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1、房地产企业的利润总额与其收入构成的相关性研究以2007年房地产企业营业数据为例一、数据选择本文选择的数据为2007年全国31个省、自治区和直辖市的截面数据，研究各省区房地产企业2007年的利润总额与其收入构成（商品房销售收入、房屋出租收入和土地转让收入）之间的相关性。表1.2007年中国31省区房地产企业营业利润与收入构成表地区经营总收入土地转让收商品房屋房屋出租营业(2007)入销售收入收入利润北京228799731034695204644798101622241125天津5595697236431495684240158527771河北465258332753454924478632949
2、64山西175534713018158924023475-48201内蒙古376620379413740967572286935辽宁876174068877857502020793471886林2399140023617511669070445黑龙江3224432503130882064450259512上海287629169341642363122717869895511776江苏2170207016301920929900619541921361浙江186776045600418186819655051972895安徽530582246854510276317277272033福建8118
3、966112461740100744425946495江西34755461979433003383995316988山东121544411299701163161963053999041河南609031545874593902914200583482湖北510895232707481057117629544947湖南5044767203876457954734215-1631广东32702297752014293145796075745498023广西353156871191340331916504191231海南1184764213921104830129097482重庆7494978906
4、84691671156993420912四川9780001114589908055835132659611贵州16710338652157616414690-49016云南308889257408296859726305142347西藏1702020162858704132212陕西276280574422698491511353444甘肃91943174758643142212027719青海305942196301373175714362宁夏861927355283897915698-3520新疆20209301140197273124446109486单位：万元数据来源：中国统计年鉴二、
5、模型构造现在，我们来分析各省区房地产企业营业利润受其收入构成的影响。首先，我们构造模型的回归方程：Profiti=CCq+aiSalei+a2Renti+aiLandi+i接下来，把相关数据输入EVieWs,用普通最小二乘法求解，得道样本回归方程：PROFIT=-247265.451472+0.131961941353*SALE+2.05919332068*RENT-1.03829711341*LANDDependentVariable:PROFITMethod:LeastSquaresDate:12/08/09Time:19:01Sample:131Includedobservations:
6、31CoefficientStd.Errort-StatisticProb.SALE0.1319620.0149758.8123150.0000RENT2.0591930.4130794.9849900.0000LAND-1.0382970.662320-1.5676680.1286C-247265.596291.37-2.5678880.0161R-squared0.934357Meandependentvar786003.8AdjustedR-squared0.927064S.D.dependentvar1392977.S.E.ofregression376197.8Akaikeinfoc
7、riterion28.63353Sumsquaredresid3.82E+12Schwarzcriterion28,81856Loglikelihood-439.8197Hannan-Quinncriter.28.69385F-statistic128.1057Durbin-Watsonstat2.003651Prob(F-Statistic)0.000000通过上图可以发现，回归方程的拟合度较好，D-W检验也很好，不存在一阶序列相关。但是土地转让收入的参数估计量的P值与t检验值都不显著，于是我们再来检验解释变量间的多重共线性：CovarianceAnalysis:OrdinaryDate:1
8、2/08/09Time:20:23Sample:131Includedobservations:31CovarianceCorrelationPROFITLANDSALESRENTPROFIT1.88E+121.000000LAND2.99E+116.83E+100.8350521.000000SALES9.39E+121.55E+125.56E+130.9188910.7952921.000000RENT4.01E+118.03E+101.78E+121.21E+110.8402160.8824520.6843751.000000通过上图可以看出，土地转让收入与商品房销售收入和房屋出租收入之
9、间存在近似共线性，于是结合上面的P值和t值检验，可以去掉引起共线性的变量“土地转让收入”，从而得到新的回归方程：Profiti=a0+aiSalei+a2Renti+i同样，把相关的数据输入EVieWs,用普通最小乘法得到样本回归方程为：PROFIT=-237492.569606+0.118864183784*SALE+1.56375792454*RENTDependentvariable:PROFITMethod:LeastSquaresDate:12/08/09Time:20:35Sample:131Includedobservations:31CoefficientStd.Errort-
10、StatisticProb.SALE0.1188640.0127479.3251410.0000RENT1.5637580.2728375.7314660.0000C-237492.698558.67-2.4096570.0228R-squared0.928382Meandependentvar786003.8AdjustedR-squared0.923267S.D.dependentvar1392977.SE.ofregression385865.3Akaikeinfocriterion28,65613Sumsquaredresid4.17E+12Schwarzcriterion28.794
11、90Loglikelihood-441.1700Hannan-Quinncriter.28.70137F-Statistic181.4824Durbin-Watsonstat1.979213Prob(F-Statistic)0.000000从上图可以看出，各参数估计量的P值和t检验值都很好，D-W检验也很漂亮地接近2,方程总体的拟合度也较佳，接下来异方差检验，这里我们采用的是怀特检验：HeteroskedasticityTest:WhiteF-Statistic372.7994Prob.F(5,25)0.0000Obs*R-squared30.58973Prob.Chi-Square(三)00
12、000ScaledexplainedSS102.6637Prob.Chi-Square(三)0000TestEquation:DependentVariable:RESID2Method:LeastSquaresDate:12/08/09Time:21:04Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.C1.85E+091.84E100.1004180.9208SALE-4551.0926628.202-0.6866260.4986SALE2-9.38E-050.000344-0.2730800.787
13、0SALE*RENT0.0868280.0216414.0122220.0005RENT1943309.410161.54.7379110.0001RENTa2-2.1778950.091214-23.876800.0000R-squared0.986765Meandependentvar1.34E+11AdjustedR-squared0.984119S.D.dependentvar3.92E+11S.E.ofregression4.94E+10Akaikeinfocriterion52.25696Sumsquaredresid6.10E+22Schwarzcriterion52.53451
14、Loglikelihood-803.9829Hannan-Quinnenter.52.34744F-Statistic372.7994Durbin-Watsonstat2.658628Prob(F-Statistic)0.000000可以发现，可决系数R-squared较大，RENT2的t-Statistic很大，说明存在着异方差。此时，采用加权最小二乘法（WLS）消除异方差，得到新的样本回归方程：PROFIT=-230904.740437+0.115787008878*SALE+1.67342327822*RENTDependentVariable:PROFITMethod:LeastSqu
15、aresDate:12/08/09Time:21:19Sample:131Includedobservations:31Weightingseries:WWhiteHeteroskedasticity-ConsistentStandardErrors&CovarianceCoefficientStd.Errort-StatisticProb.SALE0.1157870.000520222.79150.0000RENT1.6734230.014427115.99460.0000C-230904.71228.626-187.93740.0000WeightedStatisticsR-squared
16、0.995989Meandependentvar173771.6AdjustedR-squared.995702S.D.dependentvar398535.8SE.ofregression15976.76Akaikeinfocriterion22.28742Sumsquaredresid7.15E*09Schwarzcriterion22.42620Loglikelihood-342.4551Hannan-Quinncriter.22.33266F-StatiStic3476.101Durbin-Watsonstat2.141876Prob(F-Statistic)0.000000Unwei
17、ghtedStatisticsR-squared0.927963Meandependentvar786003.8AdjustedR-squared0.922817S.D.dependentvar1392977.S.E.ofregression386993.6Sumsquaredresid4.19E*12Durbin-Watsonstat1.956193经过加权最小二乘法后，样本回归方程的拟合优度得到改进。三、模型改进由于房地产企业营业利润中，商品房销售收入占了很大的比重，对营业利润起着最重要的贡献，而商品房的销售收入又与居民的储蓄存款、工资收入以及商品房自身的价格有很大的关系，所以，我们引进联
18、立方程的计量经济学模型。首先，我们先分析商品房销售收入与居民的储蓄存款、工费收入以及商品房自身的价格之间相关性，从而构建一个多元回归模型:Salei=o+iSavingi+2Wagei+3Pricei+ui表2.商品房销售收入的影响变量及数据地区(2007)商品房屋销售收入职工工资总额城乡居民储蓄存款(2006)商品房平均销售价格(元)北京20464479219427438703800011553天津49568426026534280740005811河北45492449732071801416002586山西15892407849588479618002250内蒙古3740967536588
19、7227135002247辽宁857502011027967770120003490吉林23617515287046310752002302黑龙江30882068841104437359002471上海2363122714372216872700008361江苏20929900180665111.22E+084024浙江18186819192422281.05E+085786安徽51027637089072407780002664福建74010079481296447810004684江西33003384994197315169002072山东11631619199263561.04E+082
20、904河南593902914313529736737002253湖北48105718712849510340003053湖南45795478708188476231002233广东29314579285498652.16E+085914广西34033195872155294621002539海南1104830144006779057004162重庆69167114998743294905002723四川908055810915972678772002840贵州15761644392457159687002137云南29685975664925285486002455西藏162858805584
21、.113980002704陕西26984916986137406760002622甘肃8643143881377182340002191青海301373112064440628002311宁夏838979150024358113002136新疆19727315332395203563002081单位：万元（除特殊说明外）数据来源：中国统计年鉴接下来，把相关数据输入EVieWs,用普通最小二乘法求解，得道样本回归方程：SALE=-4355862.5225-0.109288949438*WAGE+0.132932918743*SAVING+1560.93435094*PRICEDependentv
22、ariable:SALEMethod:LeastSquaresDate:12/08/09Time:21:53Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.WAGE-0.1092890.241056-0.4533760.6539SAVING0.1329330.0327614.0576510.0004PRICE1560.934268.72155.8087430.0000C-4355863.810662.0-5.3732160.0000R-squared0.920904Meandependentvar6969
23、099.AdjustedR-squared0.912116S.D.dependentvar7580093.SE.ofregression2247137.Akaikeinfocriterion32.20813Sumsquaredresid1.36E+14Schwarzcriterion32,39316Loglikelihood-495.2260Hannan-Quinnenter.32.26844F-statistic104.7863Durbin-Watsonstat1.178790Prob(F-Statistic)0.000000从上图不难看出，居民的工资收入的参数估计量的P值达到了0.6539
24、,t检验值夜很小，说明居民的工资收入对商品房销售收入的影响不显著，从而可以排除居民工资收入这个解释变量。所以，构建新的回归方程：Salej=用+lSavingj+yPricei+ui然后，利用普通最小二乘法（OLS）得到样本回归方程：SALE=-4379661.241070.118868600771*SAVING+1491.35939031*PRICEDependentvariable:SALEMethod:LeastSquaresDate:12/08/09Time:22:05Sample:131Includedobservations:31CoefficientStd.Errort-Stat
25、iSticProb.SAVINGPRICEC0.1188691491.359-4379661.0.01038311.44787217.44126.858677797401.8-5.4924150.00000.00000.0000R-squared0.920302Meandependentvar6969099.AdjustedR-squared0.914609S.D.dependentvar7580093.S.E.ofregression2215029.Akaikeinfocriterion32.15119Sumsquaredresid1.37E+14Schwarzcriterion32.289
26、97Loglikelihood-495.3435Hannan-Quinnenter.32.19643F-Statistic161.6635Durbin-Watsonstat1.170001Prob(F-Statistic)0.000000可以看出，改进后的样本回归方程的参数估计量的P值和t检验都得到通过,拟合优度也较好，只是D-W值不理想,但是这并不影响回归方程选择的有效性。所以，通过以上的检验过程，我们可以得到联立方程的计量经济学模型：Profiti=a0+alSalei+a1RentiiSalej=o+xSavingi+3Pricej+uj所以，把相关数据输入EVieWS软件，利用二阶段最
27、小二乘法(TSLS)得到利润方程的估计量为：0=-255689.6a1=0.1224042=1.511910商品房销售收入方程的估计量为：A=-43796614=0.118869A=1491.359利润的样本回归方程为：PROFIT=-255689.645126+0.122403594174*SALE+1.51190976239*RENT商品房销售收入的样本回归方程为：SALE=-4379661.24107+0.11886860077*SAVING+1491.35939031*PRICESystem:SYS01EstimationMethod:Two-StageLeastSquaresDate
28、:12/08/09Time:22:26Sample:131Includedobservations:31Totalsystem(balanced)observations62CoefficientStd.Errort-StatiSticProb.J )/ %)/ JJ XJ/ 12 3 4 5 6 /Ix /I z( Zfx /k. /1% Cccccc-255689.6101580.1-2.5171230.01470.1224040.0135949.0044120.00001.5119100.2816695.3676880.0000-4379661.797401.8-5.4924150.00
29、000.1188690.01038311.447870.00001491.359217.44126.8586770.0000Determinantresidualcovariance5.98E+23Equation:PROFIT=C(1)+C(2)*SALE+C(3)*RENTInstruments:RENTSAVINGPRICECObservations:31R-squaredAdjustedR-squaredS.E.ofregressionProb(F-Statistic)0.9281850.923055386396.21.948554MeandependentvarS.D.depende
30、ntvarSumsquaredresid786003.81392977.4.18E+12Equation:SALE=C(4)+C*SAVING+C(6)*PRICEInstruments:RENTSAVINGPRICECObservations:31R-squaredAdjustedR-squaredS.E.OfregressionProb(F-Statistic)0.9203020.9146092215029.1.170001MeandependentvarS.D.dependentvarSumsquaredresid6969099.7580093.1.37E+14四、单方程计量经济学模型与
31、联立方程计量经济学模型的参数估计量比较(1)单方程计量经济学模型求得的利润样本回归方程：PROFIT=-230904.740437+0.115787008878*SALE+1.67342327822*RENT(2)联立方程计量经济学模型求得的利润样本回归方程：PROFIT=-255689.645126+0.122403594174*SALE+1.51190976239*RENT通过比较可以发现，利用联立方程计量经济学模型得到的商品房销售收入的参数估计量要稍大于利用单方程计量经济学模型得到的商品房销售收入的参数估计量(0.1224035941740.115787008878)；而利用联立方程计量经济学模型得到的房屋出租收入的参数估计量要稍小于利用单方程计量经济学模型得到的房屋出租收入的参数估计量(1.51190976239v1.67342327822)。
