计量经济学第二版第四章答案

4.1(1)存在3322ˆˆˆˆ且。因为23223223232322ˆiiiiiiiiiiixxxxxxxyxxy当32XX与之间的相关系数为零时，离差形式的032iixx有222223222322ˆˆiiiiiiiixxyxxxxy同理有：33ˆˆ(2)111ˆˆˆ会等于或的某个线性组合因为12233ˆˆˆYXX，且122ˆˆYX，133ˆˆYX由于3322ˆˆˆˆ且，则11222222ˆˆˆˆˆYYXYXX11333333ˆˆˆˆˆYYXYXX则1112233231123ˆˆˆˆˆˆˆYYYXXYXXYXX(3)存在3322ˆvarˆvarˆvarˆvar且。因为22322221ˆvarrxi当023r时，22222232222ˆvar1ˆvariixrx同理，有33ˆvarˆvar4.3(1)建立中国商品进口额为Y与国内生产总值x1、居民消费价格指数x2得回归模型123lnln1ln2tttiYXXu估计模型参数，结果为DependentVariable:LNYMethod:LeastSquaresDate:05/16/12Time:19:15Sample:19852007Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C-3.0601490.337427-9.0690590.0000LNX11.6566740.09220617.967030.0000LNX2-1.0570530.214647-4.9246180.0001R-squared0.992218Meandependentvar9.155303AdjustedR-squared0.991440S.D.dependentvar1.276500S.E.ofregression0.118100Akaikeinfocriterion-1.313463Sumsquaredresid0.278952Schwarzcriterion-1.165355Loglikelihood18.10482F-statistic1275.093Durbin-Watsonstat0.745639Prob(F-statistic)0.000000参数估计结果如下：093.1275F991.0992.0(-4.925)(17.967)(-9.069)2ln0571.11ln6567.10601.3ˆln22RRxxYt（2）)数据中有多重共线性，居民消费价格指数的回归系数的符号不能进行合理的经济意义解释，且其简单相关系数呈现正向变动。（3）DependentVariable:LNYMethod:LeastSquaresDate:05/16/12Time:19:17Sample:19852007Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C-4.0906670.384252-10.645790.0000LNX11.2185730.03519634.622220.0000R-squared0.982783Meandependentvar9.155303AdjustedR-squared0.981963S.D.dependentvar1.276500S.E.ofregression0.171438Akaikeinfocriterion-0.606254Sumsquaredresid0.617208Schwarzcriterion-0.507515Loglikelihood8.971921F-statistic1198.698Durbin-Watsonstat0.364369Prob(F-statistic)0.00000022lnY4.09071.2186ln1t=(-10.6458)(34.6222)0.98280.98201198.698xRRFDependentVariable:LNYMethod:LeastSquaresDate:05/16/12Time:19:18Sample:19852007Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C-5.4424201.253662-4.3412180.0003LNX22.6637900.22804611.680910.0000R-squared0.866619Meandependentvar9.155303AdjustedR-squared0.860268S.D.dependentvar1.276500S.E.ofregression0.477166Akaikeinfocriterion1.441037Sumsquaredresid4.781435Schwarzcriterion1.539775Loglikelihood-14.57192F-statistic136.4437Durbin-Watsonstat0.152312Prob(F-statistic)0.00000022lnY5.44242.6637ln2t=(-4.3412)(11.6809)0.86660.8603136.4437xRRFDependentVariable:LNX1Method:LeastSquaresDate:05/16/12Time:19:19Sample:19852007Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C-1.4379840.734328-1.9582310.0636LNX22.2459710.13357716.814000.0000R-squared0.930855Meandependentvar10.87007AdjustedR-squared0.927563S.D.dependentvar1.038480S.E.ofregression0.279498Akaikeinfocriterion0.371300Sumsquaredresid1.640506Schwarzcriterion0.470039Loglikelihood-2.269955F-statistic282.7107Durbin-Watsonstat0.142984Prob(F-statistic)0.00000022ln11.43802.2460ln2t=(-1.9582)(16.8140)0.93090.9276282.7107xxRRF单方程拟合效果都很好，回归系数显著，可决系数较高，GDP和CPI对进口分别有显著的单一影响,在这两个变量同时引入模型时影响方向发生了改变；GDP对CPI进行回归分析，回归系数显著，判定系数较高，说明GDP和CPI有很强的线性关系，这正是原模型多重共线性的原因。（4）如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意。4.6(1)建立对数线性多元回归模型，引入全部变量建立对数线性多元回归模型如下:变量对数线性多元回归,结果为:DependentVariable:LNYMethod:LeastSquaresDate:05/16/12Time:19:29Sample:19852007Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C3.4420512.7061121.2719540.2228LNX111.838202.3097225.1253770.0001LNX2-11.337801.932927-5.8656090.0000LNX3-0.3714500.719447-0.5163000.6132LNX40.2198910.1520831.4458570.1688LNX5-0.1821640.105332-1.7294340.1042LNX60.2255080.3029230.7444390.4681LNX71.2700520.4847282.6201340.0193R-squared0.993930Meandependentvar11.78641AdjustedR-squared0.991097S.D.dependentvar0.343125S.E.ofregression0.032375Akaikeinfocriterion-3.754629Sumsquaredresid0.015722Schwarzcriterion-3.359675Loglikelihood51.17824F-statistic350.8771Durbin-Watsonstat1.539809Prob(F-statistic)0.000000从修正的可决系数和F统计量可以看出，全部变量对数线性多元回归整体对样本拟合很好，，各变量联合起来对能源消费影响显著。可是其中的lnX4、lnX6对lnY影响不显著,而且lnX2、lnX3、lnX5的参数为负值，在经济意义上不合理。所以这样的回归结果并不理想。(2)解释变量国民总收入(亿元)X1(代表收入水平)、国内生产总值(亿元)X2(代表经济发展水平)、工业增加值(亿元)X3、建筑业增加值(亿元)X4、交通运输邮电业增加值(亿元)X5(代表产业发展水平及产业结构)、人均生活电力消费(千瓦小时)X6(代表人民生活水平提高)、能源加工转换效率(%)X7(代表能源转换技术)等很可能线性相关,计算相关系数如下变量LNX1LNX2LNX3LNX4LNX5LNX6LNX7LNX110.9999740.9997330.9969130.9935760.997170.708415LNX20.99997410.9997460.9971770.9938390.9968190.709065LNX30.9997330.99974610.9978870.9917010.9955110.71606LNX40.9969130.9971770.99788710.9895910.9899320.708962LNX50.9935760.9938390.9917010.98959110.9939370.664793LNX60.997170.9968190.9955110.9899320.99393710.685726LNX70.7084150.7090650.716060.7089620.6647930.6857261可以看出lnx1与lnx2、lnx3、lnx4、lnx5、lnx6之间高度相关，许多相关系数高于0.900以上。如果决定用表中全部变量作为解释变量，很可能会出现严重多重共线性问题。（3）因为存在多重共线性，解决方法如下：DependentVariable:YMethod:LeastSquaresDate:05/16/12Time:19:49Sample:19852007Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C-76917.33103078.4-0.7462020.4671X115.232234.6587863.2695700.0052X2-15.905044.478372-3.5515230.0029X3-2.6333783.649937-0.7214860.4817X426.2643911.126342.