中国房屋平均销售价格的影响因素分析

1、计 模量 型经 设济 计中国房屋平均销售价格影响因素分 二O一O年五月中国房屋平均销售价格影响因素分析一、前言作为国家的支柱产业,房地产业的稳定与发展关乎国计民生。从1998年开始,我国房地产业进入了新一轮快速发展期,尤其是近几年来房地产行业持续保持高速发展,房地产投资和房地产价格持续上涨。虽然从全国总体来看,房地产市场保持健康、快速发展态势,供求基本平衡,但部分地区仍然存在房价上涨过快、住宅供给结构不合理等问题。要解决这些问题,使中国房地产市场保持持续健康发展,国家的宏观经济政策对房地产价格的调节作用显得非常重要。而要进行有效调控,得首先识别在各种因素中,到底哪些因素能对房地产价格有影响,哪

2、些因素对房地产价格的影响力强,哪些对房地产价格的影响力稍弱等问题。在作此报告前，我查阅了一些资料，其中，在一本学术周刊新财经上，看到了一篇影响中国房价的主要因素的文章，但该文章并没有对这些影响因素进行具体数学上的分析。因此我想看看这些影响因素是怎样影响房价的。所以做了此计量报告，来研究中国自改革开放以来房屋平均销售价格和其影响因素之间具体的关系。二、理论背景20世纪90年代以后，各国学者就开始采用宏观经济模型来研究房价的变化，他们得出宏观经济变量在一定程度上可以解释房价波动的结论，例如：Evans指出土地利用规划以及其他方面的供给限制，会体现在地价的不断上涨，从而推进房价的提高。乔志敏用实证分

3、析表明生产成本的波动对房地产价格的波动有较强作用；张红、潘琦、郑思奇对北京市商品住宅市场进行回归分析，说明住宅实际建造成本和实际生产总值对住宅价格有着显著的影响；谢叙祎发现在短期内房价和地价相互影响，而长期内房价决定地价，并证明依靠降低地价来控制房价上涨的做法是不可行的。归纳他们的研究，从供给和需求出发，影响住宅价格的因素有：房地产投资、成本、失业率、人均收入、住宅区绿化率等。 其中我认为，对房屋平均销售价格影响较为显著的因素有竣工房屋造价、建成区绿化覆盖率、居民消费价格指数、职工年平均工资、登记失业率。而竣工房屋造价、建成区绿化覆盖率、居民消费价格指数是影响房屋平均销售价格的最主要因素。因此

4、，以下我对此展开了计量经济学模型分析。三、模型的选择与建立本模型是通过对1978年到2007年的房地产平均价格及其影响因素的定量数据进行分析，来研究其之间的关系。1.模型包含的变量。被解释变量为房屋平均销售价格，解释变量为竣工房屋造价、建成区绿化覆盖率、职工平均工资、登记失业率和居民消费价格指数。2.模型的数学形式。初步确定被解释变量与解释变量之间的数学关系式为：Y=0+1X1+2X2+3X3+4X4+5X5+解释变量有5个，0为常数项，为随机误差项，描述变量外的因素对模型的干扰。其中解释变量分别为：Y：房屋平均销售价格；X1：竣工房屋造价；X2：建成区绿化覆盖率；X3：职工共平均工资；X4：

5、登记失业率；X5：居民消费价格指数四、数据的来源与分析1、数据来源：国家统计局网站年度数据 天津财经大学图书馆中国统计年鉴2、所需数据：变量YX1X2X3X4X5年份房屋平均销售价格竣工房屋造价建成区绿化覆盖率职工年平均工资登记失业率居民消费价格指数197816610414.26155.3100197918311314.86685.4101.91980201123157624.9109.5198121613915.37723.8112.2198224514715.57983.2114.4198327016515.98262.3116.7198429818716.29741.9119.91985

6、32420516.411481.8134.2198635523116.913292143.6198740827017.114592156.219885033011717472188.5198957336717.819352.6219.2199070341319.221402.5222199178643720.123402.3233.319929955122127112.3253.41993129163221.333712.6294.21994140979122.145382.8367.81995159191123.955002.9429.619961806111124.4362103467.4

7、19971997117525.5364703.1481.919982063121826.5674793.147819992053115227.5883463.1471.320002112113928.1593713.1473.220012170112828.38108703.6476.520022250118429.75124224472.720032359127331.15140404.3478.420042778140231.66160244.2497.120053168145133.9183644.250620063367156435.1210014.1513.6200738641657

8、35.3249324538.320083890179537.4292294.2570.1注：1、房屋平均销售价格单位：元；竣工房屋造价单位：元；建成区绿化覆盖率：%；职工年平均工资：元；登记失业率：%。2、由于改革开放初期国家实行单位分房制，并无房屋销售价格，所以前几期数据是由本人按规律推写出来的；3、居民消费价格指数均是以1978年为基期计算的。3、变量间相关系数表1.000000 0.985728 0.990310 0.962989 0.310562 0.948192 0.985728 1.000000 0.983599 0.914539 0.273185 0.984957 0.99031

9、0 0.983599 1.000000 0.954206 0.289958 0.951884 0.962989 0.914539 0.954206 1.000000 0.396207 0.840497 0.310562 0.273185 0.289958 0.396207 1.000000 0.216094 0.948192 0.984957 0.951884 0.840497 0.216094 1.0000004、样本数据的散点图050010001500200001000200030004000YX1五、模型的估计与分析1、模型的回归分析（1）五元回归：t0.025 (24)=2.064 F

10、0.05 (5，24)=2.62VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C114.29990.3717970.7133959.34500.993984否X11.3389092.8933830.0080X2-3.578603-0.1682380.8678X30.0648064.0277820.0005X4-19.41561-1.0748440.2931X50.0347390.0304670.9759（2）四元回归：t0.025 (25)=2.060 F0.05 (4，25)=2.76Var

11、iableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C113.38260.3782300.70851249.0990.994225否X11.3517867.3214870.0000X2-3.369396-0.1708110.8657X30.0644136.8282970.0000X4-19.36032-1.0994260.2821VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-28.20427-0.10

12、13710.92011191.4910.993947否X11.3557682.9224370.0073X22.7540790.1343310.8942X30.0589593.8816310.0007X5-0.088386-0.0776700.9387VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-112.9568-0.3339780.7412924.48770.992210否X2-0.059381-0.0024570.9981X30.0936666.5200750.0000X4-21.187

13、14-1.0313450.3123X53.0479155.7687540.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C64.949410.7201340.47811247.6680.994218否X11.3344582.9463150.0069X30.0629335.5246830.0000X4-18.57386-1.0915370.2854X5-0.027187-0.0256970.9797VariableCoefficientt-StatisticProb. F-statist

14、icAdjusted R-squared是否通过T-F检验C-584.9202-1.8175040.0811742.81180.990321否X12.4944015.4160370.0000X355.685202.8579070.0085X45.1818840.2403100.8120X5-3.644913-4.2117390.0003（2）三元回归：t0.025 (26)=2.056 F0.05 (3，26)=2.98VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-26.88977-0.0

15、987320.92211651.8010.994178否X11.3227967.2097890.0000X22.2627150.1183090.9067X30.0599267.0181800.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-1557.951-5.4235890.0000598.91960.984090否X10.7731512.8397110.0087X299.631324.7224270.0001X432.664941.2396420.2262VariableCoef

16、ficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-560.9879-1.8672660.07321027.6390.990672是X12.5207345.7400080.0000X255.388102.9014590.0075X5-3.707847-4.5789620.0001VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-1754.699-6.4132580.0000544.97770.982540否X2128.

17、54309.2056820.0000X30.0327142.2449360.0335X4-0.947246-0.0312580.9753VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-271.7684-0.9013950.37571229.2850.992191否X26.9074720.2973470.7686X30.0876766.6646740.0000X52.9548515.6690690.0000VariableCoefficientt-StatisticProb. F-statis

18、ticAdjusted R-squared是否通过T-F检验C-2214.883-13.437740.0000469.26130.979774否X2146.199310.095730.0000X432.969201.0889280.2862X50.5142420.8914830.3808VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-113.7658-1.4975440.14631281.9560.992510否X30.09363417.873230.0000X4-21.17303-1.09

19、47100.2837X53.04671815.236840.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C63.230211.0660940.29621730.0540.994440否X11.32298117.938600.0000X30.06318110.593550.0000X4-18.57917-1.1135390.2757VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C7.7

20、817980.1055930.91671651.0030.994176否X11.3600882.9959370.0059X30.0603085.3964880.0000X5-0.041218-0.0388190.9693VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C284.77342.4076500.0234774.24950.987653否X13.62335313.548350.0000X41.2716230.0523180.9587X5-4.969380-6.0199280.0000（2

21、）二元回归：t0.025 (27)=2.052 F0.05 (2，27)=3.35VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-1508.463-5.2508360.0000880.11590.983774是X10.7496542.7330740.0109X2102.83504.8631670.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C5.1501730.1815970.85

22、732571.6060.994391是X11.34269718.671630.0000X30.06068310.932730.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-263.2276-2.2957420.0297495.95280.971538否X12.03620629.893700.0000X447.907961.3696440.1821VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过

23、T-F检验C289.52683.8958220.00061205.9140.988109是X13.62835714.803980.0000X5-4.983145-6.4897400.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-1759.704-8.0826680.0000848.87510.983186是X2128.68309.9150240.0000X30.0325242.5029250.0187VariableCoefficientt-StatisticProb. F-sta

24、tisticAdjusted R-squared是否通过T-F检验C-2315.565-19.361720.0000708.88360.979928否X2158.484735.755020.0000X427.455500.9298940.3607VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-2169.529-13.557510.0000698.49330.979635否X2150.640010.804020.0000X50.3859280.6811120.5016VariableCoeff

25、icientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C626.51113.4693120.0018188.97130.928385否X30.16084918.408870.0000X4-90.43376-1.5556840.1314VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-183.0323-4.3375690.00021908.3130.992455是X30.09130718.998630.0000X53.09816

26、315.882370.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-903.9548-4.0906990.0003137.80960.904170否X4119.04731.8826020.0706X56.05614115.698150.0000（2）二元回归：t0.025 (28)=2.048 F0.05 (1，28)=4.20VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-12

27、7.5502-2.1753350.0382959.99810.970648是X12.06169230.983840.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-2254.319-22.637500.00001423.7820.980025是X2159.679837.733040.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C369.87574.9114710.00003

28、57.39540.924753是X30.15546318.904900.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C278.29580.4286700.67142.9888350.064179否X4333.55941.7288250.0949VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通过T-F检验C-569.9175-4.1428110.0003249.41230.895462是X56.21

29、308615.792790.00002、选取较优的解释变量并拟定模型通过以上对模型回归分析的T-F检验我们可以看到，对于由被解释变量Y（房屋平均销售价格）、解释变量X1（竣工房屋造价）、X2（建成区绿化覆盖率）、X5（居民消费价格指数）建立的模型进行检验可以看到，模型总体具有较显著的线性关系；并且由t简言之可以看出，每个解释变量与被解释变量之间有较强的线性关系。总上分析，选取Y、X1、X2、X5作为分析模型的解释变量。建立模型：Y=560.9879+2.520734X1+55.38810X23.707847X5+ei (1.867266)(5.740008) (2.901459) (4.578

30、962)R2= 0.9916 = 0.9906 D.W.=1.2203 F=1027.639解释变量的统计意义：当X2、X5保持不变时，X1每增加1个单位，Y平均增加2.520743个单位；当X1、X5保持不变时，X2每增加1个单位，Y平均增加55.38810个单位；当X1、X2保持不变时，X5每增加1个单位，Y平均减少3.707847个单位；解释变量的经济意义：在建成区绿化覆盖率和居民消费价格指数不变的情况下，竣工房屋造价每增加1元，房屋平均销售价格增加2.520743元；在竣工房屋造价和居民消费价格指数不变的情况下，建成区绿化覆盖率每增加1%，房屋平均销售价格增加0.553881元；在竣工

31、房屋造价和建成区绿化覆盖率不变的情况下，居民消费价格指数每增加1%，房屋平均销售价格减少0.037078元。3、异方差性检验（1）采用E-Q方法对X1进行异方差检验1)按照X1排序由于N=30，C=N/4=7.5，所以删除位于中间的8个数据，得到两个容量为11的子样本。对两个子样本分别作OLS回归，求各自的残差平方和RSS1和RSS2：子样本1（Sample: 1978 1988）：VariableCoefficientStd. Errort-StatisticProb. C-217.4636251.2783-0.8654290.4155X10.7851790.5142221.5269260.

32、1706X29.79539416.262260.6023390.5659X51.6428200.7909272.0770820.0764R-squared0.993115 Mean dependent var288.0909Adjusted R-squared0.990165 S.D. dependent var103.6074S.E. of regression10.27494 Akaike info criterion7.772581Sum squared resid739.0209 Schwarz criterion7.917270Log likelihood-38.74919 F-st

33、atistic336.5900Durbin-Watson stat1.324676 Prob(F-statistic)0.000000由上图知Y= -217.4636+ 0.785179X1 -9.795394X2+1.642820X5+ei(-0.865429)(1.526926) (-0.602339)(2.077082)R2= 0.993115 RSS1= 739.0209子样本2（Sample: 1997 2007）：VariableCoefficientStd. Errort-StatisticProb. C-9479.519889.9965-10.651190.0000X1-0.3

34、464540.377740-0.9171750.3896X286.327009.5005479.0865290.0000X520.173162.4811808.1304730.0001R-squared0.997387 Mean dependent var2561.909Adjusted R-squared0.996268 S.D. dependent var638.6818S.E. of regression39.01794 Akaike info criterion10.44121Sum squared resid10656.80 Schwarz criterion10.58590Log

35、likelihood-53.42664 F-statistic890.8060Durbin-Watson stat2.518796 Prob(F-statistic)0.000000由上图知Y= -9479.519-0.346454X1-86.32700X2+ 20.17316X5+ei(-10.65119)(- 0.917175)(9.086529)( 8.130473)R2= 0.997387 RSS1= 10656.80计算F统计量：F= RSS2/RSS1= 10656.80/739.0209=14.4201605 在5%的显著性水平下，自由度为（7，7）的F分布的临界值为F0.05

36、(7，7) =3.79，据此拒绝两组字样方差相同的假设，表明该总体随机干扰项存在单调递减型异方差。2)采用加权最小二乘法对原模型进行回归:VariableCoefficientStd. Errort-StatisticProb. CE-530.713551.16165-10.373270.0000X1E2.5166740.07044635.724890.0000X2E52.870384.56597211.579220.0000X5E-3.6199700.278083-13.017590.0000R-squared0.999956 Mean dependent var61.43356Adjust

37、ed R-squared0.999951 S.D. dependent var146.6126S.E. of regression1.022769 Akaike info criterion3.006471Sum squared resid27.19748 Schwarz criterion3.193297Log likelihood-41.09706 Durbin-Watson stat1.474623Y=-530.7135CE+2.516674X1E+52.87038X2E-3.619970X5E+ei(-10.37327) (35.72489) (11.57922) (-13.01759

38、)Adjusted R-squared=0.999951 Durbin-Watson stat=1.474623（2）对加权后的模型进行异方差检验：1）按照X1E排序：由于N=30，C=N/4=7.5，所以删除位于中间的8个数据，得到两个容量为11的子样本。对两个子样本分别作OLS回归，求各自的残差平方和RSS1和RSS2：子样本1（Sample: 1978 1988）：VariableCoefficientStd. Errort-StatisticProb. CE1372.867587.52852.3366820.0521X1E4.5272040.8869025.1045170.0014X2

39、E-88.1393139.72235-2.2188850.0620X5E-3.9058561.554246-2.5130230.0402R-squared0.956472 Mean dependent var7.292641Adjusted R-squared0.937817 S.D. dependent var2.779201S.E. of regression0.693038 Akaike info criterion2.379822Sum squared resid3.362107 Schwarz criterion2.524512Log likelihood-9.089023 Durb

40、in-Watson stat1.802052Y= 1372.867+ 4.527204X1 -88.13931X2-3.905856X5 (2.336682) (5.104517) (-2.218885) (-2.513023)R2=0.956472 RSS1=3.362107子样本2（Sample: 1997 2007）：VariableCoefficientStd. Errort-StatisticProb. CE-571.327056.24636-10.157580.0000X1E2.5683740.07687733.408950.0000X2E57.177565.11093811.18

41、7290.0000X5E-3.9150880.316096-12.385740.0000R-squared0.999984 Mean dependent var147.3203Adjusted R-squared0.999977 S.D. dependent var222.3401S.E. of regression1.065446 Akaike info criterion3.239951Sum squared resid7.946220 Schwarz criterion3.384640Log likelihood-13.81973 Durbin-Watson stat1.007639Y=

42、 -571.3270+2.568374X1+57.17756X2-3.915088X5 (-10.15758)( 33.40895) (11.18729) (-12.38574)R2= 0.999984 RSS1= 7.946220由上有F= RSS2/RSS1= 7.946220/3.362107=2.363464 F0.05 (7，7) =3.79, 据此我们可以认为加权后的模型已经消除了异方差。2）按照X2E排序：由于N=30，C=N/4=7.5，所以删除位于中间的8个数据，得到两个容量为11的子样本。对两个子样本分别作OLS回归，求各自的残差平方和RSS1和RSS2：子样本1（Samp

43、le: 1978 1988）：RSS2= 7.997950子样本2（Sample: 2006:1 2008:4）：RSS1= 8.157957计算F统计量：F= RSS2/RSS1=8.157957/ 7.997950=1.02在5%的显著性水平下，自由度为（7,7）的F分布的临界值为F0.05 ( 7,7) =3.79，据此我们可以认为加权后的模型已经消除了异方差。3）按照X5E排序：由于N=30，C=N/4=7.5，所以删除位于中间的8个数据，得到两个容量为11的子样本。对两个子样本分别作OLS回归，求各自的残差平方和RSS1和RSS2：子样本1（Sample:1978 1988）：RSS

44、2=8.056220子样本2（Sample: 1997 2007）：RSS1=7.946220计算F统计量：F= RSS2/RSS1=7.946220/8.056220=0.986345在5%的显著性水平下，自由度为（7,7）的F分布的临界值为F0.05 (7,7) =3.79，据此我们可以认为加权后的模型已经消除了异方差。4、自相关性检验现在我们采用杜宾-瓦森检验法检验是否存在序列自相关：VariableCoefficientStd. Errort-StatisticProb. CE-530.713551.16165-10.373270.0000X1E2.5166740.07044635.7

45、24890.0000X2E52.870384.56597211.579220.0000X5E-3.6199700.278083-13.017590.0000R-squared0.999956 Mean dependent var61.43356Adjusted R-squared0.999951 S.D. dependent var146.6126S.E. of regression1.022769 Akaike info criterion3.006471Sum squared resid27.19748 Schwarz criterion3.193297Log likelihood-41.

46、09706 Durbin-Watson stat1.474623DW = =1.474623由课本378页D.W.检验上下表可知，D.W.（30,4）的上界du=1.65,下界dl=1.21。当D.W.在（0,1.21）之间时，存在正自相关；在（1.21,1.65）之间时，不能确定是否存在自相关；在（1.65，2.35）之间时，无自相关；在（2.35,2.79）之间时，不能确定是否存在自相关；在（2.79，4）之间时，存在负自相关。而此模型中D.W.为1.474623，在（1.21,1.65）之间，可知，不能确定是否存在自相关。下面采用1阶广义差分法后E-views软件的输出结果：Variab

47、leCoefficientStd. Errort-StatisticProb. CE-513.110056.78305-9.0363220.0000X1E2.5156000.07628932.974530.0000X2E51.383145.2353059.8147380.0000X5E-3.5658850.325969-10.939350.0000AR(1)0.2870720.2083541.3778050.1810R-squared0.999960 Mean dependent var63.43539Adjusted R-squared0.999954 S.D. dependent var1

48、48.7899S.E. of regression1.012359 Akaike info criterion3.018029Sum squared resid24.59689 Schwarz criterion3.253769Log likelihood-38.76142 Durbin-Watson stat1.923739由上结果可知，采用1阶广义差分法后的模型为：Y=513.1100+2.515600X1+51.38314X23.565885X5+0.287072AR(1)+ei (-9.036322)（32.97453）(9.814738) (-10.93935) (1.377805) =0.999954 D.W.= 1.923739经检验，D.W.（29,4）的上界du=1.65,下界dl=1.20。当D.W.在（0,1.20）之间时，存在正自相关；在（1.20,