1、計量經(jīng)濟上機題及答案 習題6.1Dependent Variable: YMethod: Least SquaresDate: 12/11/08 Time: 15:28Sample: 1960 1995Included observations: 36VariableCoefficientStd. Errort-StatisticProb. C-9.4287452.504347-3.7649510.0006X0.9358660.007467125.34110.0000R-squared0.997841 Mean dependent var289.9444Adjusted R-squared0.

2、997777 S.D. dependent var95.82125S.E. of regression4.517862 Akaike info criterion5.907908Sum squared resid693.9767 Schwarz criterion5.995881Log likelihood-104.3423 F-statistic15710.39Durbin-Watson stat0.523428 Prob(F-statistic)0.000000(2.5043) (0.0075)t = (-3.7650) (125.3411)DW = 0.52342時， ，DW=0.523

3、428 dU，說明廣義差分模型中已無自相關(guān)。同時，判定系數(shù)R2、t、F統(tǒng)計量均到達理想水平。最終的消費模型為:Y t = 14.043975+0.948671X t習題6.6Dependent Variable: LOG(Y)Method: Least SquaresDate: 12/11/08 Time: 15:44Sample: 1980 2000Included observations: 21VariableCoefficientStd. Errort-StatisticProb. X-0.0006870.000137-5.0062310.0001LOG(X)1.3642040.013

4、92497.978020.0000R-squared0.930002 Mean dependent var8.039307Adjusted R-squared0.926318 S.D. dependent var0.565486S.E. of regression0.153498 Akaike info criterion-0.819866Sum squared resid0.447671 Schwarz criterion-0.720388Log likelihood10.60859 Durbin-Watson stat0.83934910.000137 0.013924 DW=0.8393

5、49 原模型存在一階正自相關(guān)。2Dependent Variable: DYMethod: Least SquaresDate: 12/12/08 Time: 15:57Sample(adjusted): 1981 2000Included observations: 20 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1.2135700.2002896.0591080.0000DX0.8398610.07502311.194670.0000R-squared0.874407 Mean depen

6、dent var3.443699Adjusted R-squared0.867430 S.D. dependent var0.254543S.E. of regression0.092679 Akaike info criterion-1.824701Sum squared resid0.154611 Schwarz criterion-1.725128Log likelihood20.24701 F-statistic125.3206Durbin-Watson stat1.407541 Prob(F-statistic)0.0000000.200289 0.075023查5%顯著水平的DW統(tǒng)

7、計表可知，模型中 DW = 1.407541 該模型無一階自相關(guān)習題7.2 1 Dependent Variable: YMethod: Least SquaresDate: 12/12/08 Time: 16:18Sample(adjusted): 1981 2001Included observations: 21 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-15.104034.729450-3.1936130.0050X0.6292730.0978196.4330310.0000Y(-1

8、)0.2716760.1148582.3653150.0294R-squared0.987125 Mean dependent var109.2167Adjusted R-squared0.985695 S.D. dependent var51.78550S.E. of regression6.193728 Akaike info criterion6.616515Sum squared resid690.5208 Schwarz criterion6.765733Log likelihood-66.47341 F-statistic690.0561Durbin-Watson stat1.51

9、8595 Prob(F-statistic)0.000000 =1.297278 查標準正態(tài)分布臨界值=1.96，由于h=1.297278，那么接受原假設(shè)，說明自回歸模型不存在一階自相關(guān)。經(jīng)濟意義：預(yù)期固定資產(chǎn)投資額與當期銷售額有關(guān)。當期銷售額每增加1元，預(yù)期固定資產(chǎn)投資平均增加0.864001元。2變換模型genr lny=log(y)genr lnx=log(x)ls lny c lnx lny(-1)Dependent Variable: LNYMethod: Least SquaresDate: 12/10/08 Time: 18:55Sample(adjusted): 1981 20

10、01Included observations: 21 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-1.0780460.184144-5.8543660.0000LNX0.9045220.1112438.1310390.0000LNY(-1)0.2600330.0877992.9616840.0084R-squared0.993725 Mean dependent var4.559823Adjusted R-squared0.993028 S.D. dependent var0.562953S

11、.E. of regression0.047007 Akaike info criterion-3.145469Sum squared resid0.039774 Schwarz criterion-2.996251Log likelihood36.02742 F-statistic1425.219Durbin-Watson stat1.479333 Prob(F-statistic)0.0000000.184144 0.111243 0.087799=0.739967 =1.303128 查標準正態(tài)分布臨界值=1.96，由于h=1.303128，那么拒絕接受原假設(shè)，說明自回歸模型存在一階自相

12、關(guān)。經(jīng)濟意義：預(yù)期銷售額每增加1元，當期固定資產(chǎn)投資額就平均增加元。4Dependent Variable: YMethod: Least SquaresDate: 12/11/08 Time: 16:41Sample(adjusted): 1984 2001Included observations: 18 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-35.492348.192884-4.3320930.0007PDL01-0.0312280.123416-0.2530310.8039PDL

13、02-0.2523360.062441-4.0411820.0012PDL030.1043920.0623111.6753380.1160R-squared0.984670Mean dependent var121.2322Adjusted R-squared0.981385S.D. dependent var45.63348S.E. of regression6.226131Akaike info criterion6.688517Sum squared resid542.7059Schwarz criterion6.886378Log likelihood-56.19666F-statis

14、tic299.7429Durbin-Watson stat1.130400Prob(F-statistic)0.000000 Lag Distribution of XiCoefficientStd. ErrorT-Statistic . *|0 0.89101 0.17456 5.10425 . * |1 0.32550 0.08998 3.61759 *. |2-0.03123 0.12342-0.25303 * . |3-0.17917 0.08488-2.11094 * . |4-0.11833 0.18034-0.65616Sum of Lags 0.88778 0.03007 29

15、.5262 DW=1.130400 DW值落在無法判斷的區(qū)域，該模型無法判斷是否存在一階自相關(guān)。經(jīng)濟意義：當期銷售額每增加1元，當期固定投資額平均增加0.89101元。前一期銷售額每增加1元，當期固定投資額平均增加0.32550元。前第二期銷售額每增加1元，當期固定投資額平均減少0.03123元。前第三期銷售額每增加1元，當期固定投資額平均減少0.17917元。前第四期銷售額每增加1元，當期固定投資額平均減少0.11833元。習題8.4答：引入虛擬變量的兩種根本方法是加法類型和乘法類型。加法分為四種情況，加法方式引入虛擬變量改變的是截距，其適用以下四個根本類型：解釋變量只有一個分成兩種相互排斥

16、類型的定性變量而無定量變量的回歸；解釋變量包含一個定量變量和一個分為兩種類型定性變量的回歸；解釋變量包含一個定量變量和一個兩種以上類型的定性變量回歸；解釋變量包含一個定量變量和兩個定性變量的回歸。乘法方式引入虛擬變量改變的是斜率，其作用在于比擬兩個回歸模型；分析因素間的交互影響；提高模型對現(xiàn)實經(jīng)濟現(xiàn)象的描述精度。做回歸模型的比擬和結(jié)構(gòu)變化檢驗時，用一個回歸替代了多個回歸，簡化了分析過程，方便的對模型結(jié)構(gòu)的差異做各種假設(shè)檢驗，合并了的回歸模型增加了自由度，提高了參數(shù)估計的精確性習題 8.2季度影響使利潤平均值發(fā)生差異，應(yīng)用加法引入虛擬變量。如果季度影響使利潤對銷售額的變化率發(fā)生變異，應(yīng)用乘法引入

17、變量如果在上述兩種情況都存在的情況下，應(yīng)引入交互效應(yīng)分析，同時引入加法乘法虛擬變量1由于有四個季度，因此引入三個虛擬變量=1時，第一季度 =0時，其他=1時，第二季度 =0時，其他 =1時，第三季度 =0時，其他在第1中情況下，建立模型為：Dependent Variable: YMethod: Least SquaresDate: 12/13/08 Time: 21:24Sample: 1965:1 1970:4Included observations: 24VariableCoefficientStd. Errort-StatisticProb. C6910.4491922.3503.5

18、947920.0019D2-187.7317660.1218-0.2843900.7792D31169.320637.07661.8354460.0821D4-417.1182640.8333-0.6509000.5229X0.0380080.0116703.2569140.0041R-squared0.517642 Mean dependent var12838.54Adjusted R-squared0.416093 S.D. dependent var1433.284S.E. of regression1095.227 Akaike info criterion17.01836Sum s

19、quared resid22790932 Schwarz criterion17.26379Log likelihood-199.2204 F-statistic5.097454Durbin-Watson stat0.396350 Prob(F-statistic)0.005810在第2種情況下，考慮利潤對銷售額的變化率發(fā)生變異，即斜率的改變，因此按乘法模型引入三個虛擬變量Dependent Variable: YMethod: Least SquaresDate: 12/13/08 Time: 12:55Sample: 1965:1 1970:4Included observations:

20、24VariableCoefficientStd. Errort-StatisticProb. C7014.7571782.9323.9343940.0009D2*X0.0361350.0125532.8785280.0096D3*X0.0449780.0117763.8193010.0012D4*X0.0346830.0119652.8986090.0092(1-D2)*(1-D3)*(1-D4)*X0.0370680.0113223.2738960.0040R-squared0.519733 Mean dependent var12838.54Adjusted R-squared0.418

21、624 S.D. dependent var1433.284S.E. of regression1092.851 Akaike info criterion17.01402Sum squared resid22692129 Schwarz criterion17.25945Log likelihood-199.1682 F-statistic5.140331Durbin-Watson stat0.429628 Prob(F-statistic)0.005594在第3種情況下，交互效應(yīng)分析，同時用加法和乘法相結(jié)合的方式引入虛擬變量，模型設(shè)定為Dependent Variable: YMethod

22、: Least SquaresDate: 12/13/08 Time: 13:03Sample: 1965:1 1970:4Included observations: 24VariableCoefficientStd. Errort-StatisticProb. C10457.394075.1992.5661050.0207D2-4752.2575441.682-0.8733070.3954D3-3764.2085484.872-0.6862890.5024D4-4635.4645570.057-0.8322110.4175D2*X0.0450760.0248321.8151890.0883

23、D3*X0.0470370.0237081.9840470.0647D4*X0.0424450.0249031.7044420.1076(1-D2)*(1-D3)*(1-D4)*X0.0158680.0252650.6280750.5388R-squared0.546701 Mean dependent var12838.54Adjusted R-squared0.348383 S.D. dependent var1433.284S.E. of regression1156.987 Akaike info criterion17.20623Sum squared resid21417911 S

24、chwarz criterion17.59891Log likelihood-198.4747 F-statistic2.756686Durbin-Watson stat0.464982 Prob(F-statistic)0.044081通過對上述三種情況分別估計利潤模型的結(jié)果如下：1922.350660.1218637.0766 640.8333 0.011670t=3.594792 -0.284390 1.835446 -0.650900 3.256914=0.517642 1782.9320.012553 0.011776 0.011965 0.011322t=3.934394 2.87

25、8528 3.819301 2.898609 3.273896=0.519733 4075.199 5441.682 5484.872 5570.057 0.024832 0.023708 0.024903 0.025265t=2.566105 -0.873307 -0.686289 -0.832211 1.815189 1.984047 1.704442 0.628075=0.546701由三組模型回歸估計的結(jié)果可以看出，除了模型二的t值較高，季度影響使利潤對銷售額的變化率發(fā)生變異較為顯著，其他模型的t值都較低。同時，三組模型的可決系數(shù)的值都不高，如果要利用模型來描述季節(jié)對利潤的影響，還需要

26、對模型進行進一步的修改和優(yōu)化。習題10.4答：單位根檢驗一般有DF檢驗和ADF檢驗，但為了防止隨機擾動項的不存在和自相關(guān)，一般采用ADF檢驗。根據(jù)所觀察的數(shù)據(jù)序列，用ols估計一階自回歸模型得到回歸系數(shù)的ols估計：提出假設(shè):,檢驗用統(tǒng)計量為常規(guī)t統(tǒng)計量計算在原假設(shè)成立的條件下t統(tǒng)計量值，查ADF檢驗臨界值表得臨界值，然后將t統(tǒng)計量與ADF檢驗臨界值進行比擬，假設(shè)t統(tǒng)計量小于ADF檢驗臨界值，那么拒絕原假設(shè)：，說明序列存在單位根。習題10.5：答：1假設(shè)與是一階單整I(1)序列，即和是平穩(wěn)的用OLS法對回歸方程進行估計，得到殘差序列：檢驗的平穩(wěn)性，假設(shè)為平穩(wěn)的，那么與是協(xié)整的，反之那么不是協(xié)整的。平穩(wěn)性即對進行單位根檢驗，可以用DF或ADF法檢驗，也可用DW統(tǒng)計量檢驗。DW越接近與0，就是不平穩(wěn)的。注意的是，變量與必須在單整階數(shù)相同的情況下，才可以判斷是否存