城鎮(zhèn)居民住房面積的多因素分析

1、內(nèi)容摘要:本文根據(jù)目前房地產(chǎn)業(yè)現(xiàn)狀，從計(jì)量經(jīng)濟(jì)學(xué)的角度來驗(yàn)證一下居民 收入水平、物價(jià)水平、國內(nèi)GN以及房地產(chǎn)銷售價(jià)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(shí)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(jià)格消費(fèi)指數(shù)檢驗(yàn)一. 經(jīng)濟(jì)背景去年中國房地產(chǎn)投資超過1億萬元，占固定資產(chǎn)投資的18.3%，直接 拉動GDP增長1.3個(gè)百分點(diǎn)。2004年房地產(chǎn)投資和消費(fèi)仍將保持一定 的增長。專家預(yù)測，到2 0 2 0年，中國城市化水平將提高到55%，城鎮(zhèn)人 口將達(dá)到7億以上，按人均需住房2 0平方米

2、計(jì)算，僅城鎮(zhèn)新增人口每年就需 增2億平方米以上，房地產(chǎn)業(yè)在國民經(jīng)濟(jì)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(jì)的發(fā)展，而且可以從增加投資的消費(fèi)， 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(jià)漲得過快、房價(jià)過高，已是一個(gè)不爭的事實(shí)，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(kuò)大，市場風(fēng)險(xiǎn)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(shí)購買力。由此可見，住房問題已經(jīng)成為我國市場經(jīng)濟(jì)發(fā)展過程中的一個(gè)重要問題。在此，我們將從計(jì)量經(jīng)濟(jì)學(xué)的角度進(jìn)行研究。二. 結(jié)合經(jīng)濟(jì)背景，建立計(jì)量經(jīng)濟(jì)學(xué)模

3、型 關(guān)于數(shù)據(jù)：數(shù)據(jù)的來源 << 中國統(tǒng)計(jì)年鑒>>附表1YX1X221662.5X3X419912745.172340103.4148719923812.21271126651.9106.4151919936035.19337134560.5114.715344667019946118.03453857494.9124.1162419956787.035500117.1167619966898.46621066850.5108.3172919977864.3647073142.7102.81790199810827.1747976967.299.2185419991299

4、7.87834680579.498.61857200016570.28937188254100.41948200119938.311087095727.9100.72017200223702.3112422103935.3100.42092200329778.8514040116603.2100.82197關(guān)于模型1建立模型：Y二C+ B 1X1+ B 2X2+ B 3X3+ B 4X4+U其中丫代表我國城鎮(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(jià)格消費(fèi)指數(shù)X4代表城鎮(zhèn)住房平均銷售價(jià)格（單位：元/平方米）2.參

5、數(shù)估計(jì)Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:08Sample: 1991 2003In cluded observati ons: 13VariableCoefficie ntStd. Error t-Statistic Prob.-35148.1233827.53-1.0390390.3292X13.5460610.9739953.6407400.0066X2-0.3368810.075928-4.4368660.0022X341.0693252.895110.7764300.4598X422.3

6、727022.601780.9898650.3512R-squared0.990517Mean depe ndent var11851.93Adjusted R-squared0.985775S.D.dependent var8327.641S.E. of regressi on993.2348Akaike info criteri on16.92353Sum squared resid7892124.Schwarz criteri on17.14082Log likelihood-105.0030F-statistic208.8926Durb in -Watson stat2.226441P

7、rob(F-statistic)0.000000= =3模型檢驗(yàn):經(jīng)濟(jì)意義的檢驗(yàn)：從經(jīng)濟(jì)意義上來說，居民住房購買面積會隨著居民平均工資以及國民生產(chǎn)總 值的增加而增加，而與城鎮(zhèn)居民價(jià)格消費(fèi)指數(shù)、城鎮(zhèn)住房平均銷售價(jià)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(jì)意義不符，估計(jì)是因?yàn)?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(jì)推斷檢驗(yàn)：從回歸結(jié)果可以看出，R2=0.990517，模型的擬合程度非常好，F(xiàn)統(tǒng)計(jì)量的 值在給定顯著性水平 a =0.05下也比較顯著，但是X3和X4的t統(tǒng)計(jì)值均不顯著， 說明X3和X4這兩個(gè)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

8、使其t值不顯著。計(jì)量經(jīng)濟(jì)學(xué)意義檢驗(yàn) 多重共線性檢驗(yàn) 由于F=208.8926>F 0.05(3,9)=3.86 (顯著性水平a =0.05表明模型從整體上看房屋購買量與4個(gè)解釋變量之間線性關(guān)系顯著。對 XI、X2、X3、X4、進(jìn)行簡單相關(guān)系數(shù)矩陣檢驗(yàn)。解釋變量相關(guān)系數(shù)矩陣:X1X2X3X4X11.0000000.980746-0.5538600.995352X20.9807461.000000-0.5517520.989377X3-0.553860-0.5517521.000000-0.587315X40.9953520.989377-0.5873151.000000由此可見，一些解釋變

9、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(jì)意義相悖，表明模 型中解釋變量確實(shí)存在嚴(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(bǔ)救。 運(yùn)用OLS方法逐一 求丫對各解釋變量的回歸，回歸結(jié)果如下Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:32Sample: 1991 2003In cluded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb

10、.C-3997.5121209.775-3.3043430.0070X12.1997140.15063914.602530.0000R-squared0.950944Mean depe ndent var11851.93Adjusted R-squared0.946484S.D.dependent var8327.641S.E. of regressi on1926.469Akaike info criteri on18.10540Sum squared resid40824123Schwarz criteri on18.19232Log likelihood-115.6851F-statis

11、tic213.2338Durb in -Watson stat0.490032Prob(F-statistic)0.000000Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:33Sample: 1991 2003In cluded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C-5711.7442477.187-2.3057380.0416X20.2568080.0334157.6853530.0000R-squared0.8

12、43002Mea n depe ndent var11851.93Adjusted R-squared0.828730S.D.dependent var8327.641S.E. of regressi on3446.380Akaike info criteri on19.26867Sum squared resid1.31E+08Schwarz criteri on19.35559Log likelihood-123.2464F-statistic59.06465Durb in -Watson stat0.307835Prob(F-statistic)0.000010Depe ndent Va

13、riable: YMethod: Least SquaresDate: 06/02/05 Time: 10:35Sample: 1991 2003In cluded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C69679.0928384.812.4548020.0320X3-545.9751267.2926-2.0426120.0658R-squared0.274993Mean depe ndent var11851.93Adjusted R-squared0.209083S.D.dependent var83

14、27.641S.E. of regressi on7406.063Akaike info criteri on20.79862Sum squared resid6.03E+08Schwarz criteri on20.88554Log likelihood-133.1911F-statistic4.172265Durb in -Watson stat0.342184Prob(F-statistic)0.065808Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:35Sample: 1991 2003In cl

15、uded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C-51348.255674.731-9.0485790.0000X435.225623.13984711.218900.0000R-squared0.919628Mean depe ndent var11851.93Adjusted R-squared0.912321S.D.dependent var8327.641S.E. of regressi on2465.861Akaike info criteri on18.59911Sum squared res

16、id66885173Schwarz criteri on18.68602Log likelihood-118.8942F-statistic125.8636Durb in -Watson stat0.462493Prob(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(qiáng)，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。Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:39Sample: 1991 2003In c

17、luded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C-799.9123798.5133-1.0017520.3401X14.4178440.37816911.682180.0000X2-0.2804370.046891-5.9805900.0001R-squared0.989281Mean depe ndent var11851.93Adjusted R-squared0.987138S.D.dependent var8327.641S.E. of regressi on944.4523Akaike inf

18、o criteri on16.73826Sum squared resid8919902.Schwarz criteri on16.86863Log likelihood-105.7987F-statistic461.4823Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05Time: 10:39Sample: 1991 2003In cluded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C-6699.90410076.73-0.6648890.

19、5212X12.2280200.18906511.784390.0000X323.5889987.264060.2703170.7924R-squared0.951300Mean depe ndent var11851.93Adjusted R-squared0.941560S.D.dependent var8327.641S.E. of regressi on2013.156Akaike info criteri on18.25197Sum squared resid40527979Schwarz criteri on18.38234Log likelihood-115.6378F-stat

20、istic97.66923Depe ndent Variable: YMethod: Least SquaresDate: 06/02/05 Time: 10:40Sample: 1991 2003In cluded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C58508.1130303.241.9307540.0823X15.0219701.3737973.6555390.0044X4-46.1725322.37106-2.0639400.0660= =R-squared0.965599Mean depe n

21、dent var11851.93Adjusted R-squared0.958718S.D.dependent var8327.641S.E. of regressi on1692.002Akaike info criteri on17.90439Sum squared resid28628718Schwarz criteri on18.03476Log likelihood-113.3785F-statistic140.3427Durb in -Watson stat1.202075Prob(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

22、入其他 變量后各個(gè)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 丫 = -3997.512 + 2.199714*X1（ 1）(-3.304343)( 14.60253)R2=0.950944S.E.=1926.469F=213.2338 異方差檢驗(yàn)ARC檢驗(yàn)ARCH Test:F-statistic0.387387Probability0.766491Obs*R-squared1.622639Probability0.654268Test Equati on:Depe ndent Variable: RESIDA2Method: Least SquaresDat

23、e: 06/02/05 Time: 13:11Sample(adjusted): 1994 2003In eluded observati ons: 10 after adjusti ng en dpo intsVariableCoefficie ntStd. Errort-StatisticProb.C4061731.2432027.1.6701020.1459RESIDA2(-1)0.1340250.4399280.3046510.7709RESIDA2(-2)-0.4461170.455407-0.9796000.3651RESIDA2(-3)-0.0887620.481546-0.18

24、43260.8598R-squared0.162264Mean depe ndent var2801902.Adjusted R-squared-0.256604S.D.dependent var3247199.S.E. of regressi on3640057.Akaike info criteri on33.34207Sum squared resid7.95E+13Schwarz criteri on33.46311Log likelihood-162.7104F-statistic0.387387Durb in -Watson stat1.386823Prob(F-statistic

25、)0.766491 =從ARCH檢驗(yàn)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(yàn)White Heteroskedasticity Test:F-statistic0.519846Probability0.609839Obs*R-squared1.224309Probability0.542182Test Equati on:Depe ndent Variable: RESIDEMethod: Least SquaresDate: 06/02/05 Time: 13:12Sample: 1991 20

26、03In cluded observati ons: 13VariableCoefficie ntStd. Errort-StatisticProb.C7020943.4048742.1.7341050.1136X1-1174.9911152.631-1.0193990.3320X1A20.0710970.0710561.0005760.3406R-squared0.094178Mean depe ndent var3140317.Adjusted R-squared-0.086987S.D.dependent var3030958.S.E. of regressi on3160037.Aka

27、ike info criteri on32.96924Sum squared resid9.99E+13Schwarz criteri on33.09961Log likelihood-211.3001F-statistic0.519846Durb in -Watson stat1.636334Prob(F-statistic)0.609839= =從WHIT檢驗(yàn)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(yàn)DW =0.49003170883,d l=1.010 ,d u=1.340, DW<d l,存在自相關(guān),其原因可能是由居民對住房的消費(fèi)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(shí)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 2003In eluded observati ons: 11 after adjusti ng en dpo intsCon verge nee achieved after 4 i