第二产业GDP增长的多因素分析

1、第二产业 GDP 增长的多因素分析主要内容：从1978年至今，第二产业的 GDP占GDP总量的比重逐年提高，到 2003 年，已经达到 52%。第二产业的发展对于国民经济的发展至关重要。本文 旨在研究资本、劳动、教育水平与第二产业 GDP 形成的关系。关键字：生产函数，就业人数，资本形成额，教育支出一、经济理论 ：产出增长是通加增加要素投入和通过源于技术进步所导致的生产率提高和 生产能力更强的劳动大军实现的。生产函数提供了投入与产出之间的数量关系。 若仅考虑劳动和资本，生产函数的一般公式是 Y=AF（K,N）,即产出丫取决于资本 和劳动投入（K , L）和技术水平A。特别的，对柯布-道格拉斯函

2、数，有Y=AKaLb。 这个函数可以对经济进行比较准确的描述，例如，对美国而言， a=0.25,b=0.75 与其现实经济相当相近。除此之外， 自然资源和人力资本也是两种重要的投入。 人力资本投资即通过 学校教育， 在职培训和其他手段来增加工人的技巧和才能， 这与实物投资导致的 实物资本增加是相同的。增加了人力资本 H 的生产函数可以写做： Y=AF（K， H，N）。在工业化国家中，人力资本的要素分额较大，比如曼昆的一篇文章中就 指出，生产函数中实物资本，非熟练劳动力和人力资本的要素分额各占 1/3。二、模型的建立和数据搜集：由Y=A*F （ K，H，L），若生产函数采用类似柯布-道格拉斯生产

3、函数的形 式，并进行对数变换得到：LNY=LNA+aLNK+bLNL+cLNH用 Y 代表第二产业 GDP， K 与 L 分别代表资本和劳动投入，人力资本用教 育费用支出 E 代替，可以得到以下模型：LNY=C+aLnK+blnL+clnE+u数据：年份第二产业第二产业教育费用资本形成就业人数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将所有数据取对数后输入EVIEWS从经济意义上考虑到当年的教育支出对产出的影响可能存在滞后，采用 Gran ger检

6、验，可以得到当之后长度为2时，E是引起丫变化的原因，故模型修 改为：LNY=C+aLnK+blnL+clnE (-2) +u三、模型的估计和检验:1)平稳性检验:单位根检验LnyADF 一阶差分只有截距项滞后3阶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%的标准LNY不存在单位根，一阶差分平稳。LNKADF 一阶差分只有截距项滞后3阶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%的标准，没有单位根，一阶差分平稳。LNL ADF只有截距项和趋势滞后1阶一阶差分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%的标准，没有单位根，一阶差分平稳LNE(-2)ADF 有趋势和截距项滞后1阶一阶差分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%的标准，没有单位根，一阶差分平稳综上，模型中的变量都是一阶差分平稳。对变量进行回归 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拟合程度很好，F=3823.231通过了 F检验，模型设定正确。回归结果，得：LNY=3.612380 +0.920368LNK 0.387481LNL+0.164260LNE(-2)(各参数均通过T检验)对残差项进行平稳性检验，单位根检验0阶，没有趋势和截距，滞后一阶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%的标准，没有单位根，平稳。说明存在协整。故说明以上长期关系方程的变量选择合理，回归系数具有经济意义，即：LNY=3.612380 +0.920368LNK 0.387481LNL+0.164260LNE(-2)误差校正：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回归得到短期动态方程:LNY1=0.021363+0.894032LNK1+0.100811LNK1(-1)-0.295141LNL1 0.070198LNE1(-4)+0.975203R-0.833137R(-1)2)计量经济学检验对长期模型进行异方差检验：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，没有异方差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，所以没有异方差长期模型存在自相关，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样本容量23个，3个解释变量，查表，得：Du=1.660,DW=1.739477>1.660且<2.340经修正后，不存在自相关。经过修正