计量经济学-李子奈-课程设计

P53例261为考察中国城镇居民2006年人均可支配收入与消费支出的关系，题

中给出中国31个省区以当年价测算的城镇居民家庭年人均收入（X）与年人均支

出（Y）两组数据，该题目为截面数据。

首先建立模型，一元回归模型为丫=80+81X+U

____1Lastupdated:06/23/15-15:09

119977.52

214283.09

310304.56

410027.70

510357.99

610369.61

79775.070

89182.310

920667.91

1014084.26

1118265.10

129771.050

1313753.28

149551.120

15_12192.24

169810.260

179802.650

10504.67

1916015.58

209898.750

219395.130

22_11569.74

239350.110

249116.610

~百10069.89

268941.080

279267.700

288920.590

299000.350

309177.260

318871.270

DependentVariable:Y

Method:LeastSquares

Date:06/23/15Time:15:09

Sample:131

Includedobservations:31

VariableCoefficientStd.Errort-StatisticProb.

C281.4993268.94971.0466620.3039

X0.7145540.02276031.395250.0000

R-squarAd0971419MeandepcndfintvarR401467

AdjustedR-squared0.970433S.D.dependentvar2388.455

S.E.ofregression410.6928Akaikeinfocriterion14.93591

Sumsquaredresid4891388.Schwarzcriterion15.02842

Loglikelihood-229.5066Hannan-Quinncriter.14.96607

F-statistic985.6616Durbin-Watsonstat1.461502

Prob(F-statistic)0.000000

可以写出分析结果%=281.50+O7146Xi；RSquare为决定系数，为0.9714,F为

985.66,D.W.=1.46

从R2看出，居民人均消费支出变化的97.14%可由人均可支配收入的变化来解释。

从斜率项的t检验值看，大于5%显著性水平下自由度为n-2=29的临界值toms

(29)=2.05,且该斜率值满足0<0.7146<1,符合经济理论中边际消费倾向在0

与1之间的绝对收入假说，表明2006年，中国城镇居民家庭人均可支配收入每

增加1元，人均消费支出增加0.7146元

预测：假设要关注2006年人均可支配收入在20000元这一档的中国城镇家庭的

人均消费支出问题，由上述回归方程可得该类家庭人均消费支出的预测值为

Yo=281.50+0.7146*20000=14572.6(元)

下面给出该家庭人均消费支出95%置信预测区间

E(X)=11363.69Var(X)=10853528

则E(Y0)置信区间为14572.6±2.045*”工+(：。。。。「1363.69)2

731-2L31(31-1)*10853528J

=14572.6±429.3或(14143.3,15001.9)

同样的，茬95%置信度下，该家庭人均消费支出的预测区间为

14572.6+2.045*/经照*口+工+(j-wsM

一yj31-2I31(31-1)*10853528J

=14572.6±943.2或(13629.3,6515.8)

P56例2.6.2表中给出了中国名义支出法国内生产总值GDP、名义居民总消费

CONS以及表示宏观税赋的税收总额TAX、表示价格变化的居民消费价格指数CPI

(1990=100),并由这些数据整理出实际支出法国内生产总值GDPC=GDP/CPI、居

民实际消费总支出Y=CONS/CPI,以及实际可支配收入X=(GDP-TAX)/CPL这些数

据是1978—2006年的时间序列数据。

首先建立模型Y=BO+B1X+口

采用Eviews软件进行回归分析；

(=)Equation:UNTITLEDWorkfile:UNTITLED::Untitled\_DX

[view]Proc]Object|\Print|Name|Freeze||Estimate|Forecast|StatsResids

DependentVariable:Y

Method:LeastSquares

Date:06/23/15Time:18:59

Sample:19782006

Includedobservations:29

VariableCoefficientStd.Errort-StatisticProb.

C2091.962334.94696.2456510.0000

X0.4375150.00929647.063800.0000

R-squared0.987957Meandependentvar14856.03

AdjustedR-squared0.987511S.D.dependentvar9471.801

S.E.ofregression1058.507Akaikeinfocriterion16.83358

Sumsquaredresid30251790Schwarzcriterion16.92787

Loglikelihood-242.0869Hannan-Quinncriter.16.86311

F-statistic2215.001Durbin-Watsonstat0.276687

Prob(F-statistic)0.000000

表明可建立如下中国居民消费函数：YA=2091.29+0.4375X

可决系数R2=0.9880,截距项与斜率的t检验值均大于5%显著性水平下自由度为

n-2=27的临界值togs(27)=2.05,且斜率项符合经济理论中边际消费倾向在0

与1之间的绝对收入假说，斜率项0.438表明，在1978—2006年间，以1990年

价计的中国居民可支配总收入每增加1亿元，居民总量消费支出平均增加C.438

亿元。

预测：2007年，以当年计价的中国GDP为263242.5亿元，税收入总额45621.9

亿元，居民消费价格指数为409.1,由此可得到以1990年价计的可支配总收入X

约95407.4亿元，由上述回归方程可得2007产居民总量消费预测的点估计值：

Y2007=2091.3±0.4375*95407.4=43834.6(亿元)

下面给出2007年中国居民总量消费的预测区间,由于E(X)=29174.1Var(X)

=463039370

在95%置信度下，E(Y2007)的预测区间为

「।2

仆”"_1_(302590141,(95407.4-29174.1)仆”“.♦、滞

43834.6±2.051*------*I—r4----------------=43834.6±1326.3或

、29-2L29(29-1)*463039370

(42508.3,45160.9)

在95%置信度下，Y2001的预测区间为

43834.6±2.051*…+广。7：2皿］)Z=43834.6±2545.1或

勺29-2L29(29-1)*463039370

(41289.5,46379.7)

P72例322通过截面数据建立2006年中国内地城镇居民家庭全年人均消费支出

的一元线性模型。在Eviws软件中输入城镇居民家庭全年人均可支配收入（XI）、

内地城镇居民人均消费支出（X2）与消费支出（Y）的数据，显示如下：

|19977.5|

____

Lastupdated:06/23/15-16:09

119977.50

214283.10

R1030460

410027.70

510358.00

610369.60

79775.100

89182.300

920667.90

1014084.30

1118265.10

129771.100

1313753.30

149551.100

1512192.20

169810.300

179802.700

1810504.70

1916015.60

209898.800

219395.100

2211569.70

239350.100

249116.600

2510069.90

268941.100

279267.700

288920.600

299000.400

309177.300

318871.300

View]Proc]Object|PropertiesPrint〔Name〔Freeze[Pefaut▼Sort]Edit+/-[Smpl+/-1Label+/-[Wide+八同

113244.2|

▲

Lastupdated:06/23/15-16:09

11324420|

29653.300

36699.700

46342.600

56928.600

67369.300一

76794.700

86178.000

913773.40

108621.800

1112253.70

126367.700

138794400

146109.400—1

157457.300

166038.000

176736.600

187505.000

1911809.90

207032.800

215928.800"■'

228623.300

236891.300

246159.300

256996.900

268617.100

276656.500

286529.200

296245.300

306404.300▼

314I.................

Path=c\users\lenovo\documentsDB=noneWF=untitled

(=)Equation:UNUTLEDWorkfile:UNTnLED::Untitled\_BX

ViewProcObjectPrintNameFreezeEstimateForecastStatsResids

DependentVariable:Y

Method:LeastSquares

Date:06/23/15Time:16:10

Sample.131

Includedobservations.31

VariableCoefficientStd.Errort-StalisticProb.

c143.3265260.40320.5504020.5864

X10.5556440.0753087.3783200.0000

X2025008501136342.2007910.0362

R-squared0975634Meandependentvar8401468

AdjustedR-squared0973893S.Ddependentvar2388459

SE,ofregression3859169Akaikeinfocriterion1484089

Sumsquaredresid417C093Schwarzcriterion1497966

Loglikelihood-2270337Hannan-Quinncriter1488612

F-statistic5605650Durbin-Watsonstat1843488

Prob{F-statistic)0000000

Eviews软件估计结果如上表所示。两个解释变量前的参数估计值分别为0.5556

和0.2501,都为正数，且都处于0与1之间，常数项的估计值也为正，这些参数

的估计值是合理的。随机误差项的方差的估计值=4170093/(31-3)=148931.9.

由此得到的多元回归方程为：

Y=143327+0.5556Xl+0.25X2。

P83例3.5.1建立中国城镇居民食品消费需求函数模型，居民对食品的消费需求

模型大致为Q=f(X,pl,p0)

其中，Q为居民对食品的需求量，X为消费者的消费支出总额，pl为食品价格指

数，P0为居民消费价格指数。引入居民消费价格总指数P0的原因主要在于研究

居民其他消费对食品的可替代性。Q还可以写成Q=f(s，卷)

同时对比两个公式，确定该函数的模型Q=AXBipiB2p()B3

经过对数变换，可以用如下双对数线性回归模型进行分析:

lnQ=PO+PII备B2唔+U

0EViews-[Group:UNTIT

fGlFileEditObjectViewProcQuickOptionsAdd-insWindowHelp

View।Proc[Object、Print|Name|FreezeDefaultv|Sort|TransposeEdrt*/-|Smpl-/-|Trtle[sample]

obsX1[XQP1P0GPFP

1985351.4000673.20001315.90026.7000028,10000111.9000116.5000

1986418.9000799.00001463.30028.6000030.10000107.0000107.2000

1987472.9000884.40001475.00032.1000032.80000108.8000112.0000

1988567.00001104.0001412.50040,1000039.50000120.7000125.2000

1989660.00001211.0001437.20045.9000046.00000116.3000114.4000

1990693.80001278.9001529.20045.4000046.60000101.300098.80000

1991782.50001453.8001636.30047.8000049.00000105.1000105.4000

1992884.80001671.7001671.40052.9000053.20000108.6000110.7000

19931058.2002110.8001715.90061.7000061.70000116.1000116.5000

19941422.5002851.3001718.70082.8000077.20000125.0000134.2000

19951771.9003537.6001732.100102.300090.10000116.8000123.6000

19961904.7003919.5001725.600110.400098.10000108.8000107.9000

19971942.6004185.6001758.200110.5000101.1000103.1000100.1000

19981926.9004331.6001799.800107.1000100.500099.4000096.90000

19991932.1004615.9001885.700102.500099.2000098.7000095.70000

20001971.3004998.0001971.300100.0000100.0000100.800097.60000

20012027.9005309.0002013.800100.7000100.7000100.7000100.7000

20022271.8006029.9002258.300100.600099.7000099.0000099.90000

20032416.9006510.9002323.500104.0000100.6000100.9000103.4000

20042709.6007182.1002370.200114.3000103.9000103.3000109.9000

20052914.4007942.9002472.700117.9000105.6000101.6000103.1000

20063111.9008696.6002573.400120.9000107.2000101.5000102.6000

(=)Equation:UNTITLEDWorkfile:UNTITLED::llntitled\_□x

[View]Pro?Object]PrintNameFreeze|Estimate|ForecastStats|Resids

DependentVariable:LOG(Q)

Method:LeastSquares

Date:06/23/15Time:21:37

Sample:19852006

Includedobservations:22

VariableCoefficientStd.Errort-StatisticProb.

C5.5319500.09310759.414890.0000

LOG(X)0.5399170.03653014.780150.0000

LOG(P1)-0.2580120.178186-1.4479940.1648

LOG(PO)-0.2885610.205184-1.4C63500.1766

R-squared0.977345Meandependentvar7.493909

AdjustedR-squared0.973569S.D.dependentvar0.193147

S.E.ofregression0.031401Akaikeinfocriterion-3.921001

Sumsquaredresid0.017748Schwarzcriterion-3.722630

Loglikelihood47.13101Hannan-Quinncriter.-3.874271

F-statistic258.8448Durbin-Watsonstat0.696202

Prob(F-statistic)0000000

Eviews输出结果为lnQ=5.53+0.540lnX-0.2581npl-0.288lnP0

R2=0.9773序=0.9735F=258.84

说明InPO与InPl相关系数有较高的共线性

0EViews-[Group:UNTITLEDWorkfile:UNTITLEI

底IFileEditObjectViewProcQuickOptionsAdd-insWindowHelp

View!ProcjObject||Print!NameFreezeDefault*।Sort(TransposeIEdit*/-Smpl♦/-TitleSampleI

obsxX1GPFPQP0PlX2X3

1985673.2000351.4000111.9000116.5000131590028.1000026.7000023.957300.950178

1986799.0000418.9000107.0000107.2000146330030.1000028.6000026.544850.950166

1987884.4000472.9000108.8000112.0000147500032.8000032.1000026.963410.978659

19881104.000567.0000120.7000125.2000141250039.5000040.1000027.949371.015190

19891211.000660.0000116.3000114.4000143720046.0000045.9000026.326090.997826

19901278.900693.8000101.300098.80000152920046.6000045.4000027444210.974249

19911453.800782.5000105.1000105.4000163630049.0000047.8000029.569390.975510

19921671.700884.8000108.6000110.7000167140053.2000052.9000031.422930.994361

19932110.8001058.200116.1000116.5000171590061.7000061.7000034.210701.000000

19942851.3001422.500125.0000134.2000171870077.2000082.8000036.933941.072539

19953537.6001771.900116.8000123.600017321009010000102.300039.263041.135405

199G3919.5001904.7001088000107.90001725GOO9810000110.400039.954131.125382

19974185.6001942.600103.1000100.10001758200101.1000110.500041,400591092977

19984331.600192690099.4000096900001799800100.5000107.100043100501065672

19994615.900193210098.70000957000018857009920000102500046,531251033266

20004998.0001971300100800097600001971300100.0000100000049980001000000

20015309.00020279001007000100.70002013800100.7000100700052720951000000

20026029.900227180099.00000999000022583009970000100600060480441009027

20036510.90024169001009000103.40002323500100.6000104000064720681033797

20047182.10027096001033000109.90002370200103.9000114300069125121100096

20057942.90029144001016000103.10002472700105.6000117900075216861116477

20068696.60031119001015000102.60002573400107.2000120900081125001127799

(=)Equation:UNTITLEDWorkfile:UNTITLED::Untitled\-nx

IViewProcObjectPrintNameFreeze|EstimateForecastStats|Resids

DependentVariable:LOG(Q)

Method:LeastSquares

Date:06/24/15Time:10:38

Sample:19852006

Includedobservations:22

VariableCoefficientStd.Errort-StatisticProb.

C5.5245690.08310866.474810.0000

LOG(X/PO)0.5344390.02319823.037760.0000

LOG(P1/P0)-0.2753470.151143-1.8217630.0843

R-squared0.977296Meandependentvar7.493909

AdjustedR-squared0.974906S.D.dependentvar0.193147

S.E.ofregression0.030596Akaikeinfocriterion-4.009741

Sumsquaredresid0.017787Schwarzcriterion-3.860963

Loglikelihood47.10715Hannan-Quinncriter.-3.974694

F-statistic408.9291Durbin-Watsonstat0.695256

Prob(F-statistic)0.000000

Eviews软件输出结果可知，lnQ=5.52+0.534ln^-0.275ln^

R2=0.9773序=0.9749F=408.9

模型的拟合度较高，I啥在5%显著性水平下显著，唔在10%的显著性水平下显

著。同样的，此期间中国城镇居民收入与消费支出总额的增加，会刺激食品消贽

需求增加，而食品相对价格的上升，对食品消费的需求则起着抑制作用。

为了比较，将公式改为InQ=5.52+0.534(InX-InPO)-0.275(InPl-InPO)

=5.52+0.534lnX-0.275lnPl-0.259lnP0

可以看出变量弹性可能为零，函数可能满足零阶齐次性特征。

P116例4.L4中国农村居民人均消费支出主要由人均纯收入来决定。农村人均纯

收入除从事农业经营的收入外，还包括从事其他产业的经营性收入以及工资性收

入、财产收入和转移支付收入等。为考察从事农业经营的收入和其他收入对农村

居民消费支出增长的影响，可使用如下双对数模型：

lnY=0O+PllnXl+p2lnX2+u,其中,Y表示农村家庭人均消费支出,XI表示从

事农业经营的纯收入，X2表示其他来源的纯收入。

1-Jt11IJI

obsX1X2Y

1958.30007317.2005724.500

21738.9004489.0003341.100

31607.1002194.7002495.300

411882001992.7002253.300

51934.6001484.8002732.500

61342.6002047.0003013.300

71313.9003765.9003886.000

81596.9001173.6002413.900

92560.800781.10002772.000

102026.1002064.3003066.900

1126232001017.9002700.700

122622900929.50002618200

13532.00008606.7008006.000

141497.9004315.3004135.200

151403.1005931.7006057.200

1614728001496.3002420.900

171691.4003143.4003591.400

181609.2001850.3002676.600

1919482002420.1003143.800

20184460014164002229300

212213.2001042.3002232.200

221234.1001639.7002205.200

231405.0001597.4002395.000

24961.400010232001627.100

251570.300680.20002195.600

261399.1001035.9002002.200

271070.4001189.8002181.000

281167.900966.20001855.500

291274.3001084.1002179.000

301535.7001124.4002247.000

312267.400469.90002032.400

DependentVariable:LOG(Y)

Method:LeastSquares

Date:06/24/15Time:10:16

Sample:131

Includedobservations:31

VariableCoefficientStd.Errort-StatisticProb.

C3.2843821.0385493.1624710.0037

LOG(X1)0.1490950.1083291.3763130.1796

LOG(X2)0.4762730.0513819.2694790.0000

R-squared0.780438Meandependentvar7.928613

AdjustedR-squared0.764754S.D.dependentvar0.355750

S.E.ofregression0.172546Akaikeinfocriterion-0.584538

Sumsquaredresid0.833621Schwarzcriterion-0.445765

Loglikelihood12.06034Hannan-Quinnenter.-0.539302

F-statistic49,76317Durbin-Watsonstat1.545190

Prob(F-statistic)0.000000

异方差检验

(=)Equation:UNTITLEDWorkfile:UNTnLED::Untitled\_nx

[View|Proc|Object)|PrintNameFreeze|EstimateForecastStatsResids

HeteroskedastidtyTest:Breusch-Pagan-Godfrey

F-statistic2.242300Prob.F(2,28)0.1249

Obs*R-squared4.279646Prob.Chi-Square(2)0.1177三

ScaledexplainedSS4.124637Prob.Chi-Square(2)0.1272

TestEquation:

DependentVariable:RESIDA2

Method:LeastSquares

Date:06/24/15Time:11:15

Sample:131

Includedobservations:31

VariableCoefficientStd.Errort-StatisticProb.

C0.2401600.2430400.9881500.3315

LOG(X1)-0.0367540.025351-1.4498080.1582

LOG(X2)0.0075160.0120240.6250690.5370

R-squared0.138053Meandependentvar0.026891

AdjustedR-squared0.076485S.D.dependentvar0.042018

S.E.ofregression0.040379Akaikeinfocriterion-3.489244

Sumsquaredresid0.045653Schwarzcriterion-3.350471

Loglikelihood57.08328Hannan-Quinncriter.-3.444007

F-statistic2.242300Durbin-Watsonstat1.897011

PrnhfC.ctQfictirXn19/1047

普通最小二乘法估计结果如下：lnY=3.266+0.1502lnXl+0.47751nX2

R2=0.7798D.W.=1.78F=49.60RSS=0.8357

结果显示，即使在10%的显著性水平下，都不拒绝从事农业经营的纯收入前参数

为零的假设，因此可以认为，其他来源的纯收入而不是从事农业经营的纯收入的

增长，对农户的人均消费支出的增长更有刺激作用，之后进行异方差性检验。

子样本1：ln?=3.14+0.398lnXl+0.235lnX2

R2=0.7397RSS1Nei?=0.0702

子样本2：lnY=3.99-0.114lnXl+0.620lnX2

R2=0.8769RSS2=Eei2=0.1912

在5%显著性水平下不拒绝两组子样本方差相同的假设，但在10%的显著性水平

下拒绝。

最后给出异方差稳健标准误差修正结果：

lnY=3.266+0.1502lnXl+0.4775lnX2

R2=0.7798D.W.=1.78F=49.60RSS=0.8357

可以看出，估计参数与普通最小二乘法结果相同，由于参数的标准差得到修正,

从而使t检验值与最小二乘法的结果不同。异方差稳健标准误差结论没有改变农

业经营纯收入不影响农户人均消费支出这一结论。

P132例421用最小二乘法建立如下中国居民总量消费指数Y=209L3+0.4375X

R2=0.9880R2=0.9875F=2214.6D.W.=0.277

(=)Equation:UNTHLEDWorkfile:UNTnLED::Untitled\-BX

ViewProcObjectPrintNameFreeze|EstimateForecastStatsResids

3,000-

2,000-

1,000-

0-

-1,000-

-2,000-

-3,000-j।jj।i।।।i।i।।ii।।।।iiiiiiii

788082S48688909294969800020406

-----YResiduals

View|ProcObjectjPrint|NameFreeze|Estimate|Forecast|Stats|ResdS

Breusch-GodfreySerialCorrelationLMTest

F-statistic55.32449Prob.F(2,25)0.0000

Obs*R-squared23.65532Prob.Chi-Square(2)0.0000

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:06/24/15Time:10:57

Sample:19782006

Includedobservations:29

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStdErrort-StatisticProb.

C100.2903170.96080.5866280.5627

X-0.0051040.005482-0.9309930.3608

RESID(-1)1.4629640.1793408.1575010.0000

RESID(-2)-0.6123230.224966-2.7218510.0117

R-squared0.815701Meandependentvar-4.94E-12

AdjustedR-squared0.793585S.D.dependentvar39.557

S.Eofregression4723013Akaikeinfocriterion-5.28055

Sumsquaredresid5576712.Schwarzcriterion15.46915

Loglikelihood-2V.5680Hannan-Quinncriter.节.33962

F-statistic36.88299Durbin-Watsonstat1.946352

Prob(F-statistic)0.000000

D.W.检验结果表明，在5%显著性水平下，n=29,k=2（包含常数项），查表可知

dL=1.34,du=1.48,由于D.W.=0.277V故存在正自相关。

在Eviews软件中，2阶广义差分的估计结果为

2

Yt=3505.7+0.1996Xt+19.24T+0.7480AR（1）

R2=0.9991溟=0.9990D.W=1.39

在5%显著性水平下，1.18=dL<D.W.<du=1.65,无法判断经广义差分变换后的模

型是否已不存在序列相关性。

Y=3643.0+0.1650X+2/1.059T2

R2=0.9974#=0.9972F=4962.0D.W=0.426

可以看出，估计的参数与普通最小二乘法的结果相同，只是由于参数的标准差得

到了修正，从而使得t检验值与普通最小二乘法的结果不同，但差异并不大。

P141例4.3.1根据理论与经验分析，影响粮食生产（Y）的主要因素有：农业化

肥施用量（XI）、粮食播种面积（X2）、成灾面积（X3）、农业机械总动力（X4）、

农业劳动力（X5）,其中，成灾面积的符号为负，其余均为正。

0EViews-[Grc

(G1FileEditObjectViewProcQuickOptionsAdd-insWindowHelp

View।ProcObjectPrintNameFreezeDefaultvSortTransposeEdit-/-Smpl*/-TitleSample

obsYX1X2X3X4X5

198338728.001660.000114047.016209.0018022.0031151.00

198440731.001740.000112884.015264.0019497.0030868.00

198537911.001776.000108845.022705.0020913.0031130.00

198639151.001931.000110933.023656.0022950.0031254.00

198740208.001999.000111268.020393.0024836.0031663.00

198839408.002142.000110123.023945.0026575.0032249.00

198940755.002357.000112205.024449.0028067.0033225.00

199044624.002590.000113466.017819.0028708.0038914.00

199143529.002806.000112314.0