第二產(chǎn)業(yè)GDP增長的多因素分析

1、第二產(chǎn)業(yè) GDP 增長的多因素分析主要內(nèi)容：從1978年至今，第二產(chǎn)業(yè)的 GDP占GDP總量的比重逐年提高，到 2003 年，已經(jīng)達(dá)到 52%。第二產(chǎn)業(yè)的發(fā)展對于國民經(jīng)濟(jì)的發(fā)展至關(guān)重要。本文 旨在研究資本、勞動、教育水平與第二產(chǎn)業(yè) GDP 形成的關(guān)系。關(guān)鍵字：生產(chǎn)函數(shù)，就業(yè)人數(shù)，資本形成額，教育支出一、經(jīng)濟(jì)理論 ：產(chǎn)出增長是通加增加要素投入和通過源于技術(shù)進(jìn)步所導(dǎo)致的生產(chǎn)率提高和 生產(chǎn)能力更強(qiáng)的勞動大軍實(shí)現(xiàn)的。生產(chǎn)函數(shù)提供了投入與產(chǎn)出之間的數(shù)量關(guān)系。 若僅考慮勞動和資本，生產(chǎn)函數(shù)的一般公式是 Y=AF（K,N）,即產(chǎn)出丫取決于資本 和勞動投入（K , L）和技術(shù)水平A。特別的，對柯布-道格拉斯函

2、數(shù)，有Y=AKaLb。 這個函數(shù)可以對經(jīng)濟(jì)進(jìn)行比較準(zhǔn)確的描述，例如，對美國而言， a=0.25,b=0.75 與其現(xiàn)實(shí)經(jīng)濟(jì)相當(dāng)相近。除此之外， 自然資源和人力資本也是兩種重要的投入。 人力資本投資即通過 學(xué)校教育， 在職培訓(xùn)和其他手段來增加工人的技巧和才能， 這與實(shí)物投資導(dǎo)致的 實(shí)物資本增加是相同的。增加了人力資本 H 的生產(chǎn)函數(shù)可以寫做： Y=AF（K， H，N）。在工業(yè)化國家中，人力資本的要素分額較大，比如曼昆的一篇文章中就 指出，生產(chǎn)函數(shù)中實(shí)物資本，非熟練勞動力和人力資本的要素分額各占 1/3。二、模型的建立和數(shù)據(jù)搜集：由Y=A*F （ K，H，L），若生產(chǎn)函數(shù)采用類似柯布-道格拉斯生產(chǎn)

3、函數(shù)的形 式，并進(jìn)行對數(shù)變換得到：LNY=LNA+aLNK+bLNL+cLNH用 Y 代表第二產(chǎn)業(yè) GDP， K 與 L 分別代表資本和勞動投入，人力資本用教 育費(fèi)用支出 E 代替，可以得到以下模型：LNY=C+aLnK+blnL+clnE+u數(shù)據(jù)：年份第二產(chǎn)業(yè)第二產(chǎn)業(yè)教育費(fèi)用資本形成就業(yè)人數(shù)GDP支出197869451745.275.051377.9197972141913.593.161474.2198077072192114.151590198180032255.5122.791581198283462383137.611760.2198386792646.2155.2420051984

4、95903105.7180.882468.61985103843866.6226.8333861986112164492.7274.7238461987117265251.6293.9343221988121526587.2356.6654951989119767278412.3960951990138567717.4462.4564441991140159102.2532.39751719921435511699.5621.71963619931496516428.5754.91499819941531222372.21018.7819260.619951565528537.91196.65

5、2387719961620333612.91415.7126867.219971654737222.71545.8228457.619981660038619.31726.329545.919991642140557.81927.3230701.620001621944935.32179.5232499.8200116284487502636.8437460.820021578052980.23105.9942304.920031607761274.13351.3251382.7將所有數(shù)據(jù)取對數(shù)后輸入EVIEWS從經(jīng)濟(jì)意義上考慮到當(dāng)年的教育支出對產(chǎn)出的影響可能存在滯后，采用 Gran ger檢

6、驗(yàn)，可以得到當(dāng)之后長度為2時，E是引起丫變化的原因，故模型修 改為：LNY=C+aLnK+blnL+clnE (-2) +u三、模型的估計(jì)和檢驗(yàn):1)平穩(wěn)性檢驗(yàn):單位根檢驗(yàn)LnyADF 一階差分只有截距項(xiàng)滯后3階ADF Test Statistic-2.81%Critical Value*-3.7856073035%Critical Value-3.011410% Critical Value-2.6457*MacKinnon critical values for rejection of hypothesis of a unit root.Augme nted Dickey-Fuller

7、Test Equati onDepe nde nt Variable: D(LNY,2)Method: Least SquaresDate: 06/14/05 Time: 10:15Sample(adjusted): 1983 2003In eluded observati ons: 21 after adjusti ng en dpo intsVariableCoefficie nt Std. Error t-Statistic Prob.D(LNY(-1)-0.5812070.207034-2.8073030.0126D(LNY(-1),2)0.5973570.2186002.732652

8、0.0148D(LNY(-2),2)0.0187300.2225440.0841650.9340D(LNY(-3),2)0.2935510.2070491.4177850.1754C0.0900170.0334642.6899590.0161R-squared0.446263Mean depe ndent var0.004307Adjusted R-squared0.307828S.D.dependent var0.066967S.E. of regressi on0.055715Akaike info criteri on-2.732888Sum squared resid0.049666S

9、chwarz criteri on-2.484192Log likelihood33.69532F-statistic3.223642Durb in -Watson stat1.883066Prob(F-statistic)0.040398以10%的標(biāo)準(zhǔn)LNY不存在單位根，一階差分平穩(wěn)。LNKADF 一階差分只有截距項(xiàng)滯后3階ADF Test Statistic-3.0123731%Critical Value*-3.78565%Critical Value-3.011410% Critical Value-2.6457*MacKinnon critical values for reject

10、ion of hypothesis of a unit root.Augme nted Dickey-Fuller Test Equati onDepe ndent Variable: D(LNK,2)Method: Least SquaresDate: 06/14/05 Time: 10:19Sample(adjusted): 1983 2003Included observations: 21 after adjusting endpointsVariableCoefficie ntStd. Errort-StatisticProb.D(LNK(-1)-0.8981760.298162-3

11、.0123730.0083D(LNK(-1),2)0.4042240.2584971.5637490.1374D(LNK(-2),2)0.2826120.2402811.1761750.2567D(LNK(-3),2)0.3104540.2277361.3632180.1917C0.1415370.0493952.8654030.0112R-squared0.380186Mean depe ndent var0.004144Adjusted R-squared0.225232S.D.dependent var0.102694S.E. of regressi on0.090392Akaike i

12、nfo criteri on-1.765057Sum squared resid0.130733Schwarz criteri on-1.516361Log likelihood23.53309F-statistic2.453546Durbi n- Watson stat2.004426Prob(F-statistic)0.088031以5%的標(biāo)準(zhǔn)，沒有單位根，一階差分平穩(wěn)。LNL ADF只有截距項(xiàng)和趨勢滯后1階一階差分ADF Test Statistic-3.6286781%Critical Value*-4.41675%Critical Value-3.621910% Critical V

13、alue-3.2474*MacKinnon critical values for rejection of hypothesis of a unit root.Augme nted Dickey-Fuller Test Equati onDependent Variable: D(LNL,2)Method: Least SquaresDate: 06/14/05 Time: 10:22Sample(adjusted): 1981 2003In cluded observati ons: 23 after adjusti ng en dpo intsVariableCoefficie ntSt

14、d. Errort-StatisticProb.D(LNL(-1)-1.3032520.359153-3.6286780.0018D(LNL(-1),2)0.0196830.2279610.0863460.9321C0.1054470.0334553.1519390.0052TREND(1978)-0.0045070.001580-2.8527530.0102R-squared0.632964Mean depe ndent var-0.002063Adjusted R-squared0.575011S.D.dependent var0.051344S.E. of regressi on0.03

15、3472Akaike info criteri on-3.799468Sum squared resid0.021287Schwarz criteri on-3.601991Log likelihood47.69389F-statistic10.92201Durb in -Watson stat1.991014Prob(F-statistic)0.000216以5%的標(biāo)準(zhǔn)，沒有單位根，一階差分平穩(wěn)LNE(-2)ADF 有趨勢和截距項(xiàng)滯后1階一階差分ADF Test Statistic-4.4199921%Critical Value*-4.44155%Critical Value-3.6330

16、10% Critical Value-3.2535*MacKinnon critical values for rejection of hypothesis of a unit root.Augme nted Dickey-Fuller Test Equati onDepe nde nt Variable: D(LNE1,2)Method: Least SquaresDate: 06/14/05 Time: 11:28Sample(adjusted): 1982 2003In cluded observati ons: 22 after adjusti ng en dpo intsVaria

17、bleCoefficie ntStd. Errort-StatisticProb.D(LNE1(-1)-1.5774320.356886-4.4199920.0003D(LNE1(-1),2)0.2059900.2192470.9395310.3599C0.0184120.0359670.5119120.6149TREND(1978)-0.0013230.002272-0.5820980.5677R-squared0.702869Mean depe ndent var0.001932Adjusted R-squared0.653348S.D.dependent var0.113284S.E.

18、of regressi on0.066698Akaike info criteri on-2.414312Sum squared resid0.080076Schwarz criterio n-2.215940Log likelihood30.55743F-statistic14.19315Durbi n-Watson stat2.064102Prob(F-statistic)0.000054以5%的標(biāo)準(zhǔn)，沒有單位根，一階差分平穩(wěn)綜上，模型中的變量都是一階差分平穩(wěn)。對變量進(jìn)行回歸 LS LNY C LNK LNL LNE (-2)Depe ndent Variable: LNYMethod:

19、Least SquaresDate: 06/14/05 Time: 11:31Sample(adjusted): 1980 2003In cluded observati ons: 24 after adjusti ng en dpo intsVariableCoefficie ntStd. Errort-StatisticProb.C3.6123801.0467783.4509510.0025LNK0.9203680.07564512.166900.0000LNL-0.3874810.141687-2.7347670.0128LNE(-2)0.1642600.0673732.4380810.

20、0242R-squared0.998259Mean depe ndent var9.374063Adjusted R-squared0.997998S.D.dependent var1.164977S.E. of regressi on0.052123Akaike info criteri on-2.919421Sum squared resid0.054336Schwarz criteri on-2.723078Log likelihood39.03305F-statistic3823.231Durb in -Watson stat0.654112Prob(F-statistic)0.000

21、000R2=0.998259擬合程度很好，F(xiàn)=3823.231通過了 F檢驗(yàn)，模型設(shè)定正確。回歸結(jié)果，得：LNY=3.612380 +0.920368LNK 0.387481LNL+0.164260LNE(-2)(各參數(shù)均通過T檢驗(yàn))對殘差項(xiàng)進(jìn)行平穩(wěn)性檢驗(yàn)，單位根檢驗(yàn)0階，沒有趨勢和截距，滯后一階ADF Test Statistic-2.1086091%Critical Value*5%Critical Value10% Critical Value-2.6756-1.9574-1.6238*MacKinnon critical values for rejection of hypothes

22、is of a unit root.Augme nted Dickey-Fuller Test Equati onDepe nde nt Variable: D(R2)Method: Least SquaresDate: 06/14/05 Time: 11:34Sample(adjusted): 1982 2003In cluded observati ons: 22 after adjusti ng en dpo intsVariableCoefficie ntStd. Error t-Statistic Prob.R2(-1)-0.4605980.218437-2.1086090.0478

23、D(R2(-1)0.2609930.2386241.0937440.2871R-squared0.146646Mean depe ndent var-0.008221Adjusted R-squared0.103978S.D.dependent var0.040171S.E. of regressi on0.038026Akaike info criteri on-3.614601Sum squared resid0.028919Schwarz criteri on-3.515415Log likelihood41.76061F-statistic3.436934Durbi n- Watson

24、 stat1.816806Prob(F-statistic)0.078563以5%的標(biāo)準(zhǔn)，沒有單位根，平穩(wěn)。說明存在協(xié)整。故說明以上長期關(guān)系方程的變量選擇合理，回歸系數(shù)具有經(jīng)濟(jì)意義，即：LNY=3.612380 +0.920368LNK 0.387481LNL+0.164260LNE(-2)誤差校正：LNYI=LNY t LNYu LNKI=LNK t LNK 口 LNLI=LNL t LNL 口 LNEI=LNE t LNER=RESIDDepe nde nt Variable: LNY1Method: Least SquaresDate: 06/14/05 Time: 10:52Sampl

25、e(adjusted): 1983 2003Included observations: 21 after adjusting endpointsVariableCoefficie ntStd. Errort-StatisticProb.C0.0213630.0053044.0275090.0012LNK10.8940320.01928746.353850.0000LNK1(-1)0.1008110.0195535.1556970.0001LNL1-0.2951410.036564-8.0719200.0000R0.9752030.04141123.549450.0000R(-1)-0.833

26、1370.051257-16.254240.0000LNE1(-4)-0.0701980.027907-2.5153950.0247R-squared0.996762Mean depe ndent var0.154619Adjusted R-squared0.995374S.D.dependent var0.083807S.E. of regressi on0.005700Akaike info criteri on-7.235415Sum squared resid0.000455Schwarz criteri on-6.887241Log likelihood82.97185F-stati

27、stic718.2057Durbi n- Watson stat2.664799Prob(F-statistic)0.000000回歸得到短期動態(tài)方程:LNY1=0.021363+0.894032LNK1+0.100811LNK1(-1)-0.295141LNL1 0.070198LNE1(-4)+0.975203R-0.833137R(-1)2)計(jì)量經(jīng)濟(jì)學(xué)檢驗(yàn)對長期模型進(jìn)行異方差檢驗(yàn)：ARCH Test:F-statistic0.874324Probability0.473763Obs*R-squared2.807036Probability0.422343Test Equati on:De

28、pe ndent Variable: RESIDEMethod: Least SquaresDate: 06/15/05 Time: 11:45Sample(adjusted): 1983 2003In eluded observati ons: 21 after adjusti ng en dpo intsVariableCoefficie ntStd. Errort-StatisticProb.C0.0016580.0013371.2406910.2316RESIDA2(-1)0.2342690.3662400.6396590.5309RESIDA2(-2)-0.3322760.34816

29、4-0.9543670.3533RESIDA2(-3)0.4128180.3547091.1638220.2606R-squared0.133668Mean depe ndent var0.002230Adjusted R-squared-0.019214S.D.dependent var0.003111S.E. of regressi on0.003141Akaike info criteri on-8.519183Sum squared resid0.000168Schwarz criteri on-8.320227Log likelihood93.45143F-statistic0.87

30、4324Durb in -Watson stat1.693624Prob(F-statistic)0.473763T值都小于2，沒有異方差White Heteroskedasticity Test:F-statistic2.726168Probability0.048331Obs*R-squared11.76869Probability0.067333Test Equati on:Depe ndent Variable: RESIDA2Method: Least SquaresDate: 06/30/05 Time: 18:41Sample: 1980 2003In eluded observ

31、ati ons: 24VariableCoefficie ntStd. Errort-StatisticProb.C-2.5804821.840997-1.4016760.1790LNK-0.0152300.056131-0.2713370.7894LNO20.0010460.0029950.3491290.7313LNL0.5794110.4186621.3839580.1843LNLA2-0.0298950.021690-1.3782800.1860LNE(-2)-0.0500310.027073-1.8479720.0821LNE(-2)A20.0035060.0020381.72056

32、30.1035R-squared0.490362Mean depe ndent var0.002264Adjusted R-squared0.310490S.D.dependent var0.002979S.E. of regressi on0.002473Akaike info criteri on-8.928022Sum squared resid0.000104Schwarz criteri on-8.584423Log likelihood114.1363F-statistic2.726168Durb in -Watson stat2.184959Prob(F-statistic)0.

33、048331T值都小于2，所以沒有異方差長期模型存在自相關(guān)，使用迭代法修正Depe ndent Variable: LNYMethod: Least SquaresDate: 06/15/05 Time: 12:18Sample(adjusted): 1981 2003In cluded observati ons: 23 after adjusti ng en dpo intsCon verge nee achieved after 21 iterati onsVariableCoeffieie ntStd. Errort-StatisticProb.C0.5225072.0845840.2

34、506530.8049LNK0.7710150.0771279.9967040.0000LNL0.0245400.2404990.1020390.9199LNE(-2)0.2496640.0830813.0050750.0076AR(1)0.7228630.1745814.1405690.0006R-squared0.999181Mean depe ndent var9.447171Adjusted R-squared0.998999S.D.dependent var1.133470S.E. of regressi on0.035853Akaike info eriteri on-3.629138Sum squared resid0.023137Schwarz eriteri on-3.382291Log likelihood46.73508F-statistic5492.676Durb in -Watson stat1.739477Prob(F-statistic)0.000000In verted AR Roots.72樣本容量23個，3個解釋變量，查表，得：Du=1.660,DW=1.739477>1.660且<2.340經(jīng)修正后，不存在自相關(guān)。經(jīng)過修正