第十章練習(xí)題參考解答

1、 第十章練習(xí)題參考解答練習(xí)題10.1 下表是某國的宏觀經(jīng)濟(jì)數(shù)據(jù)（GDP國內(nèi)生產(chǎn)總值，單位：10億美元；PDI個(gè)人可支配收入，單位：10億美元；PCE個(gè)人消費(fèi)支出，單位：10億美元；利潤公司稅后利潤，單位：10億美元；紅利公司凈紅利支出，單位：10億美元）。 某國1980年到2001年宏觀經(jīng)濟(jì)季度數(shù)據(jù)季度GDPPDIPCE利潤紅利季度GDPPDIPCE利潤紅利Jan-802878.81990.61800.544.724.5Jan-913860.52783.72475.5159.3564Feb-802860.32020.11087.544.423.9Feb-913844.42776.72476.1

2、143.768.4Mar-802896.62045.31824.744.923.3Mar-913864.52814.12487.4147.671.9Apr-802873.72045.21821.242.123.1Apr-913803.12808.82468.8140.372.4Jan-812942.92073.91849.948.823.8Jan-923756.127952484114.470Feb-812947.420981863.550.723.7Feb-923771.12824.82488.911468.4Mar-8129662106.61876.954.223.8Mar-923754.

3、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-823089.72149.11963.360.125.5Feb-933886.52867260413380.5Mar-823125.82193.91989.162.826.1Mar-933944.429032639145.783.1Apr-823175.322722032.168.326.5Apr-

4、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-833264.32337.92073.781.328.3Mar-944166.43102.72754.6141.881.7Apr-833289.12382.72067.48529.4Apr-944194.23118.52784.8136.383.4Jan-843259.42334.7205

5、0.88929.8Jan-954221.83123.62824.9125.287.2Feb-843267.72304.5205991.230.4Feb-954254.83189.62849.7124.890.8Mar-843239.123152065.597.130.9Mar-9543093156.52893.3129.894.1Apr-843226.42313.72039.986.830.5Apr-954333.53178.72895.313497.4Jan-8531542282.52051.875.830Jan-964390.53227.52922.4109.2105.1Feb-85319

6、0.42390.32086.98129.7Feb-964387.73281.42947.9106110.7Mar-853249.92354.42114.497.830.1Mar-964412.63272.62993.4111112.3Apr-853292.52389.42137103.430.6Apr-964427.13266.23012.5119.2111Jan-863356.72424.52179.3108.432.6Jan-9744603295.23011.5140.2108Feb-863369.22434.92194.7109.235Feb-974515.33241.73045.815

7、7.9105.5Mar-8633812444.7221311036.6Mar-974559.33285.73075.8169.1105.1Apr-863416.32459.52242110.338.3Apr-974625.53335.83074.6176106.3Jan-872466.424632271.3121.539.2Jan-984655.33380.13128.2195.5109.6Feb-8735252490.32280.8129.740Feb-984704.83386.33147.8207.2113.3Mar-873574.425412302.6135.141.4Mar-98477

8、9.73443.13170.6213.4117.5Apr-873567.22556.22331.6134.842.4Apr-984779.73473.93202.9226121Jan-883591.82587.32347.1137.543.5Jan-994809.83473.93200.9221.3124.6Feb-883707.72631.9239415444.5Feb-994832.43450.93208.6206.2127Mar-883735.62653.22404.515846.6Mar-994845.63446.93241.1195.7129Apr-883779.62680.9242

9、1.6167.848.9Apr-994859.734933241.6203130.7Jan-893780.82699.22437.9168.250.5Jan-004880.83531.43258.8199.1132.3Feb-893784.32697.62435.4174.151.8Feb-004832.43545.33258.6193.7132.5Mar-893807.52715.32454.7178.152.7Mar-004903.335473281.2196.3133.8Apr-893814.62728.12465.4173.457.6Apr-004855.13529.53251.819

10、9136.2Jan-903830.82742.92464.6174.357.6Jan-0148243514.83241.1189.7137.8Feb-903732.626922414.2144.558.7Feb-014840.73537.43252.4182.7136.7Mar-903733.52722.52440.315159.3Mar-014862.73539.93271.2189.6138.1Apr-903808.527772469.2154.660.5Apr-0148683547.53271.1190.3138.5（1） 畫出利潤和紅利的散點(diǎn)圖，并直觀地考察這兩個(gè)時(shí)間序列是否是平穩(wěn)的。

11、(2) 應(yīng)用單位根檢驗(yàn)分別檢驗(yàn)兩個(gè)時(shí)間序列是否是平穩(wěn)的。10.2 下表數(shù)據(jù)是1970-1991年美國制造業(yè)固定廠房設(shè)備投資Y和銷售量X，以10億美元計(jì)價(jià)，且經(jīng)過季節(jié)調(diào)整，根據(jù)該數(shù)據(jù)，判斷廠房開支和銷售量序列是否平穩(wěn)？ 年份固定廠房設(shè)備投資銷售量年份固定廠房設(shè)備投資銷售量197036.9952.8051981128.68168.129197133.655.9061982123.97163.351197235.4263.0271983117.35172.547197342.3572.0271984139.61190.682197452.4884.791985182.88194.538197553.

12、6686.5891986137.95194.657197658.5398.7971987141.06206.326197767.48113.2011988163.45223.541197878.13126.9051989183.8232.724197995.13143.9361990192.61239.4591980112.6154.391991182.81235.14210.3 根據(jù)習(xí)題10.1的數(shù)據(jù)，回答如下問題： (1) 如果利潤和紅利時(shí)間序列并不是平穩(wěn)的，而如果你以利潤來回歸紅利，那么回歸的結(jié)果會是虛假的嗎？為什么？你是如何判定的，說明必要的計(jì)算。(2) 取利潤和紅利兩個(gè)時(shí)間序列的一階

13、差分，確定一階差分時(shí)間序列是否是平穩(wěn)的。10.4 從中國統(tǒng)計(jì)年鑒中取得1978年2005年全國全社會固定資產(chǎn)投資額的時(shí)間序列數(shù)據(jù)，檢驗(yàn)其是否平穩(wěn)，并確定其單整階數(shù)。10.5 下表是19782003年中國財(cái)政收入Y和稅收X的數(shù)據(jù)（單位：億元），判斷l(xiāng)nY和lnX的平穩(wěn)性，如果是同階單整的，檢驗(yàn)它們之間是否存在協(xié)整關(guān)系，如果協(xié)整，則建立相應(yīng)的協(xié)整模型。年度財(cái)政收入Y稅收X年度財(cái)政收入Y稅收X19781132.26519.2819956242.26038.0419801159.93571.719967407.996909.8219852004.822040.7919978651.148234.041

14、9892664.92727.419989875.959262.819902937.12821.86199911444.0810682.5819913149.4829902312581.5119923483.373296.91200116386.0415301.3819934348.954255.3200218903.6417636.4519945218.15126.88200321715.2520017.31（1） 10.6 下表是某地區(qū)消費(fèi)模型建立所需的數(shù)據(jù)，對實(shí)際人均年消費(fèi)支出C和人均年收人Y（單位：元）年份人均消費(fèi)支出C人均年收人Y年份人均消費(fèi)支出C人均年收人Y

15、195092.28151.201971151.20274.08195197.92 165.60 1972163.20 286.68 1952105.00 182.40 1973165.00 288.00 1953118.08 198.48 1974170.52 293.52 1954121.92 203.64 1975170.16 301.92 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

16、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 1963132.72 232.68 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 1

17、094.64 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 分別取對數(shù)，得到：（2） 對進(jìn)行平穩(wěn)性檢驗(yàn)。（3） 用EG兩步檢驗(yàn)法對進(jìn)行協(xié)整性檢驗(yàn)并建立誤差修正模型。 分析該模型的經(jīng)濟(jì)意義。練習(xí)題參考解答練習(xí)題10.1參考解答利潤和紅利的散點(diǎn)圖如下： 從圖中看出，利潤和紅利序列存在趨勢，均值和方差不穩(wěn)定，因此可能非平穩(wěn)。下面用ADF檢驗(yàn)是否平穩(wěn)。選擇帶截距和時(shí)間趨勢的模型進(jìn)行估計(jì)，結(jié)果如

18、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 statistic-1.7970790.6978Test critical values:1% level-4.0669815% level-3.46229210% level-3.157475*MacKinnon (1996) one-sided p-values

19、.Augmented Dickey-Fuller Test EquationDependent Variable: D(PFT)Method: Least SquaresDate: 07/23/05 Time: 11:59Sample (adjusted): 1980Q2 2001Q4Included observations: 87 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.PFT(-1)-0.0722110.040182-1.7970790.0759C6.9586083.1976892.1761360.032

20、4TREND(1980Q1)0.0936840.0763551.2269520.2233R-squared0.040009Mean dependent var1.673563Adjusted R-squared0.017152S.D. dependent var9.788094S.E. of regression9.703787Akaike info criterion7.416784Sum squared resid7909.732Schwarz criterion7.501815Log likelihood-319.6301F-statistic1.750424Durbin-Watson

21、stat1.613622Prob(F-statistic)0.179976Null Hypothesis: BNU has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on SIC, MAXLAG=11)t-StatisticProb.*Augmented Dickey-Fuller test statistic-2.8935590.1698Test critical values:1% level-4.0682905% level-3.46291210% level-3.157836*M

22、acKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(BNU)Method: Least SquaresDate: 07/23/05 Time: 12:04Sample (adjusted): 1980Q3 2001Q4Included observations: 86 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.BNU(-1)-0.0667520.023069-2.8935590.

23、0049D(BNU(-1)0.5268290.0895125.8855570.0000C0.4884830.3491361.3991170.1655TREND(1980Q1)0.1067690.0349843.0519430.0031R-squared0.386247Mean dependent var1.332558Adjusted R-squared0.363793S.D. dependent var1.930647S.E. of regression1.539934Akaike info criterion3.746751Sum squared resid194.4546Schwarz

24、criterion3.860907Log likelihood-157.1103F-statistic17.20143Durbin-Watson stat1.859383Prob(F-statistic)0.000000由上表可知，利潤和紅利的t統(tǒng)計(jì)量值是大于顯著性水平為10的臨界值，不能拒絕原假設(shè)，表明序列是非平穩(wěn)的。練習(xí)題10.3參考解答 根據(jù)習(xí)題10.1的數(shù)據(jù)，回答如下問題： (1) 如果利潤和紅利時(shí)間序列并不是平穩(wěn)的，而如果你以利潤來回歸紅利，那么回歸的結(jié)果會是虛假的嗎？為什么？你是如何判定的，說明必要的計(jì)算。(2) 取利潤和紅利兩個(gè)時(shí)間序列的一階差分，確定一階差分時(shí)間序列是否是平穩(wěn)的

25、。解答：（1）回歸的結(jié)果是虛假的。以利潤回歸紅利，得到下面的結(jié)果：Dependent Variable: BNUMethod: Least SquaresDate: 07/23/05 Time: 12:09Sample: 1980Q1 2001Q4Included observations: 88VariableCoefficientStd. Errort-StatisticProb.C-13.026447.371237-1.7671980.0807PFT0.6282190.05286611.883120.0000R-squared0.621493Mean dependent var69.24

26、205Adjusted R-squared0.617092S.D. dependent var38.36748S.E. of regression23.74163Akaike info criterion9.194802Sum squared resid48475.19Schwarz criterion9.251105Log likelihood-402.5713F-statistic141.2085Durbin-Watson stat0.083355Prob(F-statistic)0.000000因?yàn)檫h(yuǎn)大于DW值，殘差序列非平穩(wěn)，說明存在偽回歸。（2）對利潤和紅利取一階差分，得以下面結(jié)果：

27、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-7.7181000.0000Test critical values:1% level-4.0682905% level-3.46291210% level-3.157836*MacKinnon (1996) one-sided p-values

28、.Augmented Dickey-Fuller Test EquationDependent Variable: D(PFT,2)Method: Least SquaresDate: 07/23/05 Time: 12:22Sample (adjusted): 1980Q3 2001Q4Included observations: 86 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(PFT(-1)-0.8351150.108202-7.7181000.0000C2.3269212.1893431.0628400

29、.2909TREND(1980Q1)-0.0204090.042661-0.4784110.6336R-squared0.417839Mean dependent var0.011628Adjusted R-squared0.403811S.D. dependent var12.70039S.E. of regression9.806382Akaike info criterion7.438205Sum squared resid7981.706Schwarz criterion7.523821Log likelihood-316.8428F-statistic29.78615Durbin-W

30、atson 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-StatisticProb.*Augmented Dickey-Fuller test statistic-6.2335670.0000Test critical values:1% level-4.0710065% level-3.46419810% level-3

31、.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 (adjusted): 1981Q1 2001Q4Included observations: 84 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(BNU(-1)-0.7434640.1192

32、68-6.2335670.0000D(BNU(-1),2)0.2961730.1128962.6234120.0104D(BNU(-2),2)0.3445050.1090163.1601280.0022C0.3832340.3578721.0708700.2875TREND(1980Q1)0.0139560.0073741.8925170.0621R-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從