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1、第4章 习题一表1给出了19651970年美国制造业利润和销售额的季度数据。假定利润不仅与销售额有关，而且和季度因素有关。要求对下列二种情况分别估计利润模型：（1）如果认为季度影响使利润平均值发生变异，应如何引入虚拟变量？（2）如果认为季度影响使利润对销售额的变化率发生变异，如何引入虚拟变量？表1利润（Y）销售额（X）利润（Y）销售额（X）1965-I1968-I12539148826II12092123968II14849158913III10834121454IIIIV12201131917IV149471684091966-I122451299111969-I14151162781II1
2、4001140976IIIII12213137828III14024172419IV12820145645IV143151833271967-I1970-I12381170415II12615145126IIIII11014141536III12174176712IV12730151776IV10985180370Quarterly 65-70Quick-Equation EstimationY c x seas(1) seas(2) seas(3)Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 18:38Sampl
3、e: 1965Q1 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C6868.0151892.7663.6285590.0018X0.0382650.0114833.3322520.0035SEAS(1)-182.1690654.3568-0.2783940.7837SEAS(2)1140.294630.68061.8080380.0865SEAS(3)-400.3371636.1128-0.6293490.5366R-squared0.525596Mean dependent var12
4、838.54Adjusted R-squared0.425721S.D. dependent var1433.284S.E. of regression1086.160Akaike info criterion17.00174Sum squared residSchwarz criterion17.24716Log likelihood-199.0208F-statistic5.262563Durbin-Watson stat0.388380Prob(F-statistic)0.005024T和P在5%情况下都不通过，第二季度相对还好一点假设第二季度显著，结果的经济含义是什么？Y c x se
5、as(2) seas(3) seas(4)Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 18:47Sample: 1965Q1 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C6685.8461711.6183.9061550.0009X0.0382650.0114833.3322520.0035SEAS(2)1322.463638.42582.0714440.0522SEAS(3)-218.1681632.1
6、991-0.3450940.7338SEAS(4)182.1690654.35680.2783940.7837R-squared0.525596Mean dependent var12838.54Adjusted R-squared0.425721S.D. dependent var1433.284S.E. of regression1086.160Akaike info criterion17.00174Sum squared residSchwarz criterion17.24716Log likelihood-199.0208F-statistic5.262563Durbin-Wats
7、on stat0.388380Prob(F-statistic)0.005024第二季度依旧显著影响四种都试一下（去掉一个季节），选一个最显著的124Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 18:51Sample: 1965Q1 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C6467.6781789.1783.6148880.0018X0.0382650.0114833.3322520.0035SEAS
8、(1)218.1681632.19910.3450940.7338SEAS(2)1540.632628.34192.4519000.0241SEAS(4)400.3371636.11280.6293490.5366R-squared0.525596Mean dependent var12838.54Adjusted R-squared0.425721S.D. dependent var1433.284S.E. of regression1086.160Akaike info criterion17.00174Sum squared residSchwarz criterion17.24716L
9、og likelihood-199.0208F-statistic5.262563Durbin-Watson stat0.388380Prob(F-statistic)0.005024134Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 18:52Sample: 1965Q1 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C8008.3091827.5434.3820090.0003X0.0382650.0114
10、833.3322520.0035SEAS(1)-1322.463638.4258-2.0714440.0522SEAS(3)-1540.632628.3419-2.4519000.0241SEAS(4)-1140.294630.6806-1.8080380.0865R-squared0.525596Mean dependent var12838.54Adjusted R-squared0.425721S.D. dependent var1433.284S.E. of regression1086.160Akaike info criterion17.00174Sum squared resid
11、Schwarz criterion17.24716Log likelihood-199.0208F-statistic5.262563Durbin-Watson stat0.388380Prob(F-statistic)0.005024（2）Y=c+x+1D1X+2D2X+3D3XD1=1（第一季度）0（其他）Y c x seas(1)*x seas(2)*x seas(3)*xDependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 19:00Sample: 1965Q1 1970Q4Included observation
12、s: 24VariableCoefficientStd. Errort-StatisticProb.C6965.8521753.6423.9722200.0008X0.0373630.0111393.3542150.0033SEAS(1)*X-0.0008930.004259-0.2095880.8362SEAS(2)*X0.0077120.0039621.9465020.0665SEAS(3)*X-0.0022910.004041-0.5669850.5774R-squared0.528942Mean dependent var12838.54Adjusted R-squared0.4297
13、71S.D. dependent var1433.284S.E. of regression1082.323Akaike info criterion16.99466Sum squared residSchwarz criterion17.24009Log likelihood-198.9359F-statistic5.333675Durbin-Watson stat0.418713Prob(F-statistic)0.004722Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 19:10Sample: 1965Q1
14、 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C8008.3091827.5434.3820090.0003X0.0382650.0114833.3322520.0035SEAS(1)-1322.463638.4258-2.0714440.0522SEAS(3)-1540.632628.3419-2.4519000.0241SEAS(4)-1140.294630.6806-1.8080380.0865R-squared0.525596Mean dependent var12838.54A
15、djusted R-squared0.425721S.D. dependent var1433.284S.E. of regression1086.160Akaike info criterion17.00174Sum squared residSchwarz criterion17.24716Log likelihood-199.0208F-statistic5.262563Durbin-Watson stat0.388380Prob(F-statistic)0.005024Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Ti
16、me: 19:11Sample: 1965Q1 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C6965.8521753.6423.9722200.0008X0.0350720.0117902.9746750.0078SEAS(1)*X0.0013980.0042410.3297360.7452SEAS(2)*X0.0100030.0040682.4588230.0237SEAS(4)*X0.0022910.0040410.5669850.5774R-squared0.528942Mean
17、 dependent var12838.54Adjusted R-squared0.429771S.D. dependent var1433.284S.E. of regression1082.323Akaike info criterion16.99466Sum squared residSchwarz criterion17.24009Log likelihood-198.9359F-statistic5.333675Durbin-Watson stat0.418713Prob(F-statistic)0.004722Dependent Variable: YMethod: Least S
18、quaresDate: 11/26/14 Time: 19:11Sample: 1965Q1 1970Q4Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C6965.8521753.6423.9722200.0008X0.0364710.0123532.9524150.0082SEAS(2)*X0.0086040.0042372.0305390.0565SEAS(3)*X-0.0013980.004241-0.3297360.7452SEAS(4)*X0.0008930.0042590.2095880.
19、8362R-squared0.528942Mean dependent var12838.54Adjusted R-squared0.429771S.D. dependent var1433.284S.E. of regression1082.323Akaike info criterion16.99466Sum squared residSchwarz criterion17.24009Log likelihood-198.9359F-statistic5.333675Durbin-Watson stat0.418713Prob(F-statistic)0.004722习题二表2给出了某地区
20、某行业的库存和销售的统计资料。假设库存额依赖于本年销售额与前三年的销售额，试用Almon变换估计以下有限分布滞后模型：表2库存Y（万元）销售额X（万元）库存Y（万元）销售额X（万元）198011267 8827 199017053 13668 198112661 9247 199119491 14956 198212968 9579 199221164 15483 198312518 99 16761 198413177 109 17852 198513454 10265 199525411 17620 198613735 10299 199625611 18639 198714553 110
21、 20672 198815011 11677 201930218 23799 198915846 12445 201936784 27359 Y=+0Xt-i+1Xt-i+2Xt-i+t3，i=0笔记11,26）在最上面输入genr z0=x+x(-1)+x(-1)+x(-3)genr z1=x(-1)+2*x(-2)+3*x(-3)genr z2=x(-1)+4*x(-2)+9*x(-3)y c z0 z1 z2Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 19:38Sample (adjusted): 1983
22、 2019Included observations: 17 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-1928.495503.5272-3.8299720.0021Z00.3440270.0918483.7456150.0024Z10.8157580.3515192.3206670.0372Z2-0.3390410.128632-2.6357390.0206R-squared0.996564Mean dependent var20467.29Adjusted R-squared0.995771S.D. de
23、pendent var6997.995S.E. of regression455.0907Akaike info criterion15.28119Sum squared resid2692398.Schwarz criterion15.47724Log likelihood-125.8902F-statistic1256.768Durbin-Watson stat1.985515Prob(F-statistic)0.000000Y c PDL(x,3,2)重新回归Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 19
24、:46Sample (adjusted): 1983 2019Included observations: 17 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-1784.821498.4654-3.5806320.0034PDL010.8482580.1350506.2810800.0000PDL020.0280670.1218910.2302640.8215PDL03-0.3239820.124899-2.5939490.0223R-squared0.996794Mean dependent var20467.
25、29Adjusted R-squared0.996054S.D. dependent var6997.995S.E. of regression439.5669Akaike info criterion15.21178Sum squared resid2511848.Schwarz criterion15.40783Log likelihood-125.3001F-statistic1347.416Durbin-Watson stat1.846084Prob(F-statistic)0.000000Lag Distribution of XiCoefficientStd. Errort-Sta
26、tistic. * |00.496210.124163.99656. *|10.848260.135056.28108. * |20.552340.123264.48121* . |3-0.391530.17618-2.22234Sum of Lags1.505280.0475031.6921习题三表3给出了印度19491965年实际货币存量、实际总国民收入和长期利率数据。假设有如下的长期货币需求关系式：其中，为长期货币需求（现金余额）；为长期利率；为实际总国民收入。请在如下存量调整假说下估计该货币需求模型，其中为实际现金存量： 表3年份实际货币M实际净收入Y长期利率R年份实际货币M实际净收入
27、Y长期利率R(千万卢比)(10亿卢比)(%)(千万卢比)(10亿卢比)(%)19491898.69 86.50 3.03 19582307.26 108.90 4.18 19501840.71 88.20 3.07 19592335.66 117.34 4.13 19511838.31 88.50 3.15 19602491.27 118.60 4.05 19521646.39 91.00 3.41 19612579.92 127.17 4.06 19531699.94 94.60 3.66 19622687.80 130.60 4.16 19541716.88 100.30 3.64 196
28、32860.83 133.10 4.49 19552054.59 102.80 3.70 19643045.80 139.70 4.66 19562328.00 104.80 3.74 19653068.64 150.50 4.80 19572277.66 110.00 3.99 LnM*t=ln0+1lnRt+2lnYt+tLnMt-LnMt-1= lnM*t- lnMt-1LnMt= ln0+1 lnRt+2 lnYt+（1- ）lnMt-1+ t求回归Quick-Equation Estimationlog(m) c log(r) log(y) log(m(-)Dependent Var
29、iable: LOG(M)Method: Least SquaresDate: 11/26/14 Time: 20:13Sample (adjusted): 1950 1965Included observations: 16 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.5551970.9380760.5918460.5649LOG(R)-0.1040010.371131-0.2802260.7841LOG(Y)0.6855480.3859631.7762010.1010LOG(M(-1)0.5299510.
30、2019392.6321330.0219R-squared0.937929Mean dependent var7.720196Adjusted R-squared0.922411S.D. dependent var0.207907S.E. of regression0.057912Akaike info criterion-2.647459Sum squared resid0.040246Schwarz criterion-2.454312Log likelihood25.17967F-statistic60.44199Durbin-Watson stat1.880213Prob(F-stat
31、istic)0.000000求1-=0.529951非线性模型如何变换，变换后还要回到估计的预原模型中拉格朗日乘数检验VIEW=R=LM testLags to 1Breusch-Godfrey Serial Correlation LM Test:F-statistic0.013865Probability0.908388Obs*R-squared0.020192Probability0.887141Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/26/14 Time: 20:22Presample m
32、issing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C0.0613611.1092060.0553200.9569LOG(R)-0.0006930.387434-0.0017880.9986LOG(Y)0.0189990.4339790.0437770.9659LOG(M(-1)-0.0195210.267675-0.0729260.9432RESID(-1)0.0478270.4061760.1177500.9084R-squared0.001259Mean dependent var5.55E-16Adjusted R-squared-0.361920S.D. dependent var0.051798S.E. of regression0.060449Akaike info criterion-2.523719Sum squared resid0.040195Schwarz criterion-2.282285Log likelihood25.18975F-statistic0.003466Durbin-Watson stat1.948575Prob(F-statistic)0.999972第 23 页