城鎮(zhèn)居民住房面積的多因素分析

1、 城鎮(zhèn)居民住房面積的多因素分析內(nèi)容摘要：本文根據(jù)目前房地產(chǎn)業(yè)現(xiàn)狀，從計量經(jīng)濟學(xué)的角度來驗證一下居民收入水平、物價水平、國內(nèi)gnp以及房地產(chǎn)銷售價格等因素對其的影響程度。從回歸結(jié)果看出，平均貨幣工資與居民住房面積之間存在正向的線性關(guān)系，同時我們也發(fā)現(xiàn)了一些問題，值得深入思考。關(guān)鍵詞 城鎮(zhèn)居民住房銷售總面積 職工平均貨幣工資 多因素分析 城鎮(zhèn)居民價格消費指數(shù) 檢驗一. 經(jīng)濟背景去年中國房地產(chǎn)投資超過億萬元，占固定資產(chǎn)投資的，直接拉動增長個百分點。年房地產(chǎn)投資和消費仍將保持一定的增長。專家預(yù)測，到年，中國城市化水平將提高到，城鎮(zhèn)人口將達(dá)到億以上，按人均需住房平方米計算，僅城鎮(zhèn)新增人口每年就需增億平方

2、米以上，房地產(chǎn)業(yè)在國民經(jīng)濟和社會發(fā)展中的重要地位將逐漸突出。房地產(chǎn)市場的發(fā)展，不僅可以推動經(jīng)濟的發(fā)展，而且可以從增加投資的消費，增加就業(yè)多方面拉動國內(nèi)的需求。 近年來部分城市房價漲得過快、房價過高，已是一個不爭的事實，房地產(chǎn)不合理增長帶來的一系列負(fù)面影響，不少專家學(xué)者直言，這種市場態(tài)勢會造成兩種后果：一是房地產(chǎn)市場的泡沫可能不斷擴大，市場風(fēng)險進(jìn)一步積累；二是相當(dāng)多的中低收入者缺乏“小康水平住房”的現(xiàn)實購買力。由此可見，住房問題已經(jīng)成為我國市場經(jīng)濟發(fā)展過程中的一個重要問題。在此，我們將從計量經(jīng)濟學(xué)的角度進(jìn)行研究。二. 結(jié)合經(jīng)濟背景，建立計量經(jīng)濟學(xué)模型 關(guān)于數(shù)據(jù)：數(shù)據(jù)的來源 附表1yx1x2x3x

3、4199127455103.4148719923812.21271126651.9106.4151919936035.19337134560.5114.7153419946118.03453846670124.1162419956787.03550057494.9117.1167619966898.46621066850.5108.3172919977864.3647073142.7102.81790199810827.1747976967.299.21854199912997.87834680579.498.61857200016570.28937188254100

4、.41948200119938.311087095727.9100.72017200223702.3112422103935.3100.42092200329778.8514040116603.2100.82197 關(guān)于模型建立模型 ：y=c+1x1+2x2+3x3+4x4+u其中y代表我國城鎮(zhèn)居民住房銷售總面積（單位；萬平方米），x1代表職工平均貨幣工資（單位：元）x2代表國民生產(chǎn)總值（單位：億元）x3代表城鎮(zhèn)居民價格消費指數(shù)x4代表城鎮(zhèn)住房平均銷售價格（單位：元/平方米）參數(shù)估計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模型檢驗：經(jīng)濟意義的檢驗：從經(jīng)濟意義上來說，居民住房購買面積會隨著居民平均工

7、資以及國民生產(chǎn)總值的增加而增加，而與城鎮(zhèn)居民價格消費指數(shù)、城鎮(zhèn)住房平均銷售價格呈反向關(guān)系。從上表可以看出x2、x3和x4的參數(shù)符號與其經(jīng)濟意義不符，估計是因為變量間存在多重共線性或者是與被解釋變量不存在線性關(guān)系。統(tǒng)計推斷檢驗：從回歸結(jié)果可以看出，r2=0.990517，模型的擬合程度非常好，f統(tǒng)計量的值在給定顯著性水平=0.05下也比較顯著，但是x3和x4的t統(tǒng)計值均不顯著，說明x3和x4這兩個變量對y的影響不顯著，或者變量之間存在多重共線的影響使其t值不顯著。計量經(jīng)濟學(xué)意義檢驗多重共線性檢驗由于f=208.8926f0.05(3,9)=3.86(顯著性水平=0.05)表明模型從整體上看房屋購

8、買量與4個解釋變量之間線性關(guān)系顯著。對x1、x2、x3、x4、進(jìn)行簡單相關(guān)系數(shù)矩陣檢驗。解釋變量相關(guān)系數(shù)矩陣：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由此可見，一些解釋變量之間存在高度線性相關(guān)。盡管整體線性回歸擬合較好，但x3,x4變量的參數(shù)t值并不顯著而且x2,x3,x4符號與經(jīng)濟意義相悖，表明模型中解釋變量確實存在

9、嚴(yán)重的多重共線性。多重共線性的修正：采用逐步回歸法對多重共線性進(jìn)行補救。運用ols方法逐一求y對各解釋變量的回歸，回歸結(jié)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從回歸的結(jié)果可以看出居民可支配收入(x1)的t值最大，線形關(guān)系強，擬合程度最好，因此把x1作為基本變量。然后將其余解釋變量逐一代入x1的回歸方程，重新回歸。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逐步回歸，將其余變量逐一代入方程（1），重新回歸。經(jīng)分析，引入其他變量后各個方程的調(diào)整后可決系數(shù)都小于方程（1）中的調(diào)整后可決系數(shù)。決定將模型設(shè)定為 y = -3997.512 + 2.199714*x1 （1）（-3.304343） （14.602

22、53）r2=0.950944 s.e.=1926.469 f=213.2338異方差檢驗arch檢驗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從arch檢驗結(jié)果可以看到，obs*r-squared=1.622639小于臨界值7.81473，所以不能拒絕原假設(shè)，認(rèn)為模型不存在異方差。white 檢驗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從white檢驗看到obs*r-squared=1.224309小于臨界值11.0705，仍然認(rèn)為不存在異方差 自相關(guān)性檢驗dw =0.49003170883,dl=1.010 ,du=1.340, dwdl,存在自相關(guān), 其原因可能是由居民對住房的消費不止與本期收入有關(guān)，而且還與前幾期的收入有關(guān)，即解釋變量對被解釋變量的影響具有時滯性。利用對數(shù)變換和c-o迭代法修正，結(jié)果如下：dependent variable: dlnymethod: least squaresdate: 06/02/05 time: 13:03sample(adjusted): 1993 2003included observat