中國保費收入主要影響因素分析

中國保費收入主要影響因素分析一、研究的目的要求保險作為金融行業(yè)的四大支柱之一，同時也是國民經(jīng)濟的重要組成部分，其成長壯大對與國民經(jīng)濟的健康發(fā)展有重要意義。近年來，我國保費收入快速增長。但是我國的保險深度和保險密度還處于世界的低水平。同時，我國保險市場結構嚴重不均衡，區(qū)域化差異非常大。因此研究保費收入的影響因素，有利于研究保險業(yè)的發(fā)展空間，對保險業(yè)的發(fā)展以及宏觀經(jīng)濟的發(fā)展有重大的意義。二、模型設定及其估計通過分析，影響中國保費收入的主要因素有：1、總人口(grosspopulation)?用P表示，包括城鎮(zhèn)人口和農(nóng)村人口，將其引入模型用來反映人口數(shù)量對保費收入的影響。2、居民可支配收入(disposableincome),用I表示，它等于城鎮(zhèn)居民人均可支配收入*城鎮(zhèn)人口+農(nóng)村居民人均純收入*農(nóng)村人口。將其引入模型來反映居民的支付能力以及經(jīng)濟發(fā)展的整體水平，將其引入模型可以觀察收入對保費收入的影響。3、城鄉(xiāng)居民儲蓄存款余額(savingdepositbalanceofcitizenandcountryinhabitant)，用S表示，反映居民的儲蓄傾向和金融資源數(shù)量，將其引入模型可以觀察儲蓄對保險的替代和收入效應。為此設定了如下形式的計量經(jīng)濟學模型y二B+Bx+px+px+卩t121t32t43tt其中，Y為保費收入，x為城鄉(xiāng)居民儲蓄存款余額，x為總人口，x為234居民可支配收入數(shù)據(jù)收集如下：我國保費收入/億元城鄉(xiāng)居民儲蓄存款/億元總人口/萬人城鎮(zhèn)居民可支配收入/億元1993456.87127295.351185172577.41994376.41548321.271198503496.21995453.31799792.7712112142831996528.333311744.11223894838.91997772.709413724.71236265160.319981255.968715952.11247615425.119991406.171218078.212578658542000159819429.912674362802001210922117.71276276859.62002305426272.91284537702.82003388030949.11292278472.22004431834374.81299889421.62005493239755.113075610493

2006564044960.313144811759.52007703645813.613212913785.82008978454621.61328021578120091113765834.813347417175二、估計參數(shù)利用Eviews軟件，生成y、X、X、X等數(shù)據(jù)，采用這些數(shù)據(jù)對模型進

234行OLS回歸，結果如下：DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:13:53Sample:19932009Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C24880.216244.7693.9841680.0016X20.1207320.0415912.9028020.0123X3-0.2275360.051949-4.3800130.0007X40.5046230.1610223.1338770.0079R-squared0.990798Meandependentvar3455.164AdjustedR-squared0.988675S.D.dependentvar3330.401S.E.ofregression354.4213Akaikeinfocriterion14.78117Sumsquaredresid1632988.Schwarzcriterion14.97722Loglikelihood-121.6400F-statistic466.5920Durbin-Watsonstat1.206695Prob(F-statistic)0.000000Y=24880.21+0.120732X-0.227536X+0.504623Xt2t3t4t（6244.769）（0.041591）（0.051949）（0.161022）

t=（3.984168）（2.902802）（-4.380013）（3.133877）R2=0.990798R2=0.988675F=466.5920DW=1.206695經(jīng)濟意義檢驗。在假定其他條件不變的情況下，城鄉(xiāng)居民儲蓄存款余額每增長1億元，保費收入增長0.120732億元；居民可支配收入每增長1億元，保費收入增長0.504623億元。這與理論分析和經(jīng)驗判斷相一致。擬合優(yōu)度：從回歸的結果來看，R2=0.990798R2=0.988675，這說明模型對樣本的擬合很好。F檢驗：針對H:P=0=P=0,給定的顯著性水平a=0.05，在F分0234布表中查出自由度為k-1=3和n一k=12的臨界值F，由回歸結果中得到的aF明顯大于F,應拒絕原假設H0：P=0=P=0,說明回歸方程顯著，即“城a0234鄉(xiāng)居民儲蓄存款余額”、“總人口”“居民可支配收入”等變量聯(lián)合起來確實對“保費收入”有顯著影響。t檢驗：分別針對H:0=0(j=1,2,3,4),給定的顯著性水平a0j=0.05,在t分布表中查出自由度為n-k=12的臨界值t(n-k)=2.179。a/2由回歸結果中的數(shù)據(jù)可得，與6、P、P對應的t統(tǒng)計分別為3?984168、12342.902802、-4.380013、3.133877，其絕對值大于t(n-k)=2.179,這說明在顯著性水平a=0.05下,a/2分別都應當拒絕H:0=0(j=1,2,3,4),也就是說，當在其他解釋變量0j不變的情況下,解釋變量城鄉(xiāng)居民儲蓄存款余額”、“總人口”“居民可支配收入”分別對被解釋變量“保費收入”有顯著影響。三、多重共線性檢驗相關系數(shù)矩陣X2X3X4X21.0000000.9309230.991817X30.9309231.0000000.923753X40.9918170.9237531.000000由于關系系數(shù)矩陣可以看出,各解釋變量互相之間的相關系數(shù)較高,正席確實存在嚴重多重共線性。四、多重共線性修正采用逐步回歸的辦法，去檢驗和解決冬蟲共線性問題。分別作Y對X、X、23X的一元回歸,回歸結果如下,4DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:11Sample:19932009Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C-1717.426273.6313-6.2764240.0000X20.1874770.00844722.195610.0000R-squared0.970452Meandependent3455.164

varAdjustedR-squared0.968482S.D.dependentvar3330.401S.E.ofregression591.2570Akaikeinfocriterion15.71251Sumsquaredresid5243773.Schwarzcriterion15.81053Loglikelihood-131.5563F-statistic492.6452Durbin-Watsonstat0.739121Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:12Sample:19932009Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C-75756.7511334.35-6.6838180.0000X30.6238030.0892036.9931060.0000R-squared0.765271Meandependentvar3455.164AdjustedR-squared0.749623S.D.dependentvar3330.401S.E.ofregression1666.457Akaikeinfocriterion17.78492Sumsquaredresid41656170Schwarzcriterion17.88294Loglikelihood-149.1718F-statistic48.90353Durbin-Watsonstat0.245450Prob(F-statistic)0.000004DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:12Sample:19932009Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C-2800.139288.7317-9.6980660.0000X40.7630310.03137424.320470.0000R-squared0.975267Meandependentvar3455.164AdjustedR-squared0.973618S.D.dependentvar3330.401S.E.ofregression540.9366Akaikeinfocriterion15.53461Sumsquaredresid4389186.Schwarzcriterion15.63264Loglikelihood-130.0442F-statistic591.4853Durbin-Watsonstat0.703141Prob(F-statistic)0.000000對回歸結果進行整理，如下表一元回歸估計結果

變量X2X3X4參數(shù)估計值0.1874770.6238030.763031t統(tǒng)計量22.195616.99310624.32047R20.9704520.7652710.975267R20.9684820.7496230.973618其中，加入X的方程R2最大，以X為基礎，順次加入其他變量逐步回歸。44結果如下表所示。DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:18Sample:19932009Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C-2443.189434.1735-5.6272170.0001X40.4978570.2441322.0392950.0608X20.0658540.0601321.0951550.2919R-squared0.977219Meandependentvar3455.164AdjustedR-squared0.973965S.D.dependentvar3330.401S.E.ofregression537.3772Akaikeinfocriterion15.57006Sumsquaredresid4042840.Schwarzcriterion15.71710Loglikelihood-129.3455F-statistic300.2730Durbin-Watsonstat0.626973Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:18Sample:19932009Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C18830.197282.5122.5856720.0216X40.9453060.06640014.236620.0000X3-0.1821090.061281-2.9717090.0101R-squared0.984834Meandependentvar3455.164AdjustedR-squared0.982667S.D.dependentvar3330.401S.E.ofregression438.4590Akaikeinfocriterion15.16319Sumsquaredresid2691448.Schwarzcriterion15.31023Loglikelihood-125.8872F-statistic454.5566Durbin-Watsonstat0.957703Prob(F-statistic)0.000000

加入X時，R2有所提高，但t檢驗變得不顯著，應予以剔除。加入X，它23的系數(shù)與經(jīng)濟意義不符，也應予以剔除。所以只保留X。4最后修正嚴重多重共線性影響后的回歸結果為Y=-2800.139+0?763031Xt4(288?7317)(0.031374)t=(-9.698066)(24.32047)R2=0.975267R2=0.973618f=591.4853DW=0?703141這說明，當居民可支配收入每增長1億元，保費收入增長0?763031億元。五、異方差檢驗利用eviews繪制出e2對X的散點圖，圖如下，4aooao-0-IJ別?1-IJ茫］4QODOO-IJ20000-&-IJD050Q01Q0QQ1ED0-C20000由圖可以看出，殘差平方e2隨解釋變量X的變動呈增大趨勢，因此，模型4很有可能存在異方差。但是否確實存在異方差還應通過更進一步的檢驗。再進行white檢驗，回歸檢驗結果如下，WhiteHeteroskedasticityTest:F-statistic5.785741Probability0.014744Obs*R-squared7.692757Probability0.021357TestEquation:DependentVariable:RESIDA2Method:LeastSquares

Date:12/15/11Time:14:43Sample:19932009Ineludedobservations:17VariableCoefficientStd.Errort-StatisticProb.C1446298.390877.13.7001350.0024X4-307.892492.63325-3.3237790.0050X4A20.0157740.0046383.4014690.0043R-squared0.452515Meandependentvar258187.4AdjustedR-squared0.374303S.D.dependentvar407216.3S.E.ofregression322112.2Akaikeinfocriterion28.36197Sumsquaredresid1.45E+12Schwarzcriterion28.50901Loglikelihood-238.0768F-statistic5.785741Durbin-Watsonstat1.279220Prob(F-statistic)0.014744由上表可知，nR2=7.692757,在a=0.05下，查表得，臨界值為3.84146而nR2>3.84146，表明模型存在異方差。六、異方差修正：運用WLS估計法，經(jīng)估計檢驗發(fā)現(xiàn)用權數(shù)W3的效果最好，下面僅給出W3的結果；DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:57Sample:19932009Includedobservations:17Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.C-2312.455294.1171-7.8623600.0000X40.7035430.04091217.196560.0000WeightedStatisticsR-squared0.919536Meandependentvar2732.370AdjustedR-squared0.914172S.D.dependentvar2055.968S.E.ofregression602.3242Akaikeinfocriterion15.74960Sumsquaredresid5441916.Schwarzcriterion15.84762Loglikelihood-131.8716F-statistic171.4199Durbin-Watsonstat0.606286Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.969339Meandependentvar3455.164AdjustedR-squared0.967295S.D.dependentvar3330.401S.E.ofregression602.2839Sumsquaredresid5441188.Durbin-Watsonstat0.596653Y=-2312.455+0.703543xt4(294.1171.)(0.040912)t=(-7.862360)(17.19656)R2=0.969339R2=0.914172f=171.4199DW=0?606286可以看出運用加權最小二乘法消除了異方差后，參數(shù)的t檢驗均顯著,可決系數(shù)大幅提高，F(xiàn)檢驗也顯著。七、自相關檢驗DependentVariable:YMethod:LeastSquaresDate:12/15/11Time:14:12Sample:19932009Ineludedobservations:17VariableCoefficientStd.Errort-StatisticProb.C-2800.139288.7317-9.6980660.0000X40.7630310.03137424.320470.0000R-squared0.975267Meandependentvar3455.164AdjustedR-squared0.973618S.D.dependentvar3330.401S.E.ofregression540.9366Akaikeinfocriterion15.53461Sumsquaredresid4389186.Schwarzcriterion15.63264Loglikelihood-130.0442F-statistic591.4853Durbin-Watsonstat0.703141Prob(F-statistic)0.000000Y=-2800.139＋0.763031Xt4(288.7317)(0.031374)

t=(-9.698066)(24.32047)R2=0.975267R2=0.973618f=591.4853DW=0.703141對樣本量為17、一個解釋變量的模型、0.05顯著水平，查DW統(tǒng)計表可知，DL=1.133,D=1.381,模型中DW=0?703141VD，說明模型存在自相關。UL八、自相關修正：生成殘差序列e,使用e進行滯后一期的自回歸，回歸結果如下：DependentVariable:EMethod:LeastSquaresDate:12/15/11Time:15:18Sample(adjusted):19942009

Ineludedobservations:16afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.E(-1)0.6791250.2316852.9312450.0103R-squared0.356072Meandependentvar-59.75093AdjustedR-squared0.356072S.D.dependentvar545.8999S.E.ofregression438.0581Akaikeinfocriterion15.06304Sumsquaredresid2878424.Schwarzcriterion15.11133Loglikelihood-119.5043Durbin-Watsonstat0.946006對原模型進行廣義差分，再對廣義差分方程進行自回歸，回歸結果如下：Depen