第十章习题答案计量经济学

1、第十章习题讲解做单位根检验有个潜规则先从最复杂的模型开始如果最复杂的模型说非平稳那就是非平稳如果最复杂的模型说平稳那么要用简单的模型检验如果所有模型都说是平稳的那就是平稳的10.1答：（1）做利润和红利的连线图 利润图 红利图从图中可以初步判断，利润和红利都是非平稳的。（2）首先对利润进行单位根检验，选择有截距项和时间趋势（trend and intercept），结果如下Null ypothesis: R has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=11)t-Statistic

2、Prob.*Augmented Dickey-Fuller test statistic-1.0.5747Test critical values:1% level-3.5% level-2.10% level-2.Null Hypothesis: PFT has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-1.0.6978Test criti

3、cal values:1% level-4.5% level-3.10% level-3.*MacKinnon (1996) one-sided p-values.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即利润是非平稳的。然后对红利进行单位根检验，选择有截距项和时间趋势，结果如下Null Hypothesis: I has a unit rootExogenous: ConstantLag Length: 3 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test s

4、tatistic1.0.9989Test critical values:1% level-3.5% level-2.10% level-2.Null Hypothesis: BNU has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-2.0.1698Test critical values:1% level-4.5% level-3.10%

5、level-3.*MacKinnon (1996) one-sided p-values.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即红利也是非平稳的。(3)首先对GDP进行平稳性检验，选择只带截距项，结果如下Null Hypothesis: GDP has a unit rootExogenous: ConstantLag Length: 2 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-0.0.8829Test critical val

6、ues:1% level-3.5% level-2.10% level-2.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即GDP是非平稳的。之后对GDP进行一阶差分，并检验其平稳性，结果如下Null Hypothesis: D(GDP) has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-10.036000.0000Test

7、critical values:1% level-4.5% level-3.10% level-3.可以看出GDP经过一阶差分后是平稳的，因此。同理可得，且。10.2（1）对固定厂房设备投资进行平稳性检验，首先先看图从图中我们可以初步判断，固定厂房设备投资可能是非平稳的。之后进行ADF检验，检验结果如下Null Hypothesis: SHEB has a unit rootExogenous: ConstantLag Length: 3 (Automatic based on SIC, MAXLAG=4)t-StatisticProb.*Augmented Dickey-Fuller tes

8、t statistic-0.0.9324Test critical values:1% level-3.5% level-3.10% level-2.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即固定厂房设备投资是非平稳的。（2）对销售量进行平稳性检验，首先先看图从图中我们可以初步判断，销售额可能是非平稳的。之后进行ADF检验，检验结果如下Null Hypothesis: X has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=4)t-StatisticProb.*Au

9、gmented Dickey-Fuller test statistic-0.0.8145Test critical values:1% level-3.5% level-3.10% level-2.Null Hypothesis: XS has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=4)t-StatisticProb.*Augmented Dickey-Fuller test statistic-1.0.6258Test critical values

10、:1% level-4.5% level-3.10% level-3.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即销售额是非平稳的。10.3答：（1）回归结果是虚假的！回归结果如下图Dependent Variable: BNUMethod: Least SquaresDate: 06/03/10 Time: 20:21Sample: 1980Q1 2001Q4Included observations: 88CoefficientStd. Errort-StatisticProb.PFT83120.0000C-13.026447.-1.0.0807R-sq

11、uared0.Mean dependent var69.24205Adjusted R-squared0.S.D. dependent var38.36748S.E. of regression23.74163Akaike info criterion9.Sum squared resid48475.19Schwarz criterion9.Log likelihood-402.5713Hannan-Quinn criter.9.F-statistic141.2085Durbin-Watson stat0.Prob(F-statistic)0.运用经验法则可以看出D.W=0.，所以此回归为伪回

12、归。（2）首先对利润进行一阶差分，选择带时间趋势和截距项Null Hypothesis: D(PFT) has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-7.0.0000Test critical values:1% level-4.5% level-3.10% level-3.*MacKinnon (1996) one-sided p-va

13、lues.可以看出ADF值小于所有临界值，且P值为0，由此可以判定经过一阶差分的利润是平稳的。然后对红利进行一阶差分，选择带时间趋势和截距项Null Hypothesis: D(BNU) has a unit rootExogenous: Constant, Linear TrendLag Length: 2 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-6.0.0000Test critical values:1% level-4.5% level-3.10

14、% level-3.*MacKinnon (1996) one-sided p-values.可以看出ADF值小于所有临界值，且P值为0，由此可以判定经过一阶差分的红利也是平稳的。由此可以看出利润和红利都是一阶单整。10.5答：（1）首先判断和的平稳性，先看图 从图中我们可以初步判断，和可能是非平稳的。之后进行ADF检验，检验结果如下表1 的ADF检验Null Hypothesis: LNY has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=7)t-Stat

15、isticProb.*Augmented Dickey-Fuller test statistic-1.0.7439Test critical values:1% level-4.5% level-3.10% level-3.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即是非平稳的。表2 的ADF检验Null Hypothesis: LNX has a unit rootExogenous: Constant, Linear TrendLag Length: 7 (Automatic based on SIC, MAXLAG=7)t-StatisticProb.*Augmen

16、ted Dickey-Fuller test statistic1.0.9999Test critical values:1% level-4.5% level-3.10% level-3.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即是非平稳的。（2）确定和的单整数，对和进行一阶差分，并进行ADF检验，检验结果如下表3 的ADF检验Null Hypothesis: D(LNY) has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=7)t-S

17、tatisticProb.*Augmented Dickey-Fuller test statistic-3.0.0708Test critical values:1% level-4.5% level-3.10% level-3.表4 的ADF检验Null Hypothesis: D(LNX) has a unit rootExogenous: Constant, Linear TrendLag Length: 6 (Automatic based on SIC, MAXLAG=7)t-StatisticProb.*Augmented Dickey-Fuller test statistic

18、-8.0.0000Test critical values:1% level-4.5% level-3.10% level-3.从表中我们可以看出和不是同阶单整，因此不存在协整关系。10.6答：（1）首先对进行平稳性检验，选择带时间趋势和截距项Null Hypothesis: X has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic1.1.000

19、0Test critical values:1% level-4.5% level-3.10% level-3.*MacKinnon (1996) one-sided p-values.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即是非平稳的。然后对进行平稳性检验，选择带时间趋势和截距项Null Hypothesis: Y has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=9)t-StatisticProb.*Augmented Dicke

20、y-Fuller test statistic0.0.9997Test critical values:1% level-4.5% level-3.10% level-3.*MacKinnon (1996) one-sided p-values.可以看到ADF值大于所有临界值且P值很大，所以不能拒绝原假设，即也是非平稳的。(2)对和分别进行一阶差分首先对进行一阶差分，选择带时间趋势和截距项Null Hypothesis: D(X) has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on

21、SIC, MAXLAG=9)t-StatisticProb.*Augmented Dickey-Fuller test statistic-5.0.0004Test critical values:1% level-4.5% level-3.10% level-3.*MacKinnon (1996) one-sided p-values.可以看出ADF值小于所有临界值，且P值几乎为0，由此可以判定经过一阶差分的是平稳的。然后对进行一阶差分，选择只带截距项Null Hypothesis: D(Y) has a unit rootExogenous: ConstantLag Length: 0 (

22、Automatic based on SIC, MAXLAG=9)t-StatisticProb.*Augmented Dickey-Fuller test statistic-4.0.0002Test critical values:1% level-3.5% level-2.10% level-2.*MacKinnon (1996) one-sided p-values.可以看出ADF值小于所有临界值，且P值几乎为0，由此可以判定经过一阶差分的也是平稳的。由此可以看出和都是一阶单整。EG两步：第一步得协整回归方程：Dependent Variable: XMethod: Least Squ

23、aresDate: 06/03/10 Time: 20:54Sample: 1950 1990Included observations: 41CoefficientStd. Errort-StatisticProb.Y61900.0000C-0.0.-3.0.0010R-squared0.Mean dependent var5.Adjusted R-squared0.S.D. dependent var0.S.E. of regression0.Akaike info criterion-3.Sum squared resid0.Schwarz criterion-3.Log likelihood73.44261Hannan-Quinn criter.-3.F-statistic7614.640Durbin-Watson stat1.Prob(F-statistic)0. 第二步：得到残差序列，对残差序列进行平稳性检验 Null Hypothesis: E has a unit rootExogenous: NoneLag Length: 0 (Automatic based on SIC, MAXLAG=9)t-Statistic