斯托克計(jì)量經(jīng)濟(jì)學(xué)第八章第九章stata實(shí)證

1、23 45 n8 g10 111213 14 IS 1 17 1019 20 2122 23 ze25 2 272S29 30313233 3435 337 3839 404142 4345 447 4049 5051 52S3 54 55 55758 5360 616263/E8.1V use C;Uju工sanunDu，k匕opcpn38.dtaw/*(1)*/recress ahe age female bachelorr rcbust est store ml/*(2)M/gen mane=m (ane) rearess Inahe aae female bachelor robust

2、 eaz store m2 /(3)/gen lnage=ln(age) rmgrwgg Irahe Inag* female bachelorr robust esc store m3/* (4)*/gen age2-(age)A2 xegrss lrah age ag2 fvmalv bachelorr rcbutc est store m4人導(dǎo)出上述回歸并以此分析(5)(6)(7)/ ml m2 m3 m4 using agaxnl. rf r2 ar2 (4)/，(8)畫出(2)(3) (4)中具有高中文憑的男性的age和Inahe的回歸關(guān)系圖/ two way ( (function

3、 Iny 0.0273*x + 1.876, range |24 35) ) / (unccon Iny - O . 00*ln(x)- 。03q5, range (2 35) ) / (function Inv = 0.0814ax - D.000915ax*x + l.G35r range (24 35) /，畫出具有大學(xué)學(xué)位的女性的回歸函數(shù)圖形，/ uwoway ( (funcclon Iny = 0.0273*x + 2118, range |24 35) ) / (function Iny = 0.804ln(x) + 0.2075, rance (24 35) ) / (funct

4、ion Iny = 0.0814*x - 0-000915*x*x + 1.327, range(24 35) /(9)a /gen rema2e*Dacneior=reiraie*Dacneiox regress Inahe age a(je2 female bachelor fen.alexbachelor# robust esr store m5 /A(10)*/gen femaleage=female*age f -1下xregress Irahe age age2 female bachelor feitalebachelor female*age femaleage2/ r est

5、 store m6 zqoz( fcmalc*agc w0)( fcale*agc2 w0) logoutr save (1) word replace:test ( feitaleage 0) ( female*age2 0)/*(11)*/gen bachelorage=bacheloraage gen bachelorMage2-bacheloraeage reg Inahe age age2 female bachelor fexalebachelor bachelorage bachelorxage2r r est store m7 test( bachelorwage =0)( b

6、achelor*age2 =0) logoutr save (2) word replace:rest( bachelorage =0)( bacheloraje2 =0)/* (12)*/reg Inahe aje age2 female bachelor female*bachelor fexaleage female*age2 bachelorxage bachelorxage2 esc store m8 esttab m6 si7 m8 using agam2.rtf, se r2 ar2(4) / E8.2” use C:UsersasusDestopTeachingRacings.

7、/a(1)a/reg coaxse_eval beaucy incxo onecredit Cemale minoxlcy nnengllsh, r est store ml/(2)/gen ag*2age10 logoutr save (6) word replace:stun dist if dist10 /* (6)/gen dadcollxmomcoll=dadcoll*momcollreg ed disc dist2 female byrest zuition black hispanic inccmehi ownhome dadcoll momcoll cue80 stwmfg80

8、 dadcollxmomcollrrest store m4/* (8)f/gen incomehi*dist-incomehiAdistgen incomehi*dist2incomehiadist*distreg ed dist dist2 female bytest cuition black hispanic inccmehi ownhome dadcoll momcoll cue80 stwmfg80 dadcollagewbachelorAagegen bachelor*age2-bachelorage.agereg Inahe age age2 female bachelor f

9、emalebachelor bachelorage bachelorage2r rest store m7reg Inahe age age2 female bachelor femalebachelor fenalexage femalexage2bachelorage bachelor*age2est store m3est store m3 gen age2=(age)2 regress Inahe age age2 female bachelorr robust unc otorc gen female*bachelor=fen.aleabachelorregress mane age

10、 agez remale Bachelor iemaiexDacneiorr iodust; est store m5 gnlexagsfemale * agegen femalexaqe2Bfemaleagetageregress Inahe age age2 female bachelor femal*bachelor femalexage female*age2r resrtat ml m2 m3 m4 m5 n.6 m7 m8 using again8.rtfr se r2 ar2 (4) ua nC: UBrsauDpkt:opcpjiQ2_09 . dta11 drop if ye

11、ar-=2008 replace ahe-1.346* ahe if year-1992 regress ahe age female bachelorr robust est store mi gen lnahealn|ahe) regress Inahe age female bachelor robust est store m2 gen lnage=ln(age) regress Inahe Inage feitale bachelorr robust est store m3 gen agc2-(age) 2 regress Inahe age age2 female bachelo

12、rr robust est score nw gen female*bachelor=feitale*bachelorregress Inahe age age2 fenale bachelor femalebachelorr robust es* store mS gen femalexage=femaleAage gun f cmaleMagc2-f eirzile* age age regress Inahe age age2 fenale bachelor female*bachelor femalexage feitalexage2r r esz store m6 gen bache

13、lorage=bachelor*age gen bachelorage2=tachelorage*aje rj Inah agp ng42 fbachelor fmalxbahlcr bachlorxbachFlor*ag2r r esz store m7 xcg Inahe age agc2 fcxnalc bachelor femaleMbahclGX fcmalcagc cmalcMagc2 bachelor*age bachelorage2 esz store m8 esztab ml m2 m3 m4 m5 m7 m8 using again9.rtfr se r2 ar2 (4)E

14、8. (1) ahe(2) lnahe(3) lnahe(4) lnahe_ _ *age0.5850.02730.0814(0.0365)(0.00186)(0.0434)*female-3.664-0.186-0.186-0.186(0.208)(0.0108)(0.0108)(0.0108)*bachelor8.0830.4280.4280.428(0.213)(0.0108)(0.0108)(0.0108)lnage*0.804(0.0545)age2-0.000915(0.000735)_cons-0.636*1.876-0.03451.085(1.083)(0.0559)(0.18

15、5)(0.635)N7711771177117711R20.2000.2010.2010.201adj. R20.19950.20030.20050.2004Standard errors in parentheses(表 1)* p 0.05, * p 0.01, * p inane （3）mane （4）具有大學(xué)學(xué)位的女性回歸函數(shù)圖形|naha（2） inare（4）相似之處：圖像都是線性的且趨勢都相同，也就是隨著年齡的增加，平均每小時(shí)的收入也增加。不同之處：以上三個(gè)回歸線的斜率不一樣，如（4）的回歸函數(shù)隨著 age的增加age對lnahe的增長效用減少。如果畫出的是具有大學(xué)學(xué)位的女性回歸

16、函數(shù)圖形，那么圖形的相對形狀與具有高中文憑男性的是一致的。不同的是，由于是女性，圖形會(huì)移動(dòng)3female個(gè)單位，由于具有大學(xué)學(xué)位，也會(huì)移動(dòng)bachelor個(gè)單位，正數(shù)上移，負(fù)數(shù)下移，經(jīng)計(jì)算三個(gè)回歸函數(shù)圖形均上移0.242個(gè)單位。(1)lnahe(2)lnahe(3)lnahe(4)lnaheage0.0810*0.1240.112*0.146(0.0434)(0.0595)(0.0596)(0.0687)age2-0.000906-0.00151-0.00156-0.00203(0.000735)(0.00101)(0.00101)(0.00116)female*-0.2201.315*-0.

17、2201.432(0.0151)(1.267)(0.0151)(1.294)bachelor_ _ _ _ *0.398_ *0.3971.0780.690(0.0149)(0.0149)(1.270)(1.286)Female xbachelor*0.0687*0.0681*0.0718*0.0716(0.0217)(0.0216)(0.0216)(0.0217)Female Xage-0.0877-0.0930(0.0865)(0.0882)Female Xage20.001200.00124(0.00147)(0.00149)Bachelor xage-0.0640-0.0404(0.0

18、867)(0.0876)Bachelor Xage20.001370.00102(0.00147)(0.00148)_cons1.1000.3610.7780.164(0.635)(0.871)(0.875)(1.008)N7711771177117711R20.2020.2040.2040.207adj. R20.20130.20320.20340.2059Standard errors in parentheses(表 2)* p 0.05, * p 0.01, * p F=0該題建立的回歸如表2第（2）列所示，該回歸相對第（1）列增加了交互項(xiàng)female age和Female*ge2。進(jìn)

19、行F檢驗(yàn)，假設(shè)兩個(gè)交互項(xiàng)的系數(shù)都為零，得 F值為 10.791, p值為0F=0該題建立的回歸如表2第（3）列所示，該回歸相對第（1）列增加了交互項(xiàng)Bachelor age和bachelor age2。進(jìn)行F檢驗(yàn)，假設(shè)兩個(gè)交互項(xiàng)的系數(shù)都為零，得F值為10.771, p值為00.05,所以可以拒絕原假設(shè)，也即在5%顯著水平下，高中畢業(yè)生和大學(xué)畢業(yè)生中age對收入的效應(yīng)是不同的。（12）該題新建立的回歸如表 2第（4）列所示。綜上所有回歸，我們總結(jié)出：擁有大學(xué)學(xué)歷的職工比擁有高中文憑的職工工資更高，并且大學(xué)學(xué)歷職工隨年齡 增長工資比高中文憑的職工增加的更快。男性比女性職工的工資更高，并且隨年齡增長

20、男性工資比女性增長得更快。年輕職工中年齡對收入效應(yīng)最大的是具有學(xué)士學(xué)位的男性職工。E8. (2)(3)course_evalcourse_evalcourse_eval*.*beauty0.1660.1600.231(0.0316)(0.0306)(0.0478)intro0.01130.00244-0.00123(0.0562)(0.0564)(0.0556)_ _ _ *_ _ *onecredit0.6350.6200.657(0.108)(0.109)(0.109)*female-0.173-0.188-0.173(0.0495)(0.0517)(0.0494)minority_ *-

21、0.167-0.180-0.135(0.0674)(0.0693)(0.0692)*nnenglish-0.244-0.243-0.268(0.0936)(0.0960)(0.0929)age0.0195(0.0235)age2-0.000222(0.000244)FemaleXbeauty.*-0.141(0.0634)*_cons4.0683.6774.075(0.0370)(0.550)(0.0373)N463463463R20.1550.1570.164adj. R20.14350.14240.1510Standard errors in parentheses* p 0.05, *

22、p 0.01, * p F = 0.534(2 )加入ag解口age所建立的回歸如上表第(2)列所示。age2勺系數(shù)并不顯著，所以沒有證據(jù)顯示ageKcourse_eval的效應(yīng)是非線性的。進(jìn)行F檢驗(yàn)，假設(shè)age和age2勺系數(shù)都為零，得F值為0.6300.05,所以不可以拒絕原假設(shè)，也即沒有證據(jù)顯示在5%的置信水平下age對course_eval有顯著影響。(3 )( 1 )Female xbeauty=0F ( 1, 455)= 4.930ProbF= 0.0268該題建立的回歸如上表第(3)列所示，相比(1)增加了交互項(xiàng)Femalebeauty。進(jìn)行F檢驗(yàn)，假設(shè)Femalexbeauty

23、的系數(shù)為零，得F值為4.9301 , p值為0.02680.05,所以可以拒絕原假設(shè)，也即在5%的置信水平下，男性和女性中 beauty的效應(yīng)之差在統(tǒng)計(jì)上顯著不同。(4 )VariableObsMeanStd.Dev.MinMaxbeauty4634.75e-080.789-1.4501.970計(jì)算得Beauty的標(biāo)準(zhǔn)差為0.79。Smith教授手術(shù)前的 Beauty值：(4.75e-08) -0.79手術(shù)后的 beauty值：(4.75e-08) +0.79Smith教授課程評價(jià)提高約為：0.231 X (2X0.79) =0.37其課程評價(jià)提高的95%置信區(qū)間為：95%置信區(qū)間為(0.22

24、, 0.51)(5 )女教授Jone球程評價(jià)提高的預(yù)測值為：至1 3beauty+ female xbeaut題標(biāo)準(zhǔn)誤，得其為間：(0.091.96X0.04) X (2X0.79)(0.231 1.96X0.0478) X (2X0.79),也即其(0.231-0.173) X (2X0.79 ) =0.09。需要用0.040。構(gòu)造其課程評價(jià)提高的 95%置信區(qū),也即其95%置信區(qū)間為(0.02, 0.27)。(2)(3)(4)(5)edlnededededdist*-0.0390*-0.00283*-0.0906*-0.0909*-0.0917(0.0193)(0.00140)(0.039

25、6)(0.0397)(0.0449)female0.05690.004250.05090.05120.0506(0.0988)(0.00703)(0.0991)(0.0991)(0.0993)*bytest0.07390.005260.07330.07330.0733(0.00647)(0.000460)(0.00650)(0.00649)(0.00650)tuition*-0.526*-0.0366*-0.523*-0.522*-0.523(0.242)(0.0174)(0.243)(0.242)(0.243)black0.08850.007500.05890.06560.0671(0.17

26、9)(0.0128)(0.180)(0.181)(0.182)hispanic0.1940.01400.1980.1950.196(0.115)(0.00823)(0.115)(0.115)(0.116)incomehi0.4150.02990.4130.4160.407(0.121)(0.00859)(0.121)(0.121)(0.169)ownhome0.1950.01430.1990.1990.199(0.127)(0.00905)(0.127)(0.126)(0.127)*dadcoll0.4760.03440.4690.4400.441(0.134)(0.00955)(0.134)

27、(0.144)(0.145)momcoll*0.371*0.0266*0.3620.2830.283(0.163)(0.0116)(0.163)(0.263)(0.263)cue80_ _ _ * 0.0446 ifc0.003190.04510.0451*0.0453(0.0226)(0.00162)(0.0226)(0.0226)(0.0227)stwmfg800.02420.001360.03160.03070.0308(0.0440)(0.00315)(0.0443)(0.0444)(0.0445)dist20.004090.004110.00409(0.00262)(0.00263)

28、(0.00311)Dadcoll xmomcoll0.1420.142(0.329)(0.330)Incomehi xdist0.00455Incomehi xdist2(0.0904)_cons*9.195(0.520)*2.292(0.0370)*9.213(0.520)*9.226(0.523)*9.228(0.524)N943943943943943R20.2290.2300.2310.2310.231adj. R20.21940.22060.22020.21960.2179-0.0000224(0.00567)Standard errors in parentheses* p 0.0

29、5, * p 0.01, * p 10時(shí)回歸函數(shù)（3）的斜率為正。如上表所示，dist10時(shí)，觀測值有17個(gè)，占總體943個(gè)樣本的1.8%,所以這部分的回歸函數(shù)預(yù)測不夠準(zhǔn)確。（6）本題建立的回歸如上表第（4）列所示，相較（3）加入了交互項(xiàng)dadcoll Xmomcoll。交互項(xiàng)系數(shù)度量的是dadcoll和momcoll同時(shí)增加一單位時(shí)產(chǎn)生的效應(yīng)。（7）Jan麗Mary受教育年數(shù)之差的回歸預(yù)測值：也就是 dadcoll的系數(shù)0.440年。Alexis和Mary受教育年數(shù)之差的回歸預(yù)測值：也就是 momcoll的系數(shù)0.283年。Bonnie和Mary受教育年數(shù)之差的回歸預(yù)測值：0.440+0.2

30、83+0.142=0.865年。(8)(1)Incomehi xdist=0(2 )Incomehi Xdist2=0F (2,926)ProbF=0.0100=0.993在（4）的基礎(chǔ)上增加交互項(xiàng) Incomehi xdist和Incomehi Xdist2 ,新建立的回歸如上表第（ 5） 列所示。進(jìn)行F檢驗(yàn)，假設(shè)兩個(gè)交互項(xiàng)的系數(shù)都為零，得F值為0.010.05,所以不可以拒絕原假設(shè)，也即在5%顯著水平下，沒有證據(jù)表明disted的效應(yīng)依賴于家庭收入。（9）綜合上述回歸，我們總結(jié)出：dist越小，預(yù)期受教育年數(shù)越多。disted的效應(yīng)對高收入家庭來說幾乎沒有影響，對低收入家庭來說有輕微的影響

31、。的回歸如上表所示。 growth(2) growth(3) growth(4) growth(5) growthtradeshare士1.898*1.7491.1041.883-5.702(0.866)(0.794)(0.748)(1.344)(8.183)yearsschool*0.243(0.0759)Inyearsschool_*1.016.*2.161_ _ *2.525_*2.133(0.204)(0.400)(0.639)(0.416)rev_coups*-2.300*-2.350*-2.035(0.921)(0.921)(0.938)assasinations0.2280.22

32、40.102(0.335)(0.337)(0.364)lnrgdp60*-1.621*-1.641_ *-1.584(0.440)(0.440)(0.477)Tradesharexlnyearsschool-0.690(0.809)tradeshare28.488(15.83)tradeshare3-2.760(8.527)_cons-0.122-0.186. *11.75_ *11.50_*12.93(0.691)(0.566)(3.297)(3.345)(3.055)N6464646464R20.1610.2870.4530.4570.471adj. R20.13310.26380.406

33、00.39990.4050Standard errors in parentheses* p 0.05, * p 0.01, * p 0.001E8.44681口(1)兩者的關(guān)系看上去是非線性的。因?yàn)榛貧w的回歸是線性關(guān)系，而回歸是非線 性的，所以回歸擬合數(shù)據(jù)的效果優(yōu)于回歸。(2)回歸的growth預(yù)測增長情況:0.243X (6-4) =0.486回歸的growth預(yù)測增長情況：1.016 x (ln6-ln4) =0.414(3)回歸的結(jié)果如上表第(3)列所示，rev_coups和assasinations的系數(shù)都不為0。(4)回歸的結(jié)果如上表第(4)列所示，從表可得 Tradesharex

34、lnyearsschool的系數(shù)不顯-if-*者。(1 )TradeshareF=0.397進(jìn)行F檢驗(yàn)，假設(shè)交互項(xiàng) Tradeshare lnyearsschool的系數(shù)為零，得F值為0.7300.05,所以不可以拒絕原假設(shè)，也即在 5%置信水平下沒有證據(jù)顯示 age course eval有顯著影響。(5)回歸如上表第(5)列所示，如表所示，tradeshare開口tradeshare對系數(shù)不顯著。(1 )tradeshare2=0(2 )tradeshare3=0F( 2, 56)= 1.960ProbF= 0.150進(jìn)行F檢驗(yàn)，假設(shè)交互項(xiàng) Tradeshare inyearsschool

35、的系數(shù)為0,得p值為0.150.05, 所以不可以拒絕原假設(shè)，也即在 5%置信水平下，沒有證據(jù)表明tradeshar親口 growth之間存在非線性關(guān)系。(6)回歸的growth預(yù)測增長情況:1.104X (1-0.5) =0.552回歸的 growth 預(yù)測增長情況：-5.702 X (1-0.5) + (8.488X1-8.488X0.52) + (-2.76X1+2.76X0.5X0.5X0.5) =1.1ahe(2)lnahe(3)lnahe(4)lnahe(5)lnahe(6)lnahe(7)lnahe(8)lnaheage0.5850.02730.08140.08100.1240.

36、1120.146(0.0365)(0.00186)(0.0434)(0.0434)(0.0595)(0.0596)(0.0687)*female-3.664-0.186-0.186-0.186-0.2201.315-0.2201.432(0.208)(0.0108)(0.0108)(0.0108)(0.0151)(1.267)(0.0151)(1.294)bachelor8.0830.4280.4280.4280.3980.3971.0780.690(0.213)(0.0108)(0.0108)(0.0108)(0.0149)(0.0149)(1.270)(1.286)lnage_ _ _ *

37、0.804(0.0545)age2-0.000915-0.000906-0.00151-0.00156-0.00203(0.000735)(0.000735)(0.00101)(0.00101)(0.00116)Female xbachelor0.06870.06810.07180.0716(0.0217)(0.0216)(0.0216)(0.0217)Female Xage-0.0877-0.0930(0.0865)(0.0882)Female Xage20.001200.00124(0.00147)(0.00149)Bachelor xage-0.0640-0.0404(0.0867)(0

38、.0876)Bachelor Xage20.001370.00102(0.00147)(0.00148)_cons-0.636*1.876-0.03451.0851.1000.3610.7780.164(1.083)(0.0559)(0.185)(0.635)(0.635)(0.871)(0.875)(1.008)N77117711771177117711771177117711R20.2000.2010.2010.2010.2020.2040.2040.207adj. R20.19950.20030.20050.20040.20130.20320.20340.2059Standard err

39、ors in parentheses* p 0.05, * p 0.01, * p 0.001 (表1此表是2008年的數(shù)據(jù))(2)(3)(4)(5)(6)(7)(8)ahelnahelnahelnahelnahelnahelnahelnaheage*0.465*0.0268*0.162*0.161*0.127*0.1460.112(0.0277(0.00181(0.0419)(0.0419)(0.0571)(0.0549)(0.0635)female-*-0.167*-0.167*-0.167*-0.200-1.238*-0.199-1.073*2.725(0.153)(0.0102)(0.

40、0102)(0.0102)(0.0134)(1.227)(0.0133)(1.242)bachelor_ _ _ _ *5.984_ _ _ . *0.381_ _ _ . *0.381_ _ _ . *0.381_ _ _ *0.345_ _ . _ *0.346-0.268-0.417(0.171)(0.0103)(0.0103)(0.0103)(0.0143)(0.0143)(1.240)(1.262)Inage*0.794(0.0532)age2*-0.00228*-0.00226-0.00157*-0.00207-0.00139(0.000708 )(0.000707)(0.0009

41、65)(0.000926)(0.00107)Female*0.0826*0.0765*0.0844*0.0781xbachelor(0.0206)(0.0206)(0.0206)(0.0210)Female0.08670.0761xage(0.0835)(0.0845)Female-0.00172-0.00156Xage2(0.00141)(0.00143)Bachelo0.03080.0402rxage(0.0846)(0.0859)Bachelo-0.000338-0.000486rxage2(0.00143)(0.00145)_cons0.671 *1.764-0.129-0.211-0

42、.1970.2110.09320.491(0.820)(0.0544)(0.180)(0.616)(0.615)(0.840)(0.809)(0.934)N76057605760576057605760576057605R20.1960.1830.1840.1840.1860.1880.1870.189adj. R20.19590.18300.18340.18400.18560.18740.18630.1882Standard errors in parentheses* p 0.05, * p 0.01, * p 0.001（表2此表是1992年的數(shù)據(jù)，已根據(jù)通貨膨脹的情況進(jìn)行了調(diào)整）E9.

43、12008年的數(shù)據(jù)如表1所示。遺漏變量偏差：當(dāng)回歸中漏掉了某個(gè)不僅是lnahe的決定因素而且與一個(gè)或多個(gè)回歸變量相關(guān)的變量時(shí)就會(huì)產(chǎn)生遺漏變量偏差。這里不得不提工人的個(gè)人能力。擁 有更高能力的工人平均來說每小時(shí)工資會(huì)更高，并且他們更可能擁有大學(xué)學(xué)位。遺漏掉工人的能力很可能會(huì)導(dǎo)致遺漏變量偏差，特別影響ed又ahe的估計(jì)效應(yīng)。同時(shí)，工人的職業(yè)也是可能的遺漏變量。因?yàn)閾碛型瑯訉W(xué)歷的工人很可能會(huì)選擇不 同的職業(yè)，而有著不同的收入。某些程度上說，職業(yè)也與性別有關(guān)。以上均會(huì)導(dǎo) 致遺漏變量偏差?；貧w函數(shù)的誤設(shè)：如果真實(shí)的總體回歸函數(shù)是非線性的而估計(jì)出的回歸是線性的，則這種函數(shù)形式誤設(shè)將會(huì)導(dǎo)致OLS估計(jì)量有偏。

44、在E8.1中，根據(jù)題目要求已經(jīng)檢查過沒有證據(jù)能夠表明 age對ahe的效應(yīng)是非線性的。變量有測量誤差：年齡或許不能很好地測量工人的經(jīng)驗(yàn)，因?yàn)橛械墓と丝赡?23歲 就開始工作了，有的工人 26歲才開始工作；或者，有的工人休了一年產(chǎn)假，而有 的工人沒有。同時(shí)，ahe的調(diào)查是2008年以后回憶2008年所得的數(shù)據(jù)，所以ahe也 有潛在的測量誤差。樣本選取：數(shù)據(jù)都是從全職工人中選取的，所以可能造成樣本選取偏差。雙向因果：在這道題目中并不是個(gè)問題，因?yàn)閍h壞太可能影響age或gender等。OLS標(biāo)準(zhǔn)誤差非一致：本題是利用異方差穩(wěn)健標(biāo)準(zhǔn)誤并利用異方差穩(wěn)健的方差估計(jì)量構(gòu)造F統(tǒng)計(jì)量，所以異方差不構(gòu)成問題。抽樣過程的隨機(jī)性保證了不同觀測 間的誤差是獨(dú)立分布的，所以不同觀測間的誤差項(xiàng)的相關(guān)性不構(gòu)成問題。1998年的數(shù)據(jù)如表2所示。根據(jù)2008年的數(shù)據(jù)，我們分析得：具有大學(xué)學(xué)歷的工人比具有高中文憑的工人收入更高，并且大學(xué)畢業(yè)生在25-32歲間收入增長更快；男性工人比女性工人收入更高，并且男性工人在25-32歲間收入增長更快；對于所有類型