1、住房价格方程研究问题：住房价格和住房自身特征间的关系 (根据 Wooldrige 计量经济学导论 P219，259,288 改编)数据集：hprice1变量：price：住房价格lotsize：住房占地面积 (加上院子)sqrft：住房面积bdrms：卧室数量1.RESET 检验用变量的水平值建立模型 bdrmssqftlotizeprice3210_cons -21.77031 29.47504 -0.74 0.462 -80.38466 36.84405bdrms 13.85252 9.010145 1.54 0.128 -4.065141 31.77018 sqrft .1227782
2、.0132374 9.28 0.000 .0964541 .1491022lotsize .0020677 .0006421 3.22 0.002 .0007908 .0033446 price Coef. Std. Err. t P|t| 95% Conf. Interval Total 917854.506 87 10550.0518 Root MSE = 59.833 Adj R-squared = 0.6607Residual 300723.805 84 3580.0453 R-squared = 0.6724 Model 617130.701 3 205710.234 Prob F
3、= 0.0000F( 3, 84) = 57.46 Source SS df MS Number of obs = 88Prob F = 0.0076 F(3, 81) = 4.26Ho: model has no omitted variablesRamsey RESET test using powers of the fitted values of price. estat ovtest Prob F = 0.0000 F(9, 75) = 6.10Ho: model has no omitted variablesRamsey RESET test using powers of t
4、he independent variables. estat ovtest, rhs结果说明函数设定错误，可能漏掉了自变量高次方项，也有可能需要对变量做变换。这个检验不能得到可能存在异方差的结论。2.异方差检验Prob chi2 = 0.0019 chi2(1) = 9.65Variables: fitted values of price Ho: Constant varianceBreusch-Pagan / Cook-Weisberg test for heteroskedasticity . estat hettest, iidProb chi2 = 0.0028 chi2(3) =
5、 14.09Variables: lotsize sqrft bdrms Ho: Constant varianceBreusch-Pagan / Cook-Weisberg test for heteroskedasticity . estat hettest, rhs iidTotal 44.78 13 0.0000Kurtosis 2.91 1 0.0882Skewness 8.14 3 0.0432 Heteroskedasticity 33.73 9 0.0001Source chi2 df pCameron & Trivedi's decomposition of
6、IM-testProb chi2 = 0.0001 chi2(9) = 33.73against Ha: unrestricted heteroskedasticityWhite's test for Ho: homoskedasticity两种检验都说明存在异方差，注意这种异方差可能是变量间函数关系设定错误造成的，也可能是真正的异方差。3. 对变量做对数变换，除 bdrms 外，因它是离散变量。拟合模型 bdrmssqrftlotsizeprice 3210 )ln()n()ln(_cons -1.297042 .6512836 -1.99 0.050 -2.592191 -.001
7、893 bdrms .0369584 .0275313 1.34 0.183 -.0177906 .0917074lsqrft .7002324 .0928652 7.54 0.000 .5155597 .8849051 llotsize .1679667 .0382812 4.39 0.000 .0918404 .244093lprice Coef. Std. Err. t P|t| 95% Conf. IntervalTotal 8.01760352 87 .092156362 Root MSE = .1846 Adj R-squared = 0.6302Residual 2.862563
8、24 84 .034078134 R-squared = 0.6430 Model 5.15504028 3 1.71834676 Prob F = 0.0000F( 3, 84) = 50.42 Source SS df MS Number of obs = 88Ramsey RESET test using powers of the fitted values of lpriceHo: model has no omitted variablesF(3, 81) = 2.45Prob F = 0.0692Ramsey RESET test using powers of the inde
9、pendent variablesHo: model has no omitted variablesF(9, 75) = 2.01Prob F = 0.0494变换后的模型存在设定错误的证据较弱。Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant varianceVariables: fitted values of lpricechi2(1) = 1.39Prob chi2 = 0.2379Breusch-Pagan / Cook-Weisberg test for heteroskedasticit
10、y Ho: Constant varianceVariables: llotsize lsqrft bdrmschi2(3) = 4.22Prob chi2 = 0.2383Total 13.81 13 0.3872Kurtosis 2.57 1 0.1090Skewness 1.69 3 0.6381 Heteroskedasticity 9.55 9 0.3882Source chi2 df pCameron & Trivedi's decomposition of IM-testProb chi2 = 0.3882 chi2(9) = 9.55against Ha: un
11、restricted heteroskedasticityWhite's test for Ho: homoskedasticity这些异方差检验说明，对数变换后的模型不存在异方差。至此，说明: (1)最初的模型存在设定错误；(2) 最初模型的异方差也是由于函数关系错误设定造成的。对因变量和自变量作对数变换后，两个问题都得到了解决。当检验出模型存在异方差时，则给我们一个提醒，可能模型的设定有问题，也可能模型设定没问题而是真正的存在异方差(研究对象差别太大导致 )。理智而有经验的研究者首先会把它当作模型设定错误的信号，而不是一股脑地去做 FGLS 了事。首先去仔细检查模型设定是否存在问题；在确保设定没有问题后，如果还存在异方差，才考虑用 OLS+异方差稳健标准误差，或者 FGLS 来解决。
