2023年計(jì)量經(jīng)濟(jì)學(xué)計(jì)算機(jī)作業(yè)

數(shù)量經(jīng)濟(jì)學(xué)付歡計(jì)量經(jīng)濟(jì)學(xué)計(jì)算機(jī)作業(yè)

C13.ll

(i)在其他自變量不變的情況下：

根據(jù)：log(Xi)-log(Xo)~(X]-Xo)/X0=AX/X0

Amath4it=plAlog(rexppit)=(pl/100)*[100*Alog(rexppit)]?(p1/100)*(%Arexppit),因此

if%Arexppit=10,thenAmath4it=(pl/100)*(10)=pl/10o

所以，平均每個(gè)學(xué)生的真實(shí)支出提高10%,則math4it約改變[31/10個(gè)百分點(diǎn)。

(ii)用一階差分估計(jì)第一部分中的模型(包括1994-1998年度虛擬變量)

regc>ath4y94y9by9/y98grexppgeniolclunch

SourceSSdfMSNumberofobs=3300

F(8,3291)=108.03

Model122398.669815299.8336Prob>F=0.0000

Residual466100.0283291141.628693R-squared=0.2080

AdjR-squared=0.2061

Total588498.6973299178.386995RootMSE=11.901

cmath4Coef.Std.Err.tP>l11[95%Conf.Interval1

W4

5.5210521.72837710.720.474-.90706611.94917

y966.812446.77866368.750.0005.2857328.339161

y97-5.23489.7271019-7.200.000-6.660508-3.809272

y9$-8.488463.7222014-11.750.000-9.904472-7.072453

y98.967841.719233512.470.0007.5576510.37803

grexpp-3.4472682.760079-1.250.212-8.8589131.964377

genrol.63453351.0286030.620.537-1.3822332.6513

clunch.025074.05547340.450.651-.083692.1338399

cons5.954963.518234711.490.0004.9388686.971058

Amath4=5.95+.52y94+6.81y95-5.23y96-8.49y97+8.97y98

(0.52)(0.73)(0.78)(0.73)(0.72)(0.72)

-3.45Alog(rexpp)+0.635Alog(enroll)+0.025Alunch

(2.76)(1.029)(0.055)

當(dāng)rexpp增加10%,math4降低0.35%(3.45/10?0.35)

(iii)在模型中添加支出變量的一階滯后，并利用一階差分估計(jì)得

Amath4=6.16+5.70y95-6.80y96-8.99y97+8.45y98

(0.55)(0.77)(0.79)(0.74)(0.74)

-1.41Alog(rexpp)+11.04Alog(rexpp-1)+2.14Alog(enroll)

(3.04)(2.79)

(1.18)

+0.073Alunch

(0.061)

n=2,750,R2=0.238.

回歸圖如下

regc>ath4力5力6y^7y98grexppgrexpp_lgenro1clunch

SourceSSdfMSNumberofobs=2750

F(8,2741)=106.75

Model124773.729815596.7161Prob>F=0.0000

Residual400464.322741146.101539R-squared=0.2376

AdjR-squared=0.2353

Total525238.0482749191.065132RootMSE=12.087

cmath4Coef.Std.Err.tP>ltl[95%Conf.Interval]

y955.704738.77436967.370.0004.1863317.223145

y96-6.795939.7896773-8.610.000-8.344362-5.247516

y97-8.989378.7376818-12.190.000-10.43585-7.54291

y988.453018.743523111.370.0006.9950969.91094

grexpp-1.4106993.037452-0.460.642-7.3666264.545228

grexpp.l11.040262.7858333.960.0005.57771716.50281

genrol2.1400171.1768861.820.069-.16765544.447689

clunch.0723056.06148691.180.236-.0477598.193371

_cons6.158613.55131711.170.0005.0775747.239652

由回歸圖所示：即期支出變量的系數(shù)為-1.41,t統(tǒng)計(jì)量為-0.46,統(tǒng)計(jì)上不顯著

滯后支出變量的系數(shù)為11.04,t統(tǒng)計(jì)量為3.96,統(tǒng)計(jì)上顯著

(iv)

.regc?ath4y95y96y97y98grexppgrexpp」genro1clunch,robust

LinearregressionNumberofobs=2750

F(8,2741)=107.96

Prob>F=0.0000

R-squared=O.ZJ/b

RootMSE=12.087

Robust

cmath4Coef.Std.Err.tP>ltl[95%Conf.Interva1]

y955.704738.79417697.180.0004.1474927.261983

y96-6.795939.8399903-8.090.000-8.443017-5.148861

y97-8.989378.7516618-11.960.000-10.46326-7.515497

y9$8.453018.771376310.960.0006.940489.965556

grexpp-1.4106994.282755-0.330.742-9.8084526.987054

grexpp.111.040264.3796872.520.0122.45244119.62808

genrol2.1400171.3929861.540.125-.59139214.871426

clunch.0728056.14129030.520.606-.2042407.3498519

_cons6.158613.583310.560.0005.0148617.302365

比較:的異方差穩(wěn)健標(biāo)準(zhǔn)誤為4.28,從而降低了Alog(rexpp)的統(tǒng)計(jì)顯著性

A

黑-pQ的異方差穩(wěn)健標(biāo)準(zhǔn)誤為4.38,其t統(tǒng)計(jì)量降低為2.52。在1%的顯著性水

平雙側(cè)檢驗(yàn)下Alog(rexpp-1)仍然是統(tǒng)計(jì)顯著的,(t統(tǒng)計(jì)量大于1.96)

(v)

xtregcsath4y95y96y97y98gexppgexpp_lgenrolclnnch,robust

【andom-effectsGLSregressionNumberofobs2750

roupvariable:distidNumberofgroups=550

1-sq:within=0.2465Obspergroup:min=5

between=0.0054avg二5.0

overal1=0.2376max=5

'andomeffectsu_i?GaussianWaldchi2(8)=762.12

：on(u_i,X)=0(assumed)Prob>chi2二0.0000

(Std.Err.adjustedfor550clustersindistid)

Robust

cmath4Coef.Std.En.zP>lzl[95%Conf.Interval]

y955.755012.90977856.330.0003.9718797.538145

y96-6.773436.8658133-7.820.000-8.470399-5.076473

y97-8.988665.7754606-11.590.000-10.50854-7.46879

y988.514353.803080410.600.0006.94034410.08836

gexpp-1.4107084.944105-0.290.775-11.100988.279559

gexpp」11.040265.1315022.150.031.982702321.09782

genrol2.1400191.645121.300.193-1.0843575.364396

clunch.0728056.16545640.440.660-.251483.3970942

_cons5.868631.77859637.540.0004.342617.394652

sigma_u0

sigma_e13.187739

rho0(fractionofvananceduetou_i)

ks)異方差序列相關(guān)穩(wěn)健標(biāo)準(zhǔn)誤為4.94,Nog(rexpp)的t統(tǒng)計(jì)量降低了。

%SPG的標(biāo)準(zhǔn)誤為5.13,Alog(rexpp-l)的t統(tǒng)計(jì)量為2.15.雙側(cè)檢驗(yàn)的p值為0.032

(vi)使用1995,1996,1997,1998年進(jìn)行混合的OLS可得力=-0.423

這表明差分誤差有很強(qiáng)的負(fù)序列相關(guān)

(vii)基于充分穩(wěn)健的聯(lián)合檢驗(yàn)，如下圖

■testgenro1clunch

(1)genro1=0

(2)clunch=□

ch12(2)=1.86

Probachi2=O.3944

所以模型中沒有必要包含學(xué)生注冊的人數(shù)和午餐項(xiàng)目變量

C14.10

(i)根據(jù)回歸可知利用混合OLS估計(jì)的B1=0.36,

當(dāng)Aconcen=0.10,則Alfare=0.36*0.10=0.036.airfare增加3.6%、

.regIfareconcenIdistIdistsq

SouiceSSdfMSNumberofobs=4596

-IUI0.oj

Model349.0895913116.363197Prob>F=0.0000

Residua1526.0047824592.11454808R-squared=0.3989

AuJK-SQUalOQ—u■jyuj

Tota1875.0943744595.190444913RootMSE=.33845

IfareCoef.Std.En.tP>l11[95%Conf.Inters1]

concen.3526892.030210111.670.000.2934628.4119157

Idist?.899166.1290132-6.970.000-1.152094?.6462382

Idistsq.1027463.009781610.500.000.0835697.1219228

_cons6.249577.422965614.780.0005.4203617.073793

(ii)Bl的95%的置信區(qū)間為[0.3090419]只有當(dāng)復(fù)合誤差序列無關(guān)，得出的標(biāo)準(zhǔn)誤才是

有效的，所以有點(diǎn)不太可能，充分穩(wěn)健下的95%的置信區(qū)間為[0.245,0.475],條件為允許存在

序列相關(guān)和異方差，所以充分穩(wěn)健下的置信區(qū)間比一般的置信區(qū)間要大。忽略序列相關(guān)會(huì)導(dǎo)

致參數(shù)估計(jì)產(chǎn)生不確定性.

(iii).斜率變?yōu)檎甭实膌og(fare)的值為0.902/[2*0.103]=4.38。dist的值為exp(4.38)=80.o

該值表示的是fare對dist的正彈性系數(shù)。

(iv)B1的RE估計(jì)值為0.209,表示fare與concern之間正相關(guān)。因?yàn)閠=7.88估計(jì)值統(tǒng)計(jì)

上顯著

.xtregIfarey98y99yOOIdistIdistsq,re

Random-effectsGLSregressionNumberofobs4596

Groupvariable:idNumberofgroups1149

R-sq:within=0.1270Obspergroup:min4

between=0.4018avg4.0

overal1=0.3876max4

Randomeffectsu_i?GaussianValdchi2(5)1270.63

cori(u_i,X)=0(assumed)Prob>chi20.0000

IfareCoef.Std.Err.zP>lzl[95%Conf.Interva1]

y98.024341.00446445.450.000.0155911.033091

y99.0350861.00446447.860.000.0263361.043836

yOO.0959191.004464421.490.000.0871691.1046691

Idist-.783627.2501516-3.130.002-1.273915-.2933389

Idistsq.0897726.0188994.750.000.0527313.1268139

_cons6.239633.82252837.590.0004.6275087.851759

sigma.u.32471182

sigma_e.10700501

rho.90204224(ftactionofvarianceduetou,i)

(V)FE估計(jì)值為0.169,RE的X估計(jì)值為0.9.我們可以預(yù)計(jì)RE估計(jì)值與FE估計(jì)值非常

相似。

,xtregIfarey98y99yOOconcenIdistIdistsq.fe

note:Idistomittedbecauseofcollinearity

note:Idistsqomittedbecauseofcollinearity

Fixed-effects(within)regressionNumberofobsss4596

Groupvariable:idNumberofgroups1149

R-sq:within=0.1352Obspergroup:minsx

between=0.0576avg=4.0

overall=0.0083max=

F(4,3443)=134.61

corr(u_i,Xb)=-0.2033Prob>F=0.0000

IfareCoef.Std.Err.tP>|t|[95%Conf,interval]

y98.0228328.00445155.130.000.0141048.0315607

y99.0363819.00444958.180.000.0276579.0451058

yOO.0977717.004455521.940.000.089036.1065073

concen.168859.02941015.740.000.1111959.226522

Idist(omitted)

Idistsq(omitted)

_cons4.953331.0182869270.870.0004.9174764.989185

sigma_u.43389176

sigma_e.10651186

rho.94316439(fractionofvarianceduetou_i)

Ftestthatallu_i=0:F(1148,3443)=36.90Prob>F=0.0000

(Vi)在一個(gè)航班線上的兩個(gè)機(jī)場附近的城市影響航行的因素為人口，教育水平，雇主類

型等。高速路及鐵路的便利情況及周圍的地理環(huán)境，可以考慮為固定不變的。這些因素和

concern相關(guān)。

(vii)考慮到無法觀測效應(yīng)，我們可以使用固定效應(yīng)模型得出估計(jì)值為正,且統(tǒng)計(jì)上顯

著。用FE估計(jì)得到的估計(jì)值為0.169concern與時(shí)間常量正相關(guān)

C15.8

(i)

.regpirap401kincinesqageagesq

SourceSSdfMSNumberofobs=9275

,yay)一quo.<>□

Model316.571003563.3142007Prob>F=0.0000

Residual1442.441839269.155620005R-squared=0.1800

AGJK?SQUftI6Q—U?1

Total1759.012839274.189671429RootMSE=.39449

piraCoef.Std.Err.tP>ltl[95%Conf.Interva1]

p401k.0536598.00957135.610.000.0348978.0724217

inc.0086788.00051116.980.000.0076771.0096806

inesq-.000022s4.03e-06-5.650.000-.0000307-.0000149

age-.0015936.0033302-0.480.632-.0081216.0049343

agesq.0001173.00003823.070.002.0000424.0001922

_cons-.1977236.06864462880.004-.332282-.0631651

OLS估計(jì)方程:n=9,275,R2=0.180

Pira=-0.198+0.054p40lk+0.0087inc-0.000023inc2-0.0016age+0.00012age2

(0.069)(0.010)(0.0005)(0.000004)(0.0033)(0.00004)

p401k的系數(shù)表示保持收入和年齡不變的情況下，參加401(K)計(jì)劃與擁有一個(gè)個(gè)人退

休金賬戶的比沒有參加401(K)計(jì)劃與擁有一個(gè)個(gè)人退休金賬戶的概率多0.054。

(ii)在上題的回歸方程中，保持收入和年齡不變下，在給定的收入和年齡等級(jí)中，該方程

并不能解釋不同的人有不同的儲(chǔ)蓄計(jì)劃。而是解釋了儲(chǔ)蓄的人會(huì)參加401(k)計(jì)劃和(IRA)

計(jì)劃.在保持其他條件不變的情況下，如果無法控制個(gè)人的儲(chǔ)蓄計(jì)劃，用普通的OLS估計(jì)

無法得到我們想要的結(jié)果

(iii)欲使c401k成為p401k的有效IV,應(yīng)該滿足兩個(gè)條件:c401k對p401k有偏效應(yīng)和c401ko

與u無法觀測的儲(chǔ)蓄計(jì)劃不相關(guān).如果雇主會(huì)提供401(k)退休計(jì)劃的，工人會(huì)儲(chǔ)蓄。則

u與e401(k)相關(guān)。

(iv)p401(k)的約簡型方程P401k=0.059+0.689e401k+0.0011inc-0.0000018

inc2-0.0047age+0.000052age2

(0.046)(0.008)(0.0003)(0.0000027)(0.0022)(0.000026)

n=9,275,R2=.596

.regp401kincincsqageagesqe40Ikyrobust

LinearregressionNumberofobs=9275

F(5,9269)=1915.11

Prob>F=0.0000

R-squared=0.5963

RootMSE=.2B418

Robust

p401kCoef.Std.Err.tP>l11[95%Conf.Interval]

324

inc.0011117.00034340690.001.0004384.0017349

incsq1.84e-062.67e-060.491-3.40e-067.08e-06

-21o

age-.0047205.00224332o20.035-.0091179-.0003231

agesq.000052.0000257862/0.0431.64e-06.0001024

e401k.6888454.00799031zO0.000.6731827.7045082

cons.0591493.0461749Q0.200-.0313637.1496623

e401k的系數(shù)表示，在保持收入與年齡不變的情況下，有資格參與一項(xiàng)401(k)計(jì)劃的人

參加401(k)的計(jì)劃會(huì)多0.69,明顯的是，c401k符合成為p401k工具變量的兩個(gè)要求之

(V)用c401k作為p401k的工具變量來估計(jì)

Pira=-0.207+0.021p401k+0.0090inc-0.000024inc2-0.0011age+0.00011age2

(0.065)(0.013)(0.0005)(0.000004)(0.0032)(0.00004)

n=9,275,R2=0.180

regpirayhatincageincsqagesq,robust

.inearregressionNumberofobs=9275

5,9269)=411.13

Prob>F=0.0000

R-squared=0.1774

RootMSE=.3951

Robust

piracoef.std.Err.VP>|t|[95%Conf.Interval]

yhat.0207012.01324561560.1180052631.0466654

inc?0089982.000491618300.000.0080345.009962

age-.0011466.0032527-0350.724-.0075227.0052294

incsq-.00002413.89e-06-6210.000-.0000318-.0000165

agesq.0001121.00003842920.004.0000368.0001873

_cons-.2073136.0654498-3170.0023356097-.0790176

IV估計(jì)出來的Bp401k0.021低于OLS估計(jì)值0.054的一半。相應(yīng)的I統(tǒng)計(jì)量值為1.56.約簡

人

型中/川。山就是給定無法觀測的儲(chǔ)蓄計(jì)劃下的估計(jì)值。但是我們?nèi)匀粺o法估計(jì)參加401

(K)計(jì)劃與擁有個(gè)人退休金賬戶之間的替換關(guān)系。

C17.ll

.dropIfhcxjrs=O

"2348observationsdeleted)

.sumhours

variableobsMeanstd.Dev.Minrax

hours328635.5292110.90291120

(i)參加勞動(dòng)的婦女的比率為3286/5634(總數(shù))=0.583.

(ii)

.regIwageeducexperexpersqblackhispanic

sourcessdfMSNumberofobs=3286

'XJ9nJW=169.08

Model185.581829537.1163657Prob>F=0.0000

Residual720.0075723280.219514504R-squared=0.2049

AdjR-squared=0.2037

Total905.5894013285.275674095RootM5E=.46852

Ivzagecoef.Std.Err.tp>ltl[95%Conf.Interval]

educ.0991502.003589827.620.000.0921118.1061887

exper.0198554.00328566.040.000.0134133.0262974

expersq-.0003489.000077-4.530.000-.0004999-.0001979

black-.0295532.0343431-0.860.390-.0968892.0377828

hispanic.0136158.03635650.370.708-.0576679.0848996

_cons.648842.059965910.820.000.5312675.7664164

.testblackhispanic

(1)black=0

(2)hispanic=0

F(2,3280)=0.46

Prob>F=0.6324

只利用工作女性的數(shù)據(jù)用OLS估計(jì)工資方程:

log(vvage)=0.649+0.099cduc+0.020exper-0.00035exper2-0.030black+0.014

hispanic

(0.060)(0.004)(0.003)(0.00008)(0.034)(0.036)

n=3,286,R2=0.205

平均來說與非黑種人及非西班牙人群組相比，黑種多賺3%,西班牙人多賺1.3%,聯(lián)合F檢

驗(yàn)的p值為0.63.所以當(dāng)控制教育及經(jīng)驗(yàn)水平下，不同種族之間工資差別不明顯。

(iii)nwifeinc的系數(shù)為-0.0091,t統(tǒng)計(jì)量為-13.47,kidlt6的系數(shù)為-0.5且t統(tǒng)計(jì)量為-11.05

我們期待這兩個(gè)系數(shù)為負(fù)。如果一個(gè)女人的丈夫賺更多的，她不太可能工作。有一個(gè)年輕

的孩子在家庭中也降低了概率的女人。每個(gè)變量是非常顯著。

.probitinlfeducexperexpersqblackhispanicnwifeinckidlt6

iteration0:loglikelihood=-3826.743

iteration1:loglikelihood=-3537.4368

iteration2:loglikelihood=-3537.2544

Iteration3:loglikelihood=-3537.2544

ProbitregressionNumberofobs5634

LRchi2(7)578.98

Prob>chi20.0000

Loglikelihood=-3537.2544PseudoR20.0756

inlfCoef.Std.Err.zP>|z|[95%Conf.interval]

educ.0964837.007785412.390.000.0812246.1117428

exper.0077141.00723851.070.287-.0064732.0219014

expersq-.0006143.0001577-3.900.000-.0009234-.0003052

black.0167548.07558960.220.825-.1313981.1649077

hispanic-.1219554,0704695-1.730.084-.260073.0161623

nwifeinc-.0091239.0006775-13.470.000-.0104518-.007796

kidlt6-.500167.0452776-11.050.000-.5889096-.4114245

_cons-.4393231.1338545-3.280.001-.7016732-.176973

(iv)我們需要至少一個(gè)影響參加勞動(dòng)的變量，這個(gè)變量并不會(huì)直接影響工資的多少。所

以,我們必須假定，控制教育、經(jīng)驗(yàn)和種族差異變量下，其他收入和有一個(gè)孩子的情況并不不

影響工資。如果雇主歧視有小孩或是丈夫有工作的婦女。這些假定就不會(huì)成立。此外，如果

有一個(gè)孩子會(huì)降低勞動(dòng)力，也就是說她必須花時(shí)間去照顧生病的孩子。這樣，我們就不能從

工資方程中遺漏掉kidlt6o

(v)每個(gè)觀測的逆米爾斯比為1.77,相應(yīng)的雙側(cè)p值為0.77.在3286個(gè)觀測中，它并不是特

別小的，力的檢驗(yàn)并沒有提供有力的證據(jù)對零假設(shè)沒有選擇偏差。

(vi)把逆米爾斯比加到工資方程中去，斜率系數(shù)并沒有改變多少。例如,education的系數(shù)

從0.099變動(dòng)到0.103,同樣在OLS估計(jì)下的95%的置信區(qū)間內(nèi)［0.092,0.106］°exper的系

數(shù)變化很小，black和Hispanic的系數(shù)變化很大，但是這些估計(jì)值在統(tǒng)計(jì)上并不顯著。

最重要的變化是在-截距估計(jì)從［649,539］：從0.649變化至U0.539.在本例中，微距為log(wagc)

的非黑人非西班牙裔婦女且沒有受過教育和工作經(jīng)驗(yàn)的估計(jì)值。在全樣本下并沒有一個(gè)婦

女是這種情況的。因?yàn)樾甭氏禂?shù)會(huì)發(fā)生改變，我們不能說,Heckman估計(jì)意味著與沒有修正

的估計(jì)相比，工資水平會(huì)更低。

CI8.5

(i)估計(jì)的方程如下：

hy6t=0.078+1.027hy3t-l-1.021Ahy3t-0.085Ahy3(-i-0.104AhyS^

(0.028)(0.016)(0.038)(0.037)(0.037)

n=121,R2=0.982,=0.123.

使用t檢驗(yàn)原假設(shè)Ho：。二1的t統(tǒng)計(jì)量為(1.027-1)/0.016"1.69.在5%的顯著性

水平下的使用雙側(cè)檢驗(yàn)中，我們不能拒絕Ho：。=1,但在10%的水平上我們會(huì)拒絕原假設(shè)

(P=l)o

.genchy3_B=chy3[_n-2]

(3missingvaluesgenerated)

.reghybhy3_lchy3chy3_lchy3_>

SourceSSdfMSN

>umberofobs=121