机动车辆保险发展影响因素的实证分析.doc

机动车辆保险发展影响因素的实证分析一、 问题的提出近年来福建省汽车产业发展迅速，汽车消费的增长必将带动机动车辆保险业迅速发展，特别是按照入世协议我国将逐步开放保险市场，中国机动车辆保险业将面临严峻的挑战，如何应对这一挑战，成为我国机动车辆保险业不容忽视的问题。汽车消费的增长为福建省汽车保险业提供了广阔的发展空间 ,中国是世界上最大最有潜力的汽车保险市场。在未来的国际汽车保险市场竞争中 ,中国汽车保险行业无疑具有近水楼台先得月的优势 ,但与发达国家相比 ,中国汽车保险业实力相对薄弱 ,能否抓住机遇扬长避短 ,充分发挥我国保险业的地域优势占领更多的市场 ,我国保险业面临着严峻的挑战。面对挑战 ,福建省保险公司应当充分认识我国汽车保险业存在的问题和与发达国家的差距 ,积极开发汽车保险品种 ,提高服务质量 ,以应对未来的竞争。随着改革开放形式的发展，社会经济和人民生活发生了巨大变化，机动车辆迅速普及和发展，机动车辆保险业务也随之得到迅速发展。如何促进机动车辆保险的发展，有哪些因素影响着福建省机动车辆保险的发展，一直是人们关注的焦点。二、 模型设定经分析，影响福建省机动车辆保险发展的因素有：城镇居民可支配收入X1、民用汽车数量X2、赔款及给付X3、政府财政支出X4，把机动车辆保险年保费收入作为被解释变量Yt。为此设定了如下形式的计量经济模型： Yt=1+2X1+3X2+4X3+5X4+Ut其中，Yt为第t年福建省机动车辆保险保费收入（万元）；X1为城镇居民可支配收入（元）；X2为民用汽车数量（辆）；X3为赔款及给付（万元）；X4为政府财政支出（亿元元）。三、 数据的收集 为估计模型参数，收集福建省机动车辆保险发展及其影响因素19982010年的统计数据，如下表所示。年份机动车辆保险保费收入（Y）万元城镇居民可支配收入（元）X1民用汽车数量（辆）X2赔款及给付（万元）X3政府财政支出（亿元）X41998113459.2648624806271780281.421999122141686027821875733312.572000135004743232127867066369.672001153218831336670769880428.332002167589918943625488719476.20200317998610000520751103007551.00200424333611175632739134164622.57200527388212321742611173923788.112006361257137539354101918801012.7720074996521550511430592734641282.8420085818401796113398363689911516.5120096963661957716221234250301694.6320109816962178119965294602822056.01资料来源：中国统计年鉴1998-2010 四、 模型的估计与调整 1、利用EViews软件，生成Y、x1、x2、x3、x4等数据，如下obsYX1X2X3X41998113459.2648624806271780281.421999122141686027821875733312.572000135004743232127867066369.672001153218831336670769880428.332002167589918943625488719476.2200317998610000520751103007551200424333611175632739134164622.57200527388212321742611173923788.112006361257137539354101918801012.7720074996521550511430592734641282.8420085818401796113398363689911516.5120096963661957716221234250301694.6320109816962178119965294602822056.01 2、 采用这些数据模型进行OLS回归，结果如表1.1所示 表1.1 OLS回归结果Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 12:13Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C223349.20903753106.14608764.205713001070.002973221319X1-53.600455375910.6248308948-5.044829033670.000995629474403X20.7705477368940.1496773794445000876411787684X3-0.09218286618940.296868989622-0.3105169937310.764103711622X4199.82632877170.7311562741.170415131780.275516324842R-squared0.996176069299 Mean dependent var346878.938462Adjusted R-squared0.994264103948 S.D. dependent var268843.547629S.E. of regression20361.0539099 Akaike info criterion22.9643584196Sum squared resid3316580130.58 Schwarz criterion23.181646634Log likelihood-144.268329727 F-statistic521.02203057Durbin-Watson stat2.5705032404 Prob(F-statistic)1.06580916685e-09 由此可见，该模型R=0.9962，R修正后为0.9943可决系数很高，F检验值521.022，明显显著。但是当=0.05时，t/2(n-k)=t0.025(13-5)=2.31,x3、x4的系数t检验不显著，而且x1、x3系数的符号与预期相反，这表明很可能存在严重的多重共线性。 3、计算各解释变量的相关系数，选择x1、x2、x3、x4数据，点“view/correlation”得相关系数矩阵（表1.2） 表1.2 相关系数矩阵变量X1X2X3X4X110.9928552334280.983152579270.993675603147X20.99285523342810.9875768523850.997420436091X30.983152579270.98757685238510.990319735953X40.9936756031470.9974204360910.9903197359531 由相关系数矩阵可以看出，各解释变量相互之间的相关系数较高，证实确实存在严重多重共线性。需要对其进行修正。 4、采用逐步回归的办法，去检查和解决多重共线性问题。分别作Y对X1、X2、X3、X4的一元回归，结果如下所示。表1.3 Y对x1作一元回归结果为Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 12:53Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-290719.79403350236.3705779-5.787038169540.000121576246397X151.69085406843.789681347313.63989457993.08626254192e-08R-squared0.944175676873 Mean dependent var346878.938462Adjusted R-squared0.939100738407 S.D. dependent var268843.547629S.E. of regression66344.6078001 Akaike info criterion25.1837507579Sum squared resid48417676825.6 Schwarz criterion25.2706660437Log likelihood-161.694379926 F-statistic186.04672415Durbin-Watson stat0.797357493688 Prob(F-statistic)3.08626254192e-08表1.4 Y对X2作一元回归结果为Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 12:57Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-40511.649585118071.3637749-2.241759398450.0465575239032X20.4758389006480.018515276724825.69979956133.57600042588e-11R-squared0.983618268667 Mean dependent var346878.938462Adjusted R-squared0.982129020364 S.D. dependent var268843.547629S.E. of regression35939.6462136 Akaike info criterion23.957707856Sum squared resi5 Schwarz criterion24.0446231418Log likelihood-153.725101064 F-statistic660.479697489Durbin-Watson stat1.0835042218 Prob(F-statistic)3.57600042588e-11表1.5Y对X3作一元回归结果为Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 13:00Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-7517.420835828055.5219825-0.2679479939990.793697293481X31.839976720840.11861615451115.51202471898.00038995487e-09R-squared0.956283790051 Mean dependent var346878.938462Adjusted R-squared0.952309589147 S.D. dependent var268843.547629S.E. of regression58710.414916 Akaike info criterion24.9392600555Sum squared resid37916041015.7 Schwarz criterion25.0261753413Log likelihood-160.105190361 F-statistic240.62291088Durbin-Watson stat1.68902945844 Prob(F-statistic)8.00038995487e-09表1.6 Y对X4作一元回归结果为Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 13:01Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-50195.362222439.4336248-2.236926432250.0469533900268X4453.09695027421.541606416221.0335729623.11060649775e-10R-squared0.97573946077 Mean dependent var346878.938462Adjusted R-squared0.973533957203 S.D. dependent var268843.547629S.E. of regression43736.5097762 Akaike info criterion24.3503922156Sum squared resid21041705161.4 Schwarz criterion24.4373075013Log likelihood-156.277549401 F-statistic442.411191548Durbin-Watson stat0.982374650174 Prob(F-statistic)3.11060649775e-10其中，经过分析对比可知，加入X2的方程修正后的R最大。5、所以以X2为基础，顺次加入其他变量逐步回归。结果如下：表1.7 在x2基础上加入x1进行回归Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 13:09Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C204553.2426148777.18784684.193625168640.00184729276796X20.9108380169010.085373343017810.66888076198.75409780575e-07X1-48.57838793369.46592242723-5.131923307750.000442933959656R-squared0.995491676512 Mean dependent var346878.938462Adjusted R-squared0.994590011814 S.D. dependent var268843.547629S.E. of regression19774.1478044 Akaike info criterion22.8213125913Sum squared resid3910169213.9 Schwarz criterion22.9516855199Log likelihood-145.338531843 F-statistic1104.05972322Durbin-Watson stat2.65113179108 Prob(F-statistic)1.86241025059e-12表1.8 在x2基础上加入x3进行回归Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 13:10Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-41983.386563919824.6699784-2.117734449540.0602529241314X20.5057111307840.1232094248754.104484143930.00212924945374X3-0.1186230333650.483188079361-0.2455007448060.811033716886R-squared0.983716410861 Mean dependent var346878.938462Adjusted R-squared0.980459693033 S.D. dependent var268843.547629S.E. of regression37580.7383668 Akaike info criterion24.1055450384Sum squared resiSchwarz criterion24.235917967Log likelihood-153.686042749 F-statistic302.057612259Durbin-Watson stat1.01218006854 Prob(F-statistic)1-09表1.9 在x2基础上加入x4进行回归Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 13:11Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-37094.343586719955.6443339-1.858839682950.0926913486261X20.6078834735480.2672731959892.274389960050.0462244362187X4-126.566814045255.524743513-0.4953211665730.631076341416R-squared0.984010558514 Mean dependent var346878.938462Adjusted R-squared0.980812670217 S.D. dependent var268843.547629S.E. of regression37239.761226 Akaike info criterion24.0873158363Sum squared resi7 Schwarz criterion24.2176887649Log likelihood-153.567552936 F-statistic307.70635715Durbin-Watson stat1Prob(F-statistic)1.04512074949e-09 在X2的基础上加入X1后方程R修正=0.9946，改进最大，而且各参数的t检验显著，选择保留。在X2的基础上加入X3、X4后，虽然R有改进，但是参数的t检验不显著，应给予剔除。从相关系数也可以看出，X3、X4与其他变量高度相关，这说明主要是X3、X4引起了多重共线性，予以剔除。 6、模型中，解释变量保留X1、X2，进行最小二乘计算结果见表1.9Dependent Variable: YMethod: Least SquaresDate: 12/18/11 Time: 13:26Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C204553.2426148777.18784684.193625168640.00184729276796X1-48.57838793369.46592242723-5.131923307750.000442933959656X20.9108380169010.085373343017810.66888076198.75409780575e-07R-squared0.995491676512 Mean dependent var346878.938462Adjusted R-squared0.994590011814 S.D. dependent var268843.547629S.E. of regression19774.1478044 Akaike info criterion22.8213125913Sum squared resid3910169213.9 Schwarz criterion22.9516855199Log likelihood-145.338531843 F-statistic1104.05972322Durbin-Watson stat2.65113179108 Prob(F-statistic)1.86241025059e-121）经济意义检验。从回归结果可以看出，随着民用汽车数量的增加，机动车辆保险保费的收入也在逐年的增加。因为X1前面的系数为负数表明随着城镇居民可支配收入的增加，机动车辆保险保费的收入会减少，呈负相关，因为机动车辆保险中交强险和三者险有一定的强制性，是政府要求必须缴纳的保险，而城镇居民可支配收入是在扣除了国家税法及有关规定必须缴纳的费用之后居民可以自由支配的收入，所以两者呈一定的负相关。2） 统计推断检验。从回归结果看，可决系数R=0.9955，模型的拟合优度较；系数显著性检验：给定=0.05，查t分布表，在自由度为n-3=10时得临界值2.228,由于各解释变量系数的t值均大于临界值，所以城镇居民可支配收入与民用汽车数量对机动车辆保险保费收入有显著影响。3） 计量经济学检验。给定显著性水平0.05，查DW表，当n=13,k=2时，得下限临界值dl=0.861,得下限临界值du=1.562，因为DW统计量为2.651处于du4du范围内，根据判定区域知不存在自相关。7、作异方差的white检验如表2.1所示。White Heteroskedasticity Test:F-statistic3.37272409523 Probability0.0674174525869Obs*R-squared8.16074163885 Probability0.0858643490596Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/18/11 Time: 14:15Sample: 1998 2010Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C1274101266.341873748717.520.6799744567820.515711238543X1-342273.254771481115.834759-0.7114154846760.497043286886X1227.72836938414.97089487741.852151765880.101142067563X2-160.8629040954683.51119692-0.03434664663560.973442244986X22-0.001567260406940.00122250820449-1.282003998990.235742984573R-squared0.627749356835 Mean dependent var300782247.223Adjusted R-squared0.441624035252 S.D. dependent var389351733.324S.E. of regression290941363.854 Akaike info