第十章练习题参考解答

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1、Four short words sum up what has lifted most successful individuals above the crowd: a little bit more.-author-date第十章练习题参考解答第十章习题解答 第十章练习题参考解答练习题10.1 下表是某国的宏观经济数据（GDP国内生产总值，单位：10亿美元；PDI个人可支配收入，单位：10亿美元；PCE个人消费支出，单位：10亿美元；利润公司税后利润，单位：10亿美元；红利公司净红利支出，单位：10亿美元）。 某国1980年到2001年宏观经济季度数据季度GDPPDIPCE利润红利季度G

2、DPPDIPCE利润红利Jan-802878.81990.61800.544.724.5Jan-913860.52783.72475.5159.3564Feb-802860.32020.11087.544.423.9Feb-913844.42776.72476.1143.768.4Mar-802896.62045.31824.744.923.3Mar-913864.52814.12487.4147.671.9Apr-802873.72045.21821.242.123.1Apr-913803.12808.82468.8140.372.4Jan-812942.92073.91849.948.82

3、3.8Jan-923756.127952484114.470Feb-812947.420981863.550.723.7Feb-923771.12824.82488.911468.4Mar-8129662106.61876.954.223.8Mar-923754.428292502.5114.669.2Apr-812980.82121.11904.655.723.7Apr-923759.62832.62539.3109.972.5Jan-823037.32129.71929.359.425Jan-933783.32843.62556.5113.677Feb-823089.72149.11963

4、.360.125.5Feb-933886.52867260413380.5Mar-823125.82193.91989.162.826.1Mar-933944.429032639145.783.1Apr-823175.322722032.168.326.5Apr-934012.12960.62678.2141.684.2Jan-833253.32300.72063.979.127Jan-944221.83123.62824.3125.287.2Feb-833267.62315.2206281.227.8Feb-9441443065.92741152.682.2Mar-833264.32337.

5、92073.781.328.3Mar-944166.43102.72754.6141.881.7Apr-833289.12382.72067.48529.4Apr-944194.23118.52784.8136.383.4Jan-843259.42334.72050.88929.8Jan-954221.83123.62824.9125.287.2Feb-843267.72304.5205991.230.4Feb-954254.83189.62849.7124.890.8Mar-843239.123152065.597.130.9Mar-9543093156.52893.3129.894.1Ap

6、r-843226.42313.72039.986.830.5Apr-954333.53178.72895.313497.4Jan-8531542282.52051.875.830Jan-964390.53227.52922.4109.2105.1Feb-853190.42390.32086.98129.7Feb-964387.73281.42947.9106110.7Mar-853249.92354.42114.497.830.1Mar-964412.63272.62993.4111112.3Apr-853292.52389.42137103.430.6Apr-964427.13266.230

7、12.5119.2111Jan-863356.72424.52179.3108.432.6Jan-9744603295.23011.5140.2108Feb-863369.22434.92194.7109.235Feb-974515.33241.73045.8157.9105.5Mar-8633812444.7221311036.6Mar-974559.33285.73075.8169.1105.1Apr-863416.32459.52242110.338.3Apr-974625.53335.83074.6176106.3Jan-872466.424632271.3121.539.2Jan-9

8、84655.33380.13128.2195.5109.6Feb-8735252490.32280.8129.740Feb-984704.83386.33147.8207.2113.3Mar-873574.425412302.6135.141.4Mar-984779.73443.13170.6213.4117.5Apr-873567.22556.22331.6134.842.4Apr-984779.73473.93202.9226121Jan-883591.82587.32347.1137.543.5Jan-994809.83473.93200.9221.3124.6Feb-883707.72

9、631.9239415444.5Feb-994832.43450.93208.6206.2127Mar-883735.62653.22404.515846.6Mar-994845.63446.93241.1195.7129Apr-883779.62680.92421.6167.848.9Apr-994859.734933241.6203130.7Jan-893780.82699.22437.9168.250.5Jan-004880.83531.43258.8199.1132.3Feb-893784.32697.62435.4174.151.8Feb-004832.43545.33258.619

10、3.7132.5Mar-893807.52715.32454.7178.152.7Mar-004903.335473281.2196.3133.8Apr-893814.62728.12465.4173.457.6Apr-004855.13529.53251.8199136.2Jan-903830.82742.92464.6174.357.6Jan-0148243514.83241.1189.7137.8Feb-903732.626922414.2144.558.7Feb-014840.73537.43252.4182.7136.7Mar-903733.52722.52440.315159.3M

11、ar-014862.73539.93271.2189.6138.1Apr-903808.527772469.2154.660.5Apr-0148683547.53271.1190.3138.5（1） 画出利润和红利的散点图，并直观地考察这两个时间序列是否是平稳的。(2) 应用单位根检验分别检验两个时间序列是否是平稳的。10.2 下表数据是1970-1991年美国制造业固定厂房设备投资Y和销售量X，以10亿美元计价，且经过季节调整，根据该数据，判断厂房开支和销售量序列是否平稳？ 年份固定厂房设备投资销售量年份固定厂房设备投资销售量197036.9952.8051981128.68168.1291

12、97133.655.9061982123.97163.351197235.4263.0271983117.35172.547197342.3572.0271984139.61190.682197452.4884.791985182.88194.538197553.6686.5891986137.95194.657197658.5398.7971987141.06206.326197767.48113.2011988163.45223.541197878.13126.9051989183.8232.724197995.13143.9361990192.61239.4591980112.6154.

13、391991182.81235.14210.3 根据习题10.1的数据，回答如下问题： (1) 如果利润和红利时间序列并不是平稳的，而如果你以利润来回归红利，那么回归的结果会是虚假的吗？为什么？你是如何判定的，说明必要的计算。(2) 取利润和红利两个时间序列的一阶差分，确定一阶差分时间序列是否是平稳的。10.4 从中国统计年鉴中取得1978年2005年全国全社会固定资产投资额的时间序列数据，检验其是否平稳，并确定其单整阶数。10.5 下表是19782003年中国财政收入Y和税收X的数据（单位：亿元），判断lnY和lnX的平稳性，如果是同阶单整的，检验它们之间是否存在协整关系，如果协整，则建立相

14、应的协整模型。年度财政收入Y税收X年度财政收入Y税收X19781132.26519.2819956242.26038.0419801159.93571.719967407.996909.8219852004.822040.7919978651.148234.0419892664.92727.419989875.959262.819902937.12821.86199911444.0810682.5819913149.482990.17200013395.2312581.5119923483.373296.91200116386.0415301.3819934348.954255.3200218

15、903.6417636.4519945218.15126.88200321715.2520017.31（1） 10.6 下表是某地区消费模型建立所需的数据，对实际人均年消费支出C和人均年收人Y（单位：元）年份人均消费支出C人均年收人Y年份人均消费支出C人均年收人Y195092.28151.201971151.20274.08195197.92 165.60 1972163.20 286.68 1952105.00 182.40 1973165.00 288.00 1953118.08 198.48 1974170.52 293.52 1954121.92 203.64 1975170.16 3

16、01.92 1955132.96 211.68 1976177.36 313.80 1956123.84 206.28 1977181.56 330.12 1957137.88 255.48 1978200.40 361.44 1958138.00 226.20 1979219.60 398.76 1959145.08 236.88 1980260.76 491.76 1960143.04 245.40 1981271.08 501.00 1961155.40 240.00 1982290.28 529.20 1962144.24 234.84 1983318.48 522.72 196313

17、2.72 232.68 1984365.40 671.16 1964136.20 238.56 1985418.92 811.80 1965141.12 239.88 1986517.56 988.44 1966132.84 239.04 1987577.92 1094.64 1967139.20 237.48 1988655.76 1231.80 1968140.76 239.40 1989756.24 1374.60 1969133.56 248.04 1990833.76 1522.20 1970144.60 261.48 分别取对数，得到：（2） 对进行平稳性检验。（3） 用EG两步检

18、验法对进行协整性检验并建立误差修正模型。 分析该模型的经济意义。练习题参考解答练习题10.1参考解答利润和红利的散点图如下： 从图中看出，利润和红利序列存在趋势，均值和方差不稳定，因此可能非平稳。下面用ADF检验是否平稳。选择带截距和时间趋势的模型进行估计，结果如下： Null Hypothesis: PFT has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test s

19、tatistic-1.7970790.6978Test critical values:1% level-4.0669815% level-3.46229210% level-3.157475*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(PFT)Method: Least SquaresDate: 07/23/05 Time: 11:59Sample (adjusted): 1980Q2 2001Q4Included observations: 87

20、 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.PFT(-1)-0.0722110.040182-1.7970790.0759C6.9586083.1976892.1761360.0324TREND(1980Q1)0.0936840.0763551.2269520.2233R-squared0.040009Mean dependent var1.673563Adjusted R-squared0.017152S.D. dependent var9.788094S.E. of regression9.703787Aka

21、ike info criterion7.416784Sum squared resid7909.732Schwarz criterion7.501815Log likelihood-319.6301F-statistic1.750424Durbin-Watson stat1.613622Prob(F-statistic)0.179976Null Hypothesis: BNU has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on SIC, MAXLAG=11)t-StatisticPr

22、ob.*Augmented Dickey-Fuller test statistic-2.8935590.1698Test critical values:1% level-4.0682905% level-3.46291210% level-3.157836*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(BNU)Method: Least SquaresDate: 07/23/05 Time: 12:04Sample (adjusted): 1980

23、Q3 2001Q4Included observations: 86 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.BNU(-1)-0.0667520.023069-2.8935590.0049D(BNU(-1)0.5268290.0895125.8855570.0000C0.4884830.3491361.3991170.1655TREND(1980Q1)0.1067690.0349843.0519430.0031R-squared0.386247Mean dependent var1.332558Adjusted

24、 R-squared0.363793S.D. dependent var1.930647S.E. of regression1.539934Akaike info criterion3.746751Sum squared resid194.4546Schwarz criterion3.860907Log likelihood-157.1103F-statistic17.20143Durbin-Watson stat1.859383Prob(F-statistic)0.000000由上表可知，利润和红利的t统计量值是大于显著性水平为10的临界值，不能拒绝原假设，表明序列是非平稳的。练习题10.3

25、参考解答 根据习题10.1的数据，回答如下问题： (1) 如果利润和红利时间序列并不是平稳的，而如果你以利润来回归红利，那么回归的结果会是虚假的吗？为什么？你是如何判定的，说明必要的计算。(2) 取利润和红利两个时间序列的一阶差分，确定一阶差分时间序列是否是平稳的。解答：（1）回归的结果是虚假的。以利润回归红利，得到下面的结果：Dependent Variable: BNUMethod: Least SquaresDate: 07/23/05 Time: 12:09Sample: 1980Q1 2001Q4Included observations: 88VariableCoefficient

26、Std. Errort-StatisticProb.C-13.026447.371237-1.7671980.0807PFT0.6282190.05286611.883120.0000R-squared0.621493Mean dependent var69.24205Adjusted R-squared0.617092S.D. dependent var38.36748S.E. of regression23.74163Akaike info criterion9.194802Sum squared resid48475.19Schwarz criterion9.251105Log like

27、lihood-402.5713F-statistic141.2085Durbin-Watson stat0.083355Prob(F-statistic)0.000000因为远大于DW值，残差序列非平稳，说明存在伪回归。（2）对利润和红利取一阶差分，得以下面结果：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 s

28、tatistic-7.7181000.0000Test critical values:1% level-4.0682905% level-3.46291210% level-3.157836*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(PFT,2)Method: Least SquaresDate: 07/23/05 Time: 12:22Sample (adjusted): 1980Q3 2001Q4Included observations:

29、86 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(PFT(-1)-0.8351150.108202-7.7181000.0000C2.3269212.1893431.0628400.2909TREND(1980Q1)-0.0204090.042661-0.4784110.6336R-squared0.417839Mean dependent var0.011628Adjusted R-squared0.403811S.D. dependent var12.70039S.E. of regression9.806

30、382Akaike info criterion7.438205Sum squared resid7981.706Schwarz criterion7.523821Log likelihood-316.8428F-statistic29.78615Durbin-Watson stat1.995853Prob(F-statistic)0.000000Null Hypothesis: D(BNU) has a unit rootExogenous: Constant, Linear TrendLag Length: 2 (Automatic based on SIC, MAXLAG=11)t-St

31、atisticProb.*Augmented Dickey-Fuller test statistic-6.2335670.0000Test critical values:1% level-4.0710065% level-3.46419810% level-3.158586*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(BNU,2)Method: Least SquaresDate: 07/23/05 Time: 12:23Sample (adju

32、sted): 1981Q1 2001Q4Included observations: 84 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(BNU(-1)-0.7434640.119268-6.2335670.0000D(BNU(-1),2)0.2961730.1128962.6234120.0104D(BNU(-2),2)0.3445050.1090163.1601280.0022C0.3832340.3578721.0708700.2875TREND(1980Q1)0.0139560.0073741.89251

33、70.0621R-squared0.338294Mean dependent var0.007143Adjusted R-squared0.304790S.D. dependent var1.834330S.E. of regression1.529451Akaike info criterion3.745373Sum squared resid184.7984Schwarz criterion3.890065Log likelihood-152.3057F-statistic10.09710Durbin-Watson stat2.058616Prob(F-statistic)0.000001

34、从检验结果看，在1、5、10三个显著性水平下， t检验统计量值均小于相应临界值，从而拒绝，表明利润和红利的差分序列不存在单位根，是平稳序列。即两个序列是一阶单整的。练习题10.5参考解答 首先判断lnY 和lnX的平稳性。由上表可知，lnY 和lnX的t统计量值是大于显著性水平为10的临界值，不能拒绝原假设，表明序列是非平稳的。对其进行一阶差分，结果如下：可见lnY和lnX都是一阶单整的，可以进行协整性分析。下面进行协整性分析：为了lnY 和lnX之间是否存在协整关系，我们先作两变量之间的回归，然后检验回归残差的平稳性。Dependent Variable: LNYMethod: Least

35、SquaresDate: 07/21/05 Time: 14:38Sample(adjusted): 1978 1995Included observations: 18 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1.3924910.3371084.1306900.0008LNX0.8503690.03942521.569210.0000R-squared0.966752 Mean dependent var8.611693Adjusted R-squared0.964674 S.D. dep

36、endent var0.908082S.E. of regression0.170676 Akaike info criterion-0.593657Sum squared resid0.466086 Schwarz criterion-0.494727Log likelihood7.342914 F-statistic465.2306Durbin-Watson stat0.657467 Prob(F-statistic)0.000000估计的回归模型为： 下面检查残差的平稳性：ADF Test Statistic-2.441856281 1% Critical Value*-2.71583455574 5% Critical Value-1.96271170588 10% Critical Value-1.62624704838从t统计量的结果看，t 值大于显著性水平为1%时的临界值，小于显著性水平为5%的临界值，说明在5%的显著性水平性我们可以拒绝原假设，即在5%的显著性水平性不存在单位根，也就是说残差序列此时是平稳的。说明lnY和lnX具有协整性关系。-