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y取决于资本和劳动投入（k，l）和技术水平a。特别的，对柯布-道格拉斯函数，有y=akalb。这个

2、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-道格拉斯生产函数的形式，并进行对数变换得到：lny=lna+alnk+

3、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：年份第二产业就业人数第二产业gdp教育费用支出资本形成197869451745.275.051377.9197972141913.593.161474.2198077072192114.151590198180032255.5122.791581198283462383137.611760.2198386792646.2155.242005198495903105.7180.882468.61985103843866.62

4、26.8333861986112164492.7274.7238461987117265251.6293.9343221988121526587.2356.6654951989119767278412.3960951990138567717.4462.4564441991140159102.2532.39751719921435511699.5621.71963619931496516428.5754.91499819941531222372.21018.7819260.619951565528537.91196.652387719961620333612.91415.7126867.2199

5、71654737222.71545.8228457.619981660038619.31726.329545.919991642140557.81927.3230701.620001621944935.32179.5232499.8200116284487502636.8437460.820021578052980.23105.9942304.920031607761274.13351.3251382.7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granger检验，可以得到当之后长度为2时，e是引起y变化的原因，故模型修改为：lny=c+a

6、lnk+blnl+clne（-2）+u三、模型的估计和检验：1）平稳性检验：单位根检验lny adf 一阶差分 只有截距项 滞后3阶adf test statistic-2.807303 1% critical value*-3.7856 5% critical value-3.0114 10% critical value-2.6457*mackinnon critical values for rejection of hypothesis of a unit root.augmented dickey-fuller test equationdependent variable: d(l

7、ny,2)method: least squaresdate: 06/14/05 time: 10:15sample(adjusted): 1983 2003included observations: 21 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. d(lny(-1)-0.5812070.207034-2.8073030.0126d(lny(-1),2)0.5973570.2186002.7326520.0148d(lny(-2),2)0.0187300.2225440.0841650.934

8、0d(lny(-3),2)0.2935510.2070491.4177850.1754c0.0900170.0334642.6899590.0161r-squared0.446263 mean dependent var0.004307adjusted r-squared0.307828 s.d. dependent var0.066967s.e. of regression0.055715 akaike info criterion-2.732888sum squared resid0.049666 schwarz criterion-2.484192log likelihood33.695

9、32 f-statistic3.223642durbin-watson stat1.883066 prob(f-statistic)0.040398以10%的标准lny不存在单位根，一阶差分平稳。lnk adf 一阶差分 只有截距项 滞后3阶adf test statistic-3.012373 1% critical value*-3.7856 5% critical value-3.0114 10% critical value-2.6457*mackinnon critical values for rejection of hypothesis of a unit root.augme

10、nted dickey-fuller test equationdependent variable: d(lnk,2)method: least squaresdate: 06/14/05 time: 10:19sample(adjusted): 1983 2003included observations: 21 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. d(lnk(-1)-0.8981760.298162-3.0123730.0083d(lnk(-1),2)0.4042240.258497

11、1.5637490.1374d(lnk(-2),2)0.2826120.2402811.1761750.2567d(lnk(-3),2)0.3104540.2277361.3632180.1917c0.1415370.0493952.8654030.0112r-squared0.380186 mean dependent var0.004144adjusted r-squared0.225232 s.d. dependent var0.102694s.e. of regression0.090392 akaike info criterion-1.765057sum squared resid

12、0.130733 schwarz criterion-1.516361log likelihood23.53309 f-statistic2.453546durbin-watson stat2.004426 prob(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-3.628678 1% critical value*-4.4167 5% critical value-3.6219 10% critical value-3.2474*mackinnon critical va

13、lues for rejection of hypothesis of a unit root.augmented dickey-fuller test equationdependent variable: d(lnl,2)method: least squaresdate: 06/14/05 time: 10:22sample(adjusted): 1981 2003included observations: 23 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. d(lnl(-1)-1.3032

14、520.359153-3.6286780.0018d(lnl(-1),2)0.0196830.2279610.0863460.9321c0.1054470.0334553.1519390.0052trend(1978)-0.0045070.001580-2.8527530.0102r-squared0.632964 mean dependent var-0.002063adjusted r-squared0.575011 s.d. dependent var0.051344s.e. of regression0.033472 akaike info criterion-3.799468sum

15、squared resid0.021287 schwarz criterion-3.601991log likelihood47.69389 f-statistic10.92201durbin-watson stat1.991014 prob(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-4.419992 1% critical value*-4.4415 5% critical value-3.6330 10% critical value-3.2535*mackin

16、non critical values for rejection of hypothesis of a unit root.augmented dickey-fuller test equationdependent variable: d(lne1,2)method: least squaresdate: 06/14/05 time: 11:28sample(adjusted): 1982 2003included observations: 22 after adjusting endpointsvariablecoefficientstd. errort-statisticprob.

17、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-squared0.702869 mean dependent var0.001932adjusted r-squared0.653348 s.d. dependent var0.113284s.e. of regression0.066698 akaike info crite

18、rion-2.414312sum squared resid0.080076 schwarz criterion-2.215940log likelihood30.55743 f-statistic14.19315durbin-watson stat2.064102 prob(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）dependent variable: lnymethod: least squaresdate: 06/14/05 time: 11:31sam

19、ple(adjusted): 1980 2003included observations: 24 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. c3.6123801.0467783.4509510.0025lnk0.9203680.07564512.166900.0000lnl-0.3874810.141687-2.7347670.0128lne(-2)0.1642600.0673732.4380810.0242r-squared0.998259 mean dependent var9.37406

20、3adjusted r-squared0.997998 s.d. dependent var1.164977s.e. of regression0.052123 akaike info criterion-2.919421sum squared resid0.054336 schwarz criterion-2.723078log likelihood39.03305 f-statistic3823.231durbin-watson stat0.654112 prob(f-statistic)0.000000r2=0.998259 拟合程度很好， f=3823.231 通过了f检验，模型设定正

21、确。回归结果，得： lny=3.612380 +0.920368lnk0.387481lnl+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-2.108609 1% critical value*-2.6756 5% critical value-1.9574 10% critical value-1.6238*mackinnon critical values for rejection of hypothesis of a unit root.augmented dickey-full

22、er test equationdependent variable: d(r2)method: least squaresdate: 06/14/05 time: 11:34sample(adjusted): 1982 2003included observations: 22 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. r2(-1)-0.4605980.218437-2.1086090.0478d(r2(-1)0.2609930.2386241.0937440.2871r-squared0.1

23、46646 mean dependent var-0.008221adjusted r-squared0.103978 s.d. dependent var0.040171s.e. of regression0.038026 akaike info criterion-3.614601sum squared resid0.028919 schwarz criterion-3.515415log likelihood41.76061 f-statistic3.436934durbin-watson stat1.816806 prob(f-statistic)0.078563以5%的标准，没有单位

24、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 +0.920368lnk0.387481lnl+0.164260lne(-2)误差校正：lnyi=lnytlnyt-1 lnki=lnktlnkt-1 lnli=lnltlnlt-1 lnei=lnetlnet-1 r=residdependent variable: lny1method: least squaresdate: 06/14/05 time: 10:52sample(adjusted): 1983 2003included observations: 21 afte

25、r adjusting endpointsvariablecoefficientstd. 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)-0.8331370.051257-16.254240.0000lne1(-4)-0.0701980.027907-

26、2.5153950.0247r-squared0.996762 mean dependent var0.154619adjusted r-squared0.995374 s.d. dependent var0.083807s.e. of regression0.005700 akaike info criterion-7.235415sum squared resid0.000455 schwarz criterion-6.887241log likelihood82.97185 f-statistic718.2057durbin-watson stat2.664799 prob(f-stat

27、istic)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-statistic0.874324 probability0.473763obs*r-squared2.807036 probability0.422343test equation:dependent variable: resid2method: least squaresdat

28、e: 06/15/05 time: 11:45sample(adjusted): 1983 2003included observations: 21 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. c0.0016580.0013371.2406910.2316resid2(-1)0.2342690.3662400.6396590.5309resid2(-2)-0.3322760.348164-0.9543670.3533resid2(-3)0.4128180.3547091.1638220.2606

29、r-squared0.133668 mean dependent var0.002230adjusted r-squared-0.019214 s.d. dependent var0.003111s.e. of regression0.003141 akaike info criterion-8.519183sum squared resid0.000168 schwarz criterion-8.320227log likelihood93.45143 f-statistic0.874324durbin-watson stat1.693624 prob(f-statistic)0.47376

30、3t值都小于2，没有异方差white heteroskedasticity test:f-statistic2.726168 probability0.048331obs*r-squared11.76869 probability0.067333test equation:dependent variable: resid2method: least squaresdate: 06/30/05 time: 18:41sample: 1980 2003included observations: 24variablecoefficientstd. errort-statisticprob. c-

31、2.5804821.840997-1.4016760.1790lnk-0.0152300.056131-0.2713370.7894lnk20.0010460.0029950.3491290.7313lnl0.5794110.4186621.3839580.1843lnl2-0.0298950.021690-1.3782800.1860lne(-2)-0.0500310.027073-1.8479720.0821lne(-2)20.0035060.0020381.7205630.1035r-squared0.490362 mean dependent var0.002264adjusted r

32、-squared0.310490 s.d. dependent var0.002979s.e. of regression0.002473 akaike info criterion-8.928022sum squared resid0.000104 schwarz criterion-8.584423log likelihood114.1363 f-statistic2.726168durbin-watson stat2.184959 prob(f-statistic)0.048331t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dependent variable: ln

33、ymethod: least squaresdate: 06/15/05 time: 12:18sample(adjusted): 1981 2003included observations: 23 after adjusting endpointsconvergence achieved after 21 iterationsvariablecoefficientstd. errort-statisticprob. c0.5225072.0845840.2506530.8049lnk0.7710150.0771279.9967040.0000lnl0.0245400.2404990.102

34、0390.9199lne(-2)0.2496640.0830813.0050750.0076ar(1)0.7228630.1745814.1405690.0006r-squared0.999181 mean dependent var9.447171adjusted r-squared0.998999 s.d. dependent var1.133470s.e. of regression0.035853 akaike info criterion-3.629138sum squared resid0.023137 schwarz criterion-3.382291log likelihood46.73508 f-statistic5492.676durbin-watson stat1.739477 prob(f-statistic)0.000000inverted ar roots .72样本容量23个，3个解释变量，查表，得：du=1.660,dw=1.7394771.660