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1、影响城镇居民住房面积的因素分析2011级国贸2班 王泽桐 201100620729 一、背景资料 自从改革开放以来，建筑业和房地产业蓬勃发展，居民的居住环境日益改善，人均住房使用面积逐步增加，居民生活水平也大幅提高，因此，我国目前正处于旺盛的住房需求时期。而从我国目前的实际情况来看，我国城市居民住房的人均居住面积水平还比较低，制约我国城市居民居住水平的主要因素还是住房面积。特别是伴随着我国城市化的进程，大量农村人口进入城市，这导致了对住房需求的进一步加剧。因此，城市居民的人均住房使用面积是现今阶段我们衡量城市居民居住水平的主要方面居民住房的人均使用面积的大小关系到广大居民的切身利益，是居民生活
2、水平的重要体现。本文依据当前房地产业现状，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，城镇居民人均住房面积与人均可支配收入呈正向的线性关系，与城镇居民价格消费指数呈负向的线性关系，同时我们也发现一些问题，值得深入思考。本文利用中国城市统计年鉴和国家统计局的数据资料，从计量经济学的角度来对城镇居民住房人均使用面积的影响因素进行分析。二、指标体系的建立：（1）变量的选取 纵观我国的房地产现状，我国正处于住房需求旺盛时期，这种现象的出现很大程度上是由于人民生活水平的大幅提高。与此同时城市居民的收入和消费习惯以及城市住房的价格水平等因素都对
3、其人均使用面积有着不同程度的影响。本文选取了城镇居民家庭人均可支配收入、城镇居民消费指数、城镇住房平均销售价格三个变量进行分析。（2）数据的选取 数据来源:中国统计年鉴；中国统计局时间Y（平方米）X1（元）X2X3（元）199013.71510.2101.31320199114.21700.6105.11487199214.82026.6108.61519199315.22577.4116.11534199415.73496.21251624199516.24283116.816761996174838.9108.81729199717.85160.3103.11790199818.75425
4、.199.41854199919.4585498.71857200020.36280100.819482001216859.6100.72017200222.87702.8992092200323.78472.2100.921972004259421.6103.32778200526.110493101.63168200627.111759.5101.5336720072813785.8104.53564200828.615780.8105.63743200929.417147.799.1386020103019109.4103.24120201132.721809.8105.44681Y:城
5、镇居民人均住房面积; X1:城镇居民家庭人均可支配收入； X2: 城镇居民消费指数；X3: 城镇住房平均销售价格。 实证分析（1）模型建立 Y=C+1X1+2X2+3X3+U参数估计：Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:14Sample: 1990 2011Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C23.392564.8300034.8431780.0001X10.0004630.0002791.6
6、612510.1140X2-0.1179430.044307-2.6619850.0159X30.0027640.0016001.7272120.1012R-squared0.960041 Mean dependent var21.70000Adjusted R-squared0.953381 S.D. dependent var5.901977S.E. of regression1.274316 Akaike info criterion3.485661Sum squared resid29.22984 Schwarz criterion3.684032Log likelihood-34.3
7、4227 F-statistic144.1548Durbin-Watson stat0.278721 Prob(F-statistic)0.000000（2）计量检验：多重共线性的检验解释变量相关系数矩阵：YX1X2X3Y 1.000000 0.968241-0.450079 0.961444X1 0.968241 1.0000000.361063 0.980109X2-0.450079-0.361063 1.000000-0.322265X3 0.961444 0.9801090.322265 1.000000由此得，X1与X3相关系数高达0.980109，两者高度正相关。运用OLS方法逐一
8、求Y对各个解释变量的回归Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:27Sample: 1990 2011Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C13.170700.56537723.295450.0000X10.0010276.08E-0516.880500.0000R-squared0.937490 Mean dependent var21.17619Adjusted R-squared0.93420
9、0 S.D. dependent var5.498809S.E. of regression1.410528 Akaike info criterion3.616198Sum squared resid37.80221 Schwarz criterion3.715677Log likelihood-35.97008 F-statistic284.9511Durbin-Watson stat0.221774 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:33Sa
10、mple: 1990 2011Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C59.2039417.344243.4134650.0029X2-0.3624810.164993-2.1969470.0406R-squared0.202571 Mean dependent var21.17619Adjusted R-squared0.160601 S.D. dependent var5.498809S.E. of regression5.037938 Akaike info criterion6.16
11、2264Sum squared resid482.2356 Schwarz criterion6.261742Log likelihood-62.70377 F-statistic4.826577Durbin-Watson stat0.140726 Prob(F-statistic)0.040630Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:36Sample: 1990 2011Included observations: 22VariableCoefficientStd. Errort-Statistic
12、Prob. C7.4888180.9598547.8020410.0000X30.0058370.00038315.239290.0000R-squared0.924374 Mean dependent var21.17619Adjusted R-squared0.920394 S.D. dependent var5.498809S.E. of regression1.551468 Akaike info criterion3.806673Sum squared resid45.73400 Schwarz criterion3.906151Log likelihood-37.97006 F-s
13、tatistic232.2359Durbin-Watson stat0.235617 Prob(F-statistic)0.000000综合经济意义和统计检验选出拟合效果最好的一元线性回归方程。通过以上分析，得城镇居民人均住房面积Y与城镇居民家庭人均可支配收入X1的线性关系强，拟合程度较好。Yi=13.1707+0.001X1i,再逐步回归，将剩余变量逐一代入式Yi=13.1707+0.001X1i中,得如下几个模型：Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:43Sample: 1990 2011Incl
14、uded observations: 22VariableCoefficientStd. Errort-StatisticProb. C23.278315.0156714.6411160.0002X10.0009836.05E-0516.248100.0000X2-0.0930580.045925-2.0263010.0578R-squared0.949100 Mean dependent var21.17619Adjusted R-squared0.943445 S.D. dependent var5.498809S.E. of regression1.307689 Akaike info
15、criterion3.505964Sum squared resid30.78092 Schwarz criterion3.655181Log likelihood-33.81262 F-statistic167.8187Durbin-Watson stat0.288183 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:45Sample: 1990 2011Included observations: 22VariableCoefficientStd. Err
16、ort-StatisticProb. C11.230281.8501656.0698820.0000X10.0006980.0003052.2897500.0343X30.0019210.0017451.1008430.2855R-squared0.941433 Mean dependent var21.17619Adjusted R-squared0.934926 S.D. dependent var5.498809S.E. of regression1.402729 Akaike info criterion3.646281Sum squared resid35.41770 Schwarz
17、 criterion3.795498Log likelihood-35.28595 F-statistic144.6701Durbin-Watson stat0.189415 Prob(F-statistic)0.000000经过上述逐步回归分析，表明城镇居民人均住房面积Y对城镇居民家庭人均可支配收入X1和城镇居民消费指数X2的回归模型为较优，最终回归结果如下：Y=23.27831+0.000983X1-0.093058X2异方差性的检验由G-Q检验，对样本X1由大到小排序，去除中间6个样本，剩余16个样本，再分成两个样本容量为8的子样本，对两个子样本分别用OLS法回归。子样本1：Depend
18、ent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 11:49Sample: 1 8Included observations: 8VariableCoefficientStd. Errort-StatisticProb. C17.3443811.339611.5295390.1867X10.0005516.07E-059.0822900.0003X20.0252850.1115370.2266920.8296R-squared0.944445 Mean dependent var27.23750Adjusted R-squared
19、0.922223 S.D. dependent var2.190197S.E. of regression0.610814 Akaike info criterion2.131948Sum squared resid2.265470 Schwarz criterion2.161739Log likelihood-5.527793 F-statistic42.50040Durbin-Watson stat0.890517 Prob(F-statistic)0.000727子样本2：Dependent Variable: YMethod: Least SquaresDate: 06/24/13 T
20、ime: 11:52Sample: 15 22Included observations: 8VariableCoefficientStd. Errort-StatisticProb. C13.625471.6904438.0602950.0005X10.0009518.67E-0510.967660.0001X2-0.0098910.015547-0.6362150.5526R-squared0.960862 Mean dependent var15.57500Adjusted R-squared0.945206 S.D. dependent var1.390529S.E. of regre
21、ssion0.325496 Akaike info criterion0.873063Sum squared resid0.419738 Schwarz criterion0.902853Log likelihood-0.492251 F-statistic61.37592Durbin-Watson stat1.234388 Prob(F-statistic)0.000303计算F统计量：F=5.39在5%的显著性水平下，自由度为（5,5）的F分布临界值为F0.05(5,5)=5.05,于是拒绝同方差的假设，表明原模型存在异方差。异方差性修正：采用加权最小二乘法进行估计：Dependent V
22、ariable: YMethod: Least SquaresDate: 06/24/13 Time: 11:57Sample: 1 22Included observations: 22Weighting series: 1/ABS(E1)VariableCoefficientStd. Errort-StatisticProb. C22.871831.92953111.853570.0000X10.0009783.27E-0529.858330.0000X2-0.0888640.016949-5.2429300.0001Weighted StatisticsR-squared0.998248
23、 Mean dependent var19.64801Adjusted R-squared0.998053 S.D. dependent var14.71744S.E. of regression0.649352 Akaike info criterion2.105880Sum squared resid7.589843 Schwarz criterion2.255097Log likelihood-19.11174 F-statistic699.2485Durbin-Watson stat0.714927 Prob(F-statistic)0.000000Unweighted Statist
24、icsR-squared0.949032 Mean dependent var21.17619Adjusted R-squared0.943369 S.D. dependent var5.498809S.E. of regression1.308569 Sum squared resid30.82237Durbin-Watson stat0.278962得到：Y=22.87183+0.000978X1-0.088864X2 R2=0.998248； D.W.= 0.714927; F=699.2485从结果来看，拟合优度提高了，t统计量也有了改进。此时，模型已不存在异方差。自相关性的检验在5%
25、的显著性水平下，样本容量为21，D.W.的临界值du=1.42;dl=1.22,D.W.= 0.714927d1,所以该模型存在一阶正自相关。修正：用杜宾两步法估计模型第一步：Dependent Variable: YMethod: Least SquaresDate: 06/24/13 Time: 12:01Sample(adjusted): 2 22Included observations: 20 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1.1913762.6530530.449059
26、0.6603X17.14E-050.0003830.1866670.8546X2-0.0346490.022306-1.5533370.1427X1(-1)-0.0002180.000401-0.5450730.5943X2(-1)0.0157170.0146661.0716790.3020Y(-1)1.1260860.06643616.949990.0000R-squared0.998189 Mean dependent var21.55000Adjusted R-squared0.997542 S.D. dependent var5.360921S.E. of regression0.26
27、5791 Akaike info criterion0.431110Sum squared resid0.989025 Schwarz criterion0.729829Log likelihood1.688905 F-statistic1543.106Durbin-Watson stat2.766506 Prob(F-statistic)0.000000第二步：Dependent Variable: Y1Method: Least SquaresDate: 06/24/13 Time: 12:04Sample(adjusted): 2 22Included observations: 20
28、after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C0.8413041.0025820.8391370.4130X110.0001221.24E-059.8451240.0000X22-0.0159470.009234-1.7269180.1023R-squared0.918963 Mean dependent var-1.799393Adjusted R-squared0.892370 S.D. dependent var0.634200S.E. of regression0.251794 Akaik
29、e info criterion0.217070Sum squared resid1.077804 Schwarz criterion0.366430Log likelihood0.829299 F-statistic51.76785Durbin-Watson stat2.266995 Prob(F-statistic)0.000000在5%的显著性水平下，样本容量为21，D.W.的临界值du=1.42;dl=1.22,因为D.W.=2.27，duD-W4-du,所以该模型已无自相关。经过计量检验得到最终模型Y=0.841304+0.000122X1-0.015947X2.该模型的经济意义是：
30、经过计量检验得出，城镇居民人均住房面积与城镇居民家庭人均可支配收入呈正相关，随着家庭人均收入的增加，城镇居民的购房需求也会相应上升；城镇居民居民人均住房面积与城镇居民价格消费指数呈负相关，随着价格消费指数的增加，居民的购房热情会随之下降。该模型的统计检验：经计算此模型R2=0.918963修正后的R2=0.892370 ，表明模型在整体上拟合的比较好。再从t检验值看，5%显著性水平下自由度为n-k-1=21-2-1=18的t分布临界值为t0.025(18)=2.101,说明该模型通过了显著性检验；最后从F检验来看，模型的F值为 F=51.76785，而5%显著性水平下自由度分别为k=2和n-k
31、-1=18的F分布临界值为F0.05(2,18)=3.55，说明模型在总体上是高度显著的。结论和建议分析结果表明城市居民人均可支配收入,消费习惯对城镇居民人均住房使用面积的影响是较为显著的。城市住房的价格水平对其人均使用面积也有着一定程度的影响。随着家庭人均收入的增加，城镇居民的购房需求也会相应上升；随着价格消费指数的增加，居民的购房热情会随之下降。居民住房的人均使用面积的大小关系到广大居民的切身利益，是居民生活水平的重要体现。虽然中国的房地产业取得了很大的进步，为提高我国居民的住房水平作出了巨大的贡献，但是在发展中也暴露出了很多问题，房价高，有效需求不足是当前的主要难点。需要采取大力消费空置商品房，建设经济适用住房，积极开放住房二、三级市场等措施加以解决。
