计量经济学模型分析方法

1、计量经济学上机模型分析方法总结一、随机误差项的异方差问题的检验与修正模型一：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:03Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.  C1.6025280.8609781.8612880.0732LOG(X1)0.3254160.1037693.1359550.0040LOG(X2)0.5070780.04859910.4

2、33850.0000R-squared0.796506    Mean dependent var7.448704Adjusted R-squared0.781971    S.D. dependent var0.364648S.E. of regression0.170267    Akaike info criterion-0.611128Sum squared resid0.811747    Schwarz criterion-

3、0.472355Log likelihood12.47249    F-statistic54.79806Durbin-Watson stat1.964720    Prob(F-statistic)0.000000（一）异方差的检验1、GQ检验法模型二：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:19Sample: 1 12Included observations: 12VariableCoefficientStd

4、. Errort-StatisticProb.  C3.7446261.1911133.1438040.0119LOG(X1)0.3443690.0829994.1490770.0025LOG(X2)0.1689040.1188441.4212280.1890R-squared0.669065    Mean dependent var7.239161Adjusted R-squared0.595524    S.D. dependent var0.133581S.E. of regressio

5、n0.084955    Akaike info criterion-1.881064Sum squared resid0.064957    Schwarz criterion-1.759837Log likelihood14.28638    F-statistic9.097834Durbin-Watson stat1.810822    Prob(F-statistic)0.006900模型三：Dependent Variable

6、: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:20Sample: 20 31Included observations: 12VariableCoefficientStd. Errort-StatisticProb.  C-0.3533811.607461-0.2198380.8309LOG(X1)0.2108980.1582201.3329420.2153LOG(X2)0.8565220.1086017.8868560.0000R-squared0.878402    Me

7、an dependent var7.769851Adjusted R-squared0.851381    S.D. dependent var0.390363S.E. of regression0.150490    Akaike info criterion-0.737527Sum squared resid0.203824    Schwarz criterion-0.616301Log likelihood7.425163    

8、;F-statistic32.50732Durbin-Watson stat2.123203    Prob(F-statistic)0.000076进行模型二和模型三两次回归，目的仅是得到出去中间7个样本点以后前后各12个样本点的残差平方和RSS1和RSS2，然后用较大的RSS除以较小的RSS即可求出F统计量值进行显著性检验。2、怀特检验法（White）模型一的怀特残差检验结果：White Heteroskedasticity Test:F-statistic4.920995    Probability0.00

9、4339Obs*R-squared13.35705    Probability0.009657Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/29/13 Time: 09:04Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.  C3.9821372.8828511.3813190.1789LOG(X1)-0.5792890.91

10、6069-0.6323640.5327(LOG(X1)20.0418390.0668660.6257100.5370LOG(X2)-0.5636560.203228-2.7735140.0101(LOG(X2)20.0402800.0138792.9021730.0075R-squared0.430873    Mean dependent var0.026185Adjusted R-squared0.343315    S.D. dependent var0.038823S.E. of regression0.0

11、31460    Akaike info criterion-3.933482Sum squared resid0.025734    Schwarz criterion-3.702194Log likelihood65.96898    F-statistic4.920995Durbin-Watson stat1.526222    Prob(F-statistic)0.004339 一方面，根据上面的Obs*R2=31*0.4308

12、73=13.357052(4)，说明存在显著的异方差问题；另一方面，根据下面的辅助回归模型可以看出LOG(X2) 与(LOG(X2)2均通过了t检验，说明异方差的形式可以用LOG(X2) 与(LOG(X2)2的线性组合表示，权变量可以简单确定为1/LOG(X2)。（二）加权最小二乘法（WLS）修正1、方法原理：具体参见教材。2、回归结果分析模型四：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:06Sample: 1 31Included observations: 31Weighting serie

13、s: 1/LOG(X2)VariableCoefficientStd. Errort-StatisticProb.  C1.4780850.8176101.8078110.0814LOG(X1)0.3779150.0969253.8990440.0006LOG(X2)0.4734710.0483989.7828640.0000Weighted StatisticsR-squared0.872646    Mean dependent var7.423264Adjusted R-squared0.863550  &#

14、160; S.D. dependent var0.436598S.E. of regression0.161276    Akaike info criterion-0.719639Sum squared resid0.728274    Schwarz criterion-0.580866Log likelihood14.15440    F-statistic49.27256Durbin-Watson stat2.036239   

15、 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.789709    Mean dependent var7.448704Adjusted R-squared0.774688    S.D. dependent var0.364648S.E. of regression0.173088    Sum squared resid0.838862Durbin-Watson stat2.028211加权修正

16、以后的模型四怀特检验结果如下：White Heteroskedasticity Test:F-statistic6.555091    Probability0.000870Obs*R-squared15.56541    Probability0.003661可以看出并没有消除异方差性，加权修正无效。下面采用1/abs(e)权变量进行WLS回归，结果如下：模型五：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:10Sam

17、ple: 1 31Included observations: 31Weighting series: 1/ABS(E)VariableCoefficientStd. Errort-StatisticProb.  C1.2279290.2972684.1307080.0003LOG(X1)0.3757480.0568306.6117340.0000LOG(X2)0.5101200.01778128.688470.0000Weighted StatisticsR-squared0.999990    Mean dependent var

18、7.558578Adjusted R-squared0.999989    S.D. dependent var12.31758S.E. of regression0.041062    Akaike info criterion-3.455703Sum squared resid0.047210    Schwarz criterion-3.316930Log likelihood56.56339    F-statistic1960

19、.131Durbin-Watson stat2.487309    Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.794514    Mean dependent var7.448704Adjusted R-squared0.779836    S.D. dependent var0.364648S.E. of regression0.171099    Sum squ

20、ared resid0.819694Durbin-Watson stat2.007122对加权以后的模型五进行怀特检验如下：White Heteroskedasticity Test:F-statistic0.199645    Probability0.936266Obs*R-squared0.923778    Probability0.921125可以看出，模型已经不再存在异方差问题，模型五可以作为修正以后的最终模型。二、随机误差项序列相关性问题的检验与修正 模型一：Dependent Variable: Y

21、Method: Least SquaresDate: 07/29/12 Time: 09:48Sample: 1991 2011Included observations: 21VariableCoefficientStd. Errort-StatisticProb.  C178.975555.064213.2503050.0042X0.0200020.00113417.641570.0000R-squared0.942463    Mean dependent var922.9095Adjusted R-squared0.93943

22、5    S.D. dependent var659.3491S.E. of regression162.2653    Akaike info criterion13.10673Sum squared resid500270.3    Schwarz criterion13.20621Log likelihood-135.6207    F-statistic311.2248Durbin-Watson stat0.658849

23、0;   Prob(F-statistic)0.000000 初始回归模型一经济意义合理，统计指标较为理想，但DW值偏低，模型可能存在序列相关性。（一）序列相关性的检验方法1、自回归模型检验法Dependent Variable: EMethod: Least SquaresDate: 07/29/12 Time: 09:49Sample (adjusted): 1992 2011Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb. 

24、; E(-1)0.7170800.2018523.5524970.0021R-squared0.398929    Mean dependent var2.801737Adjusted R-squared0.398929    S.D. dependent var161.7297S.E. of regression125.3870    Akaike info criterion12.54939Sum squared resid298716.2  

25、;  Schwarz criterion12.59918Log likelihood-124.4939    Durbin-Watson stat1.080741说明模型一的随机误差项至少存在一阶正序列相关性，结合该自回归模型的DW值为1.08，怀疑存在更高阶的序列相关，继续引入e(-2)如下：Dependent Variable: EMethod: Least SquaresDate: 07/29/12 Time: 09:49Sample (adjusted): 1993 2011Included observations: 19

26、after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  E(-1)1.0949740.1787686.1251080.0000E(-2)-0.8150100.199977-4.0755130.0008R-squared0.692885    Mean dependent var7.790341Adjusted R-squared0.674819    S.D. dependent var164.5730S.E. of reg

27、ression93.84710    Akaike info criterion12.02051Sum squared resid149723.7    Schwarz criterion12.11993Log likelihood-112.1949    Durbin-Watson stat1.945979由于e(-2)的t检验显著，说明模型一的随机误差项确实存在二阶正序列相关性，结合该二阶自回归模型的DW值为1.95，基本确定不存在更高阶的序列相关。Breusch-God

28、frey Serial Correlation LM Test:F-statistic0.888958    Probability0.431668Obs*R-squared1.998924    Probability0.368077可以看出二阶自回归模型的随机误差项不存在序列相关性，论证了原模型仅存在二阶序列相关。2、DW检验法0<DW<dL 存在正自相关(趋近于0) DL<DW<dU 不能确定 DU<DW<4dU 无自相关（趋近于2）3、LM检验法原理：一方面，根据上面的假

29、设检验结果判断是否存在序列相关性，即根据(n-p)*R2统计量值与卡方检验临界值2(P)进行比较，其中n为原模型样本容量，P为选择的滞后阶数，R2为下面辅助回归模型的可决系数。若(n-p)*R22(P)，则拒绝不序列相关的原假设，说明模型存在显著的序列相关性；另一方面，结合下面的辅助回归模型中残差滞后变量是否通过t检验及DW值判断序列相关的具体阶数，方法与上面的自回归模型检验法相同。选择滞后一阶检验：Breusch-Godfrey Serial Correlation LM Test:F-statistic13.15036    Probability0

30、.001931Obs*R-squared8.865308    Probability0.002906Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 07/29/12 Time: 09:51Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.  C-14.2447243.18361-0.3298640.7453

31、X0.0007140.0009070.7866170.4417RESID(-1)0.7632630.2104773.6263420.0019R-squared0.422158    Mean dependent var1.30E-13Adjusted R-squared0.357953    S.D. dependent var158.1566S.E. of regression126.7275    Akaike info criterion12.65352Sum squa

32、red resid289077.4    Schwarz criterion12.80274Log likelihood-129.8619    F-statistic6.575179Durbin-Watson stat1.159275    Prob(F-statistic)0.007183说明原模型确实存在一阶序列相关性，结合该辅助回归模型的DW值为1.16，怀疑存在更高阶的序列相关，引入滞后二阶检验如下：Breusch-Godfrey Serial Correlatio

33、n LM Test:F-statistic20.49152    Probability0.000030Obs*R-squared14.84303    Probability0.000598Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 07/29/12 Time: 09:51Presample missing value lagged residuals set to zero.VariableCoefficientStd. E

34、rrort-StatisticProb.  C14.0646332.409870.4339610.6698X-0.0006280.000742-0.8463030.4091RESID(-1)1.1084880.1761276.2936960.0000RESID(-2)-0.9181750.226004-4.0626430.0008R-squared0.706811    Mean dependent var1.30E-13Adjusted R-squared0.655072    S.D. de

35、pendent var158.1566S.E. of regression92.88633    Akaike info criterion12.07027Sum squared resid146673.8    Schwarz criterion12.26923Log likelihood-122.7379    F-statistic13.66102Durbin-Watson stat1.950263    Prob(F-stati

36、stic)0.000087由于e(-2)的t检验显著，说明模型一的随机误差项确实存在二阶正序列相关性，结合该二阶自回归模型的DW值为1.95，基本确定不存在更高阶的序列相关。当然可以继续引入滞后三阶检验如下：Breusch-Godfrey Serial Correlation LM Test:F-statistic12.85743    Probability0.000157Obs*R-squared14.84303    Probability0.001956Test Equation:Dependent Var

37、iable: RESIDMethod: Least SquaresDate: 07/29/12 Time: 09:52Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.  C14.0646733.407340.4210050.6794X-0.0006280.000765-0.8209340.4237RESID(-1)1.1082060.2713274.0844010.0009RESID(-2)-0.9175590.499523-1

38、.8368700.0849RESID(-3)-0.0006010.431119-0.0013950.9989R-squared0.706811    Mean dependent var1.30E-13Adjusted R-squared0.633514    S.D. dependent var158.1566S.E. of regression95.74504    Akaike info criterion12.16551Sum squared resid146673.

39、8    Schwarz criterion12.41421Log likelihood-122.7379    F-statistic9.643071Durbin-Watson stat1.950030    Prob(F-statistic)0.000363 可以看出并不存在三阶序列相关。（二）广义差分法修正1、方法原理参考教材自己推导二元线性回归模型存在二阶序列相关时的广义差分模型。2、上机实现结果分析 模型二：Dependent Variable: YMethod:

40、Least SquaresDate: 07/29/12 Time: 09:55Sample (adjusted): 1992 2011Included observations: 20 after adjustmentsConvergence achieved after 8 iterationsVariableCoefficientStd. Errort-StatisticProb.  C160.0892182.89170.8753230.3936X0.0214690.0030726.9889750.0000AR(1)0.7300780.2033523.5902230.0

41、023R-squared0.964570    Mean dependent var958.0450Adjusted R-squared0.960402    S.D. dependent var655.9980S.E. of regression130.5388    Akaike info criterion12.71870Sum squared resid289686.3    Schwarz criterion12.86806L

42、og likelihood-124.1870    F-statistic231.4107Durbin-Watson stat1.116066    Prob(F-statistic)0.000000Inverted AR Roots      .73 由于AR(1)通过t检验，说明模型一确实至少存在一阶序列相关，结合DW值为1.12，怀疑存在更高阶序列相关性， LM检验结果如下： Breusch-Godfrey Serial Correlation LM

43、 Test:F-statistic6.380262    Probability0.009885Obs*R-squared9.193288    Probability0.010086Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 07/29/12 Time: 09:57Presample missing value lagged residuals set to zero.VariableCoefficientStd. Error

44、t-StatisticProb.  C80.86347145.26430.5566650.5860X-0.0035540.002602-1.3655560.1922AR(1)-0.5728410.437314-1.3099090.2099RESID(-1)1.0291570.3395413.0310220.0084RESID(-2)-0.1879230.598223-0.3141360.7577R-squared0.459664    Mean dependent var-7.24E-11Adjusted R-squared0.315

45、575    S.D. dependent var123.4773S.E. of regression102.1528    Akaike info criterion12.30313Sum squared resid156527.8    Schwarz criterion12.55207Log likelihood-118.0313    F-statistic3.190131Durbin-Watson stat2.021319&#

46、160;   Prob(F-statistic)0.043963说明模型一在一阶广义差分修正后仍然存在序列相关性。继续引入AR(2)进行修正。模型三：Dependent Variable: YMethod: Least SquaresDate: 07/29/12 Time: 09:58Sample (adjusted): 1993 2011Included observations: 19 after adjustmentsConvergence achieved after 5 iterationsVariableCoefficientStd. Errort-S

47、tatisticProb.  C210.523342.671174.9336180.0002X0.0189160.00098719.173600.0000AR(1)1.0954460.1852545.9131940.0000AR(2)-0.9453840.250542-3.7733570.0018R-squared0.981385    Mean dependent var998.3158Adjusted R-squared0.977662    S.D. dependent var648.07

48、72S.E. of regression96.86089    Akaike info criterion12.16909Sum squared resid140730.5    Schwarz criterion12.36792Log likelihood-111.6064    F-statistic263.6012Durbin-Watson stat2.002336    Prob(F-statistic)0.000000Inve

49、rted AR Roots .55+.80i     .55-.80i由于AR(1)和AR(2)都通过t检验，说明模型一确实至少存在二阶序列相关，结合DW值为2.00，确定不存在更高阶序列相关性，LM检验结果如下：Breusch-Godfrey Serial Correlation LM Test:F-statistic0.880914    Probability0.437745Obs*R-squared2.267656    Probability0.

50、321799 可以看出，二阶广义差分修正后的模型三不再存在序列相关性，可以作为最终选择模型。三、多元线性回归模型分析中解释变量的选取问题多重共线性的检验与修正假设用解释变量x1、x2、x3、x4来解释Y。模型一：Dependent Variable: YMethod: Least SquaresDate: 07/29/12 Time: 10:35Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.  C-43872.2714512.82-3.023002

51、0.0086X14.5610550.24699318.466320.0000X20.6704910.1300225.1567600.0001R-squared0.961029    Mean dependent var44127.11Adjusted R-squared0.955833    S.D. dependent var4409.100S.E. of regression926.6166    Akaike info criterion16.65197Sum squa

52、red resid12879274    Schwarz criterion16.80036Log likelihood-146.8677    F-statistic184.9504Durbin-Watson stat2.014913    Prob(F-statistic)0.000000模型二：Dependent Variable: YMethod: Least SquaresDate: 07/29/12 Time: 10:36Sample: 1994 2011Incl

53、uded observations: 18VariableCoefficientStd. Errort-StatisticProb.  C-11978.1814072.92-0.8511510.4090X15.2559350.26859519.568280.0000X20.4084320.1219743.3485220.0048X3-0.1946090.054533-3.5686370.0031R-squared0.979593    Mean dependent var44127.11Adjusted R-squared0.9752

54、20    S.D. dependent var4409.100S.E. of regression694.0715    Akaike info criterion16.11616Sum squared resid6744293.    Schwarz criterion16.31402Log likelihood-141.0454    F-statistic224.0086Durbin-Watson stat1.528658    Prob(