城镇居民住房面积的多因素分析

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1、 城镇居民住房面积的多因素分析内容摘要：本文根据目前房地产业现状，从计量经济学的角度来验证一下居民收入水平、物价水平、国内GNP以及房地产销售价格等因素对其的影响程度。从回归结果看出，平均货币工资与居民住房面积之间存在正向的线性关系，同时我们也发现了一些问题，值得深入思考。关键词 城镇居民住房销售总面积 职工平均货币工资 多因素分析 城镇居民价格消费指数 检验一. 经济背景去年中国房地产投资超过亿万元，占固定资产投资的，直接拉动增长个百分点。年房地产投资和消费仍将保持一定的增长。专家预测，到年，中国城市化水平将提高到，城镇人口将达到亿以上，按人均需住房平方米计算，仅城镇新增人口每年就需增亿平方

2、米以上，房地产业在国民经济和社会发展中的重要地位将逐渐突出。房地产市场的发展，不仅可以推动经济的发展，而且可以从增加投资的消费，增加就业多方面拉动国内的需求。 近年来部分城市房价涨得过快、房价过高，已是一个不争的事实，房地产不合理增长带来的一系列负面影响，不少专家学者直言，这种市场态势会造成两种后果：一是房地产市场的泡沫可能不断扩大，市场风险进一步积累；二是相当多的中低收入者缺乏“小康水平住房”的现实购买力。由此可见，住房问题已经成为我国市场经济发展过程中的一个重要问题。在此，我们将从计量经济学的角度进行研究。二. 结合经济背景，建立计量经济学模型 关于数据：数据的来源 附表1YX1X2X3X

3、419912745.17234021662.5103.4148719923812.21271126651.9106.4151919936035.19337134560.5114.7153419946118.03453846670124.1162419956787.03550057494.9117.1167619966898.46621066850.5108.3172919977864.3647073142.7102.81790199810827.1747976967.299.21854199912997.87834680579.498.61857200016570.28937188254100

4、.41948200119938.311087095727.9100.72017200223702.3112422103935.3100.42092200329778.8514040116603.2100.82197 关于模型建立模型 ：Y=C+1X1+2X2+3X3+4X4+U其中Y代表我国城镇居民住房销售总面积（单位；万平方米），X1代表职工平均货币工资（单位：元）X2代表国民生产总值（单位：亿元）X3代表城镇居民价格消费指数X4代表城镇住房平均销售价格（单位：元/平方米）参数估计Dependent Variable: YMethod: Least SquaresDate: 06/02/05

5、 Time: 10:08Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-35148.1233827.53-1.0390390.3292X13.5460610.9739953.6407400.0066X2-0.3368810.075928-4.4368660.0022X341.0693252.895110.7764300.4598X422.3727022.601780.9898650.3512R-squared0.990517 Mean dependent var1

6、1851.93Adjusted R-squared0.985775 S.D. dependent var8327.641S.E. of regression993.2348 Akaike info criterion16.92353Sum squared resid7892124. Schwarz criterion17.14082Log likelihood-105.0030 F-statistic208.8926Durbin-Watson stat2.226441 Prob(F-statistic)0.000000模型检验：经济意义的检验：从经济意义上来说，居民住房购买面积会随着居民平均工

7、资以及国民生产总值的增加而增加，而与城镇居民价格消费指数、城镇住房平均销售价格呈反向关系。从上表可以看出X2、X3和X4的参数符号与其经济意义不符，估计是因为变量间存在多重共线性或者是与被解释变量不存在线性关系。统计推断检验：从回归结果可以看出，R2=0.990517，模型的拟合程度非常好，F统计量的值在给定显著性水平=0.05下也比较显著，但是X3和X4的t统计值均不显著，说明X3和X4这两个变量对Y的影响不显著，或者变量之间存在多重共线的影响使其t值不显著。计量经济学意义检验多重共线性检验由于F=208.8926F0.05(3,9)=3.86(显著性水平=0.05)表明模型从整体上看房屋购

8、买量与4个解释变量之间线性关系显著。对X1、X2、X3、X4、进行简单相关系数矩阵检验。解释变量相关系数矩阵：X1X2X3X4X1 1.000000 0.980746-0.553860 0.995352X2 0.980746 1.000000-0.551752 0.989377X3-0.553860-0.551752 1.000000-0.587315X4 0.995352 0.989377-0.587315 1.000000由此可见，一些解释变量之间存在高度线性相关。尽管整体线性回归拟合较好，但x3,x4变量的参数t值并不显著而且x2,x3,x4符号与经济意义相悖，表明模型中解释变量确实存在

9、严重的多重共线性。多重共线性的修正：采用逐步回归法对多重共线性进行补救。运用OLS方法逐一求Y对各解释变量的回归，回归结果如下Dependent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:32Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-3997.5121209.775-3.3043430.0070X12.1997140.15063914.602530.0000R-squared0.95094

10、4 Mean dependent var11851.93Adjusted R-squared0.946484 S.D. dependent var8327.641S.E. of regression1926.469 Akaike info criterion18.10540Sum squared resid40824123 Schwarz criterion18.19232Log likelihood-115.6851 F-statistic213.2338Durbin-Watson stat0.490032 Prob(F-statistic)0.000000Dependent Variabl

11、e: YMethod: Least SquaresDate: 06/02/05 Time: 10:33Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-5711.7442477.187-2.3057380.0416X20.2568080.0334157.6853530.0000R-squared0.843002 Mean dependent var11851.93Adjusted R-squared0.828730 S.D. dependent var8327.64

12、1S.E. of regression3446.380 Akaike info criterion19.26867Sum squared resid1.31E+08 Schwarz criterion19.35559Log likelihood-123.2464 F-statistic59.06465Durbin-Watson stat0.307835 Prob(F-statistic)0.000010Dependent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:35Sample: 1991 2003Included obs

13、ervations: 13VariableCoefficientStd. Errort-StatisticProb. C69679.0928384.812.4548020.0320X3-545.9751267.2926-2.0426120.0658R-squared0.274993 Mean dependent var11851.93Adjusted R-squared0.209083 S.D. dependent var8327.641S.E. of regression7406.063 Akaike info criterion20.79862Sum squared resid6.03E+

14、08 Schwarz criterion20.88554Log likelihood-133.1911 F-statistic4.172265Durbin-Watson stat0.342184 Prob(F-statistic)0.065808Dependent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:35Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-51348.255674.731-9.

15、0485790.0000X435.225623.13984711.218900.0000R-squared0.919628 Mean dependent var11851.93Adjusted R-squared0.912321 S.D. dependent var8327.641S.E. of regression2465.861 Akaike info criterion18.59911Sum squared resid66885173 Schwarz criterion18.68602Log likelihood-118.8942 F-statistic125.8636Durbin-Wa

16、tson stat0.462493 Prob(F-statistic)0.000000从回归的结果可以看出居民可支配收入(X1)的t值最大，线形关系强，拟合程度最好，因此把X1作为基本变量。然后将其余解释变量逐一代入X1的回归方程，重新回归。Dependent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:39Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-799.9123798.5133-1.00

17、17520.3401X14.4178440.37816911.682180.0000X2-0.2804370.046891-5.9805900.0001R-squared0.989281 Mean dependent var11851.93Adjusted R-squared0.987138 S.D. dependent var8327.641S.E. of regression944.4523 Akaike info criterion16.73826Sum squared resid8919902. Schwarz criterion16.86863Log likelihood-105.7

18、987 F-statistic461.4823Dependent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:39Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-6699.90410076.73-0.6648890.5212X12.2280200.18906511.784390.0000X323.5889987.264060.2703170.7924R-squared0.951300 Mean d

19、ependent var11851.93Adjusted R-squared0.941560 S.D. dependent var8327.641S.E. of regression2013.156 Akaike info criterion18.25197Sum squared resid40527979 Schwarz criterion18.38234Log likelihood-115.6378 F-statistic97.66923Dependent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:40Sample: 1

20、991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C58508.1130303.241.9307540.0823X15.0219701.3737973.6555390.0044X4-46.1725322.37106-2.0639400.0660R-squared0.965599 Mean dependent var11851.93Adjusted R-squared0.958718 S.D. dependent var8327.641S.E. of regression1692.002

21、Akaike info criterion17.90439Sum squared resid28628718 Schwarz criterion18.03476Log likelihood-113.3785 F-statistic140.3427Durbin-Watson stat1.202075 Prob(F-statistic)0.000000逐步回归，将其余变量逐一代入方程（1），重新回归。经分析，引入其他变量后各个方程的调整后可决系数都小于方程（1）中的调整后可决系数。决定将模型设定为 Y = -3997.512 + 2.199714*X1 （1）（-3.304343） （14.602

22、53）R2=0.950944 S.E.=1926.469 F=213.2338异方差检验ARCH检验ARCH Test:F-statistic0.387387 Probability0.766491Obs*R-squared1.622639 Probability0.654268Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/02/05 Time: 13:11Sample(adjusted): 1994 2003Included observations: 10 after adjusting endp

23、ointsVariableCoefficientStd. Errort-StatisticProb. C4061731.2432027.1.6701020.1459RESID2(-1)0.1340250.4399280.3046510.7709RESID2(-2)-0.4461170.455407-0.9796000.3651RESID2(-3)-0.0887620.481546-0.1843260.8598R-squared0.162264 Mean dependent var2801902.Adjusted R-squared-0.256604 S.D. dependent var3247

24、199.S.E. of regression3640057. Akaike info criterion33.34207Sum squared resid7.95E+13 Schwarz criterion33.46311Log likelihood-162.7104 F-statistic0.387387Durbin-Watson stat1.386823 Prob(F-statistic)0.766491从ARCH检验结果可以看到，obs*R-squared=1.622639小于临界值7.81473，所以不能拒绝原假设，认为模型不存在异方差。White 检验White Heterosked

25、asticity Test:F-statistic0.519846 Probability0.609839Obs*R-squared1.224309 Probability0.542182Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/02/05 Time: 13:12Sample: 1991 2003Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C7020943.4048742.1.7341050.1136

26、X1-1174.9911152.631-1.0193990.3320X120.0710970.0710561.0005760.3406R-squared0.094178 Mean dependent var3140317.Adjusted R-squared-0.086987 S.D. dependent var3030958.S.E. of regression3160037. Akaike info criterion32.96924Sum squared resid9.99E+13 Schwarz criterion33.09961Log likelihood-211.3001 F-st

27、atistic0.519846Durbin-Watson stat1.636334 Prob(F-statistic)0.609839从WHITE检验看到Obs*R-squared=1.224309小于临界值11.0705，仍然认为不存在异方差 自相关性检验DW =0.49003170883,dL=1.010 ,dU=1.340, DWdL,存在自相关, 其原因可能是由居民对住房的消费不止与本期收入有关，而且还与前几期的收入有关，即解释变量对被解释变量的影响具有时滞性。利用对数变换和C-O迭代法修正，结果如下：Dependent Variable: DLNYMethod: Least Squa

28、resDate: 06/02/05 Time: 13:03Sample(adjusted): 1993 2003Included observations: 11 after adjusting endpointsConvergence achieved after 4 iterationsVariableCoefficientStd. Errort-StatisticProb. C-1.8470741.689093-1.0935300.3060DLNX11.4080240.3242584.3422880.0025AR(1)0.3604820.2918321.2352390.2518R-squ

29、ared0.857570 Mean dependent var5.416006Adjusted R-squared0.821962 S.D. dependent var0.345570S.E. of regression0.145811 Akaike info criterion-0.786004Sum squared resid0.170088 Schwarz criterion-0.677487Log likelihood7.323021 F-statistic24.08393Durbin-Watson stat2.025797 Prob(F-statistic)0.000412Inver

30、ted AR Roots .36此时 dU=1.340DW=1.3508124-dU=2.660,修正后模型随机误差项不存在自相关性。总结及经济意义解释经过以上计量经济学检验，本小组得出方程（2）如下：LY = -1.14463915 + 1.182378793*LX1 （2）t= (-0.441850) (4.174130)R2=0.952100 F=89.44578 DW=1.350812本模型的经济意义可解释为：城镇职工平均货币工资每增长1%，城镇居民住房购买总面积平均增长1.1824%。由此说明，城镇职工的住房购买面积的需求主要取决于其平均工资的多少，而住房价格对居民住房购买面积的影响不太显著。这是因为住房属于耐用品，住房的消费是一个长期的过程，因此可以认为短期内消费者对住房的消费受价格影响很小。此外，GNP这一变量对住房消费的影响也不易确定。