第七章練習題及參考解答

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

可支配收入(PDI)數據。

表7.41981-2015年中國城鎮居民消費支出(PCE)和可支配收入(PDI)數據(單位：元)

年度城鎮居民人均城鎮居民人均可支年度城鎮居民人均城鎮居民人均可支

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果。

(2)短期和長期邊際消費傾向(MPC)是多少？分析該地區消費同收入的關系。

(3)建立適當的分布滯后模型，用庫伊克變換轉換為庫伊克模型后進行估計，并對估計

結果進行分析判斷。

【練習題7.1參考解答】

(1)解釋這兩個回歸模型的結果。

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？分析該地區消費同收入的關系。

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

(3)建立適當的分布滯后模型，用庫伊克變換轉換為庫伊克模型后進行估計，并對估計

結果進行分析判斷。

在滯后1-5期內，根據AIC最小，選擇滯后5期，其回歸結果如下：

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。庫力克模型估計結果見上表，PCE(-1)

部分?可ri結果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m=2,運用阿爾蒙多項式變換法估計以下分布滯后模型：

Y產a+0°X戶優X-+p2X,_2+用X_+dXf+u,

表7.5中國1980-2016年固定資產投資Y與社會零售總額X數據(單位：億元)

年份固定資產投資社會消費品零售總額年份固定資產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

【練習題7.2參考解答】

直接估計結果如下：

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的數據，運用局部調整假定或自適應預期假定估計以下模型參數，并解稱

模型的經濟意義，探測模型擾動項的一階自相關性：

1）設定模型

Y；=a+flX,

其中匕'為預期最佳值。

2)設定模型

Y；=aX^e11'

其中匕?為預期最佳值。

3)設定模型

匕=a+外：+/

其中X；為預期最佳值。

【練習題7.3參考解答】

1)設定模型

y：=a+px,+wz

其中匕"為預期最佳值。

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

根據回歸結果，可算Hlh統計量為3.64,明顯大于2,表明5%顯著水平下存在相關性。根

據回歸數據，可算出調整系數為5==1-0.734=0.266,這表示了局部調整的速度。

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

2)設定模型

Y；=aXj}e

其中匕”為預期最佳值。

假設調整方程為：lnX-]n%=3(lnR-lnL),則轉化為一階自I可歸模型后的I可歸結果

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

根據回歸結果，計算h統廣量時開方部分為負，沒法計算，故沒法根據h統計量判斷相關性。

根據回歸數據，可算出調整系數為5=1-夕；=1-0.765=0.235,這表示了局部調整的速度。

P=/(^=0.2997/0.235=1.275

3)設定模型

Yt=a+0X：+ut

其中X；為預期最佳值。

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

可算出調節系數為7=1-〃；=1-0.734=0.266,這表示了預期修正的速度。=/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、城鄉居民儲蓄余額X2

的數據。

表7.6中國年末貨幣流通量、社會商品零售額、城鄉居民儲蓄余額數據（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

利用表中數據設定模型：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。成根據局部調整假設，作模型變換，估計并檢驗

參數，對參數經濟意義做出解釋。

【練習題7.4參考解答】

利用表中數據設定模型：Y：=a+°\Xz+dX?"內

Y：=aX^X^2eUl

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

參數,對參數經濟意義做出解釋。

假設局部調整方程為：乂一％=演匕"一%),對工*=。+片X“+AX〃+從，可轉化為

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

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

各回歸系數在5%顯著水Y：下均顯著。可算出調整系數為5=1-4=1-0.981=0.019,這表

示了局部調整的速度。

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

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

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