentvar117676.6

AdjustedR-squared0.997765S.D.dependentvar175881.8

S.E.ofregression8314.081Akaikeinfocriterion20.96894

Sumsquaredresid2.28E+09Schwarzcriterion21.10090

Loglikelihood-374.4410F-statistic7815.118

Durbin-Watsonstat_0.925919_Prob(F-statistic)0.000000

根據(jù)回歸結(jié)果，可算Hlh統(tǒng)計量為3.64,明顯大于2,表明5%顯著水平下存在相關(guān)性。根

據(jù)回歸數(shù)據(jù)，可算出調(diào)整系數(shù)為5==1-0.734=0.266,這表示了局部調(diào)整的速度。

P=/V/5=0.665/0.266=2.5

2)設(shè)定模型

Y；=aXj}e

其中匕”為預(yù)期最佳值。

假設(shè)調(diào)整方程為：lnX-]n%=3(lnR-lnL),則轉(zhuǎn)化為一階自I可歸模型后的I可歸結(jié)果

為：

DependentVariable:LOG(Y)

Method:LeastSquares

Date:03/10/18Time:10:11

Sample(adjusted):19812016

Includedobservations:36afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-0.5414920.692089-0.7824030.4396

LOG(X)0.2996850.2623221.1424340.2615

LOG(Y(-1))0.7649000.2006083.8129090.0006

R-squared0.997423Meandependentvar10.25491

AdjustedR-squared0.997267S.D.dependentvar1.956096

S.E.ofregression0.102265Akaikeinfocriterion-1.642847

Sumsquaredresid0.345117Schwarzcriterion-1.510887

Loglikelihood32.57124F-statistic6386.241

Durbin-Watsonstat0.873321Prob(F-statistic)0.000000

根據(jù)回歸結(jié)果，計算h統(tǒng)廣量時開方部分為負(fù)，沒法計算，故沒法根據(jù)h統(tǒng)計量判斷相關(guān)性。

根據(jù)回歸數(shù)據(jù)，可算出調(diào)整系數(shù)為5=1-夕；=1-0.765=0.235,這表示了局部調(diào)整的速度。

P=/(^=0.2997/0.235=1.275

3)設(shè)定模型

Yt=a+0X：+ut

其中X；為預(yù)期最佳值。

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:10:09

Sample(adjusted):19812016

Includedobservations:36afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-5669.5052498.919-2.2687830.0299

X0.6649820.1301835.1080430.0000

Y(-1)0.7335440.0778119.4272690.0000

R-squared0.997893Meandependentvar117676.6

AdjustedR-squared0.997765S.D.dependentvar175881.8

S.E.ofregression8314.081Akaikeinfocriterion20.96894

Sumsquaredresid2.28E+09Schwarzcriterion21.10090

Loglikelihood-374.4410F-statistic7815.118

Durbin-Watsonstat0.925919Prob(F-statistic)0.000000

可算出調(diào)節(jié)系數(shù)為7=1-〃；=1-0.734=0.266,這表示了預(yù)期修正的速度。=/3；!y=

0.665/0.266=2.5

7.4表7.6給出中國各年末貨幣流通量Y,社會商品零售額XI、城鄉(xiāng)居民儲蓄余額X2

的數(shù)據(jù)。

表7.6中國年末貨幣流通量、社會商品零售額、城鄉(xiāng)居民儲蓄余額數(shù)據(jù)（單位：億元）

年份年末貨幣流通量Y社會消費品零售總頷XI城鄉(xiāng)居民儲蓄年底余額X2

19892344.08101.45184.50

19902644.48300.17119.60

19913177.89415.69244.90

19924336.010993.711757.30

19935864.714270.415203.50

19947288.618622.921518.80

19957885.323613.829662.30

19968802.028360.238520.80

199710177.631252.946279.80

199811204.233378.153407.47

199913455.535647.959621.83

200014652.739105.764332.38

200115688.843055.473762.43

200217278.048135.986910.65

200319746.052516.3103617.65

200421468.359501.0119555.39

200524031.767176.6141050.99

200627072.676410.0161587.30

200730334.389210.0172534.19

200834219.0114830.1217885.35

200938246.0132678.4260771.66

201044628.2156998.4303302.49

201150748.5183918.6343635.89

201254659.8210306.9399551.00

201358574.4237809.9447601.57

201460259.5271896.1485261.34

利用表中數(shù)據(jù)設(shè)定模型：Y；=a+/3】X1戶員X?盧冉

Z"=aX””

其中，匕?為長期(或所需求的)貨幣流通最。成根據(jù)局部調(diào)整假設(shè)，作模型變換，估計并檢驗

參數(shù)，對參數(shù)經(jīng)濟(jì)意義做出解釋。

【練習(xí)題7.4參考解答】

利用表中數(shù)據(jù)設(shè)定模型：Y：=a+°\Xz+dX?"內(nèi)

Y：=aX^X^2eUl

其中，匕“為長期(或所需求的)貨幣流通量。試根據(jù)局部調(diào)整假設(shè)，作模型變換，估計并檢驗

參數(shù),對參數(shù)經(jīng)濟(jì)意義做出解釋。

假設(shè)局部調(diào)整方程為：乂一％=演匕"一%),對工*=。+片X“+AX〃+從，可轉(zhuǎn)化為

回歸方程：X=3a+(l—5)%+或QXk+p/Xz+K〃,，其回歸結(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:10:03

Sample(adjusted):19902014

Includedobservations:25afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C1618.034732.14892.2099790.0383

Y(-1)0.9810200.1493126.5702800.0000

X1-0.1304290.041464-3.1455900.0049

X20.0783990.0337062.3259720.0301

R-squared0.997519Meandependentvar23457.75

AdjustedR-squared0.997164S.D.dependentvar18266.54

S.E.ofregression972.7612Akaikeinfocriterion16.74380

Sumsquaredresid19871553Schwarzcriterion16.93882

Loglikelihood-205.2975F-statistic2813.916

Durbin-Watsonstat1.112498Prob(F-statistic)0.000000

各回歸系數(shù)在5%顯著水Y：下均顯著?？伤愠稣{(diào)整系數(shù)為5=1-4=1-0.981=0.019,這表

示了局部調(diào)整的速度。

假設(shè)局部調(diào)整方程為：lnX-ln%=b(lnR-lni；J,對Y*=aX^X9小，可轉(zhuǎn)化為【可

歸方程：In%=(Slna+(l-5)lnL+/?QlnX|I+A31nX2,+S4，其回歸結(jié)果如下:

DependentVariable:LOG(Y)

Method:LeastSquares

Date:03/10/18Time:10:04

Sample(adjusted):19902014

Includedobservations:25afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C0.6577880.2771622.3732960.0273

LOG(Y(-1))0.7419100.2306023.2172700.0041

LOG(X1)0.0533500.1027270.5193320.6090

LOG(X2)0.1211540.1785370.6785930.5048

R-squared0.996730Meandependentvar9.716778

AdjustedR-squared0.996263