庞皓计量经济学第二章练习题及参考解答(第四版).docx

练习题2.1表2.9中是中国历年国内旅游总花费（Y）、国内生产总值（XI）、铁路里程（X2）、 公路里程数据（X3）的数据。表2.7中国历年国内旅游总花费、国内生产总值、铁路里程、公路里程数据年份国内旅游总花费（亿元）国内生产总值（亿元）铁路里程（万公里）公路里程（万公里）19941023.548637.55.9111.7819951375.761339.96.24115.719961638.471813.66.49118.5819972112.7797156.6122.6419982391.285195.56.64127.8519992831.990564.46.74135.1720003175.5100280.16.87167.9820013522.4110863.17.01169.820023878.4121717,47.19176.5220033442.31374227.3180.9820044710.7161840.27.44187.0720055285.9187318.97.54334.5220066229.7219438.57.71345.720077770.6270232.37.8358.3720088749.3319515.57.97373.02200910183.7349081.48.55386.08201012579.8413030.39.12400.82201119305.4489300.69.32410.64201222706.2540367.49.76423.75201326276.1595244.410.31435.62201430311.964397411.18446.39201534195.1689052.112.1457.73201639390743585.512.4469.63资料来源：中国统计年鉴（1）分别建立线性回归模型，分析中国国内旅游总花费与国内生产总值、铁路里程、 公路里程数据的数量关系。（2）对所建立的回归模型进行检验，对几个模型估计检验结果进行比较。【练习题2.1参考解答】（1）分别建立亿元线性回归模型建立y与xl的数量关系如下: 费倾向(MPC)是斜率反，而平均消费倾向(APC)为©/工。由中国统计年鉴得到2016 年中国各地区居民人均消费支出和居民人均可支配收入数据：表2.92016年中国居民消费支出与可支配收入数据地区居民消费 支出(元)居民可支配 收入阮)地区居民消费 支出(元)居民可支配 收入(元)北京35415.752530.4湖北15888.721786.6天津26129.334074.5湖南15750.521114.8河北14247.519725.4广东23448.430295.8111西12682.919048.9广西12295.218305.1内蒙古18072.324126.6海南14275.420653.4辽宁19852.826039.7重庆16384.822034.1吉林14772.619967.0四川14838.518808.3黑龙江14445.819838.5贵州11931.615121.1上海37458.354305.3云南11768.816719.9江苏22129.932070.1西藏9318.713639.2浙江25526.638529.0陕西13943.018873.7安徽14711.519998.1甘肃12254.214670.3福建20167.527607.9青海14774.717301.8江西13258.620109.6宁夏14965.418832.3山东15926.424685.3新疆14066.518354.7河南12712.318443.1(1)在95%的置信度下，求夕2的置信区间。(2)以可支配收入为x轴，画出估计的MPC和APC图。(3)当居民人均可支配收入为60000元时，预计人均消费支出C的点预测值。(4)在95%的置信度下，人均消费支出C平均值的预测区间。(5)在95%的置信度下，人均消费支出C个别值的预测区间。【练习题2.3参考解答】（1）在95%的置信概率下，瓦的区间估计是多少？P?2 - ” *匏我）三4三+ ” *6强）=。95 22«2 . % * SE（2）三-2 W ?2 + 匕 * 兖（?2）得至I：I0.66 - t0 025（29）* 0.02 <fi2< 0.66 + t0 025（29）* 0.020.66 - 2.045 * 0.02 </?. < 0.66 + tn n?r（29）* 0.020.6191 < /?2 < 0,7009Dependent Variable: CONS Method: Least Squares Date: 03/12/18 Time: 23:08 Sample: 1 31Included observations: 31VariableCoefficientStd. Error t-StatisticProb.C1496.505516.32502.8983790.0071INC0.6602710.02012832.803470.0000R-squared0.973757Mean dependent var17206.92Adjusted R-squared0.972852S.D. dependent var6519.501S.E. of regression1074.189Akaike info criterion16,85886Sum squared resid33462563Schwarz criterion16.95138Log likelihood-259.3123Hannan-Quinn criter.16.88902F-statistic1076.067Durbin-Watson stat1.538680Prob(F-statistic)0.000000(2)以可支配收入为x轴，画出估计的MPC和APC图。(3)当居民人均可支配收入为60000元时，预计人均消费支出C的点预测 值。聘点预测带入到方程中去得到：Cf= 1496 505 + ° 66 * 60000 = 41096.505(4)在95%的置信概率下，人均消费支出C平均值的预测区间。平均值预测区间：2丫：二oj(几- 1) = 9743.5582 x(31 - 1) = 2848107674.980921(Yf - r)2 =(60000 - 23793.89)2 = 1310885297.82259当。二8。0。时，泌(29)= 2.045,代入计算可得：41096.505 + 2.045 X 1074.189 x口 1310885297.8225931 + 2848107674.980921=41096.505 + 1541.66(5)在95%的置信概率下，人均消费支出C个别值的预测区间。41096.505 + 2.045 X 1074.189 X11310885297.822591 + +31 2848107674.98092141096.505 + 2683.702.4假设某地区住宅建筑面积与建造单位成本的有关资料如表2.10:表2.10某地区住宅建筑面积与建造单位成本数据根据上表资料:建筑地编号建筑面积(力平方米)X建造单位成本(兀/平方米)Y10.6186020.95175031.45171042.1169052.56167863.54164073.89162084.37157694.821566105.661498116.111425126.231419(1)建立建筑面积与建造单位成本的回归方程；(2)解释回归系数的经济意义；(3)估计当建筑面积为4.5万平方米时，对建造平均单位成本作区间预测。【练习题2.4参考解答】 建立建筑面积与建造单位成本的回归方程Dependent Variable: Y Method: Least SquaresDate: 10/03/13 Time: 09:31Sample: 1 12Included observations: 12VariableCoefficientStd. Error t-StatisticProb.C1845.47519,2644695.796880.0000X-64.184004.809828-13.344340.0000R-squared0.946829Mean dependent var1619.333Adjusted R-squared0.941512S.D. dependentvar131.2252S.E. of regression31.73600Akaike info criterion9.903792Sum squared resid10071.74Schwarz criterion9.984610Log likelihood-57.42275Hannan-Quinn criter.9.873871F-statistic178.0715Durbin-Watson stat1.172407Prob(F-statistic)0.000000(2)解释回归系数的经济意义：模型的t检验和F检验均显著,说明建筑面积每扩大1万平方米,建造单位成本将下降64.184元/平方米.(3)估计当建筑面积为4.5万平方米时，预测建造的平均单位成本:/ = 1845.475-64.184x4.5 = 1556.647(元/平方米)平均单位成本的区间预测:Yfmta/2心x."已经得到y = 1556.647、r002S(10) = 2.228. 3 = 31.736、n = 12o X=4.5X的样本数据得:x _Mean3.523333Median3.715000Maximum6.230000Minimum0.600000Std._Dev.1.989419Skewness-0.060130Kurtosis1.664917Jarque-Bera0.898454Probability0.638121Sum42.28000Sum Sq. Dev.43.53567Observations12 -J2%； = Z( Xj 又)2 = b； 5 1) = 1.98942 X(12 1) = 43.5348(Xf-X)2 = (4.5 - 3.5233)2 = 0.9539当X/=4.5时，将相关数据代入计算得到10 95391556.647 m 2.228x31.736 x J+ - =1556.647 m 22.9376 V12 43.5348即是说，当建筑面积为4.5万平方米时，预测建造的平均单位成本Yf平均值置信度95%的预测区间为(1533.7094, 1579.5846)元/平方米。2.5由12对观测值估计得消费M数为：C=50 + 0.6X,其中，C是消费支出，丫是可支 配收入(元)，已知又=800, (X-X)2 =8000, ；=300, r0025(10) = 2.23o 当 X/=1000时，试计算：(I)消费支出C的点预测值；(2)在95%的置信概率下消费支出C平均值的预测区间。(3)在95%的置信概率下消费支出C个别值的预测区间。【练习题2.5参考解答】(1)当X/ = 1000时，消费支出C的点预测值；Ci = 50+ 0.6Xj=50+0.6* 1000=650(2)在95%的置信概率下消费支出C平均值的预测区间。A - 11 (xf-x)2gm"'7已经得到：又=800 , Xf = 1000 , 一 又了 =800° , Z0.025(10) = 2.23 , /2 =300布 £4300n-2 12-23 =后=回= 5.4772当 X/=1000 时：2 人 11 (Xf-X)211(1000-800)2 + 二 今=650m 2.23 x 5.4772 x Af/XxiV128000=650 m 2.23 x 5.4772 x J5.0833 = 650 m 27.5380(3)在95%的置信概率下消费支出C个别值的预测区间。个 人 f 1 (Xf -)2- EC1(1000 800)2Cf m J, Idb 二 ,=650m2.23x5.4772x J1 + 一 + /、 £七V 128000=650 m 2.23 x 5.4772 x Jl+5.0833 = 650 m 30.12502.6按照“弗里德曼的持久收入假说”：持久消费y正比于持久收入X,依此假说建立 的计量模型没有截距顶，设定的模型应该为：丫=。必卢%,这是一个过原点的回归。在 古典假定满足时，(1)证明过原点的回归中昆的OLS估计量后的计算公式是什么？对该模型是否仍有 26=。和>,乂,=。？对比有截距项模型和无截距项模型参数的OLS估计有什么不 同？/>(2)无截距项模型的后具有无偏性吗？XA(3)写出无截距项模型32的方差var(/？2)的表达式。【练习题2.6参考解答】(1)没有截距顶的过原点回归模型为：Yi=B?Xi+u因为求偏导令得因为求偏导令得Z=Z(x-AXj)2= 2£(工-四X，)(-X,) = -2凶邳2SV e； 宁 人告尸= 2Za-3Q(-x,) = o印2人 V XY人 V xy.k 丫2而有截距项的回归为尸2 =一乙 XjZ Xj对于过原点的回归，由OLS原则： 2号=0已不再成立，但是ZcXj =0是成立的。八(2)无截距项模型的32具有无偏性吗？A在古典假设满足时，无截距项的02具有无偏性。八A(3)无截距项模型62的方差var(/)的表达式？2 - - 1（X X） = 2在多元回归中Var（B）=。（X X），当为无截距项仅有一个变量时，因此无截距且仅有一个解释变量的情形性下：Var2）=还可以证明对于过原点的回归，于=/ n-1人 CT2人2 £4而有截距项的回归为vmA）= ，3 = /个二王”22.7 练习题2.2中如果将浙江省“一般预算总收入”和“地区生产总值”数据的计量单位分 别或同时由“亿元”更改为''万元”，分别重新估计参数，对比被解释变量与解释变量的计量单 位分别变动和同时变动的几种情况下，参数估计及统计检验结果与计量单位与更改之前有什 么区别？你能从中总结出什么规律性吗？【练习题2.7参考解答】以亿元为单位的一般预算总收入用Y1表示，以亿元为单位的地区生产总值用XI表示以万元为单位的一般预算总收入用Y2表示，以万元为单位的地区生产总值用X2表示表2.10浙江省财政预算收入与全省生产总值数据财政预算总收入 （亿元）全省生产总值 （亿元）财政预算总收入 （万元）全省生产总值 （元）Y1XIY2X2197827.45123.722745001237200197925.87157.752587001577500198031.13179.923113001799200198134.34204.863434002048600198236.64234.013664002340100198341.79257.094179002570900198446.67323.254667003232500198558.25429.165825004291600198668.61502.476861005024700198776.36606.997636006069900198885.55770.2585550()7702500198998.21849.4498210084944001990101.59904.69101590090469001991108.941089.331089400108933001992118.361375.71183600137570001993166.641925.911666400192591001994209.392689.282093900268928001995248.53557.552485000355755001996291.754188.532917500418853001997340.524686.113405200468611001998401.85052.624018000505262001999477.45443.924774000544392002000658.426141.036584200614103002001917.766898.3491776006898340020021166.588003.67116658008003670020031468.899705.02146889009705020020041805.1611648.71805160011648700020052115.3613417.682115360013417680020062567.6615718.472567660015718470020073239.8918753.733239890018753730020083730.0621462.693730060021462690020094122.0422998.244122040022998240020104895.4127747.654895410027747650020115925.0032363.385925000032363380020126408.4934739.136408490034739130020136908.4137756.586908410037756580020147421.7040173.037421700040173030020158549.4742886.498549470042886490020169225.0747251.36922507004725136001)练习题2.2中，财政预算总收入用亿元(Y1)表示,全省生产总值用亿元(XI)表示的回归:Dependent Variable: Y1Method: Least SquaresDate: 03/16/18 Time: 20:56Sample: 1978 2016Included observations: 39VariableCoefficientStd. Error t-StatisticProb.C-227.051846,34713-4.8989400.0000X10.1917650.00259873.800830.0000R-squared0.993253Mean dependent var1903.106Adjusted R-squared0.993070S.D. dependent var2720.360S.E. of regression226.4575Akaike info criterion13.73291Sum squared resid1897471.Schwarz criterion13.81822Log likelihood-265.7918Hannan-Quinn criter.13.76352F-statistic5446.562Durbin-Watson stat0.276451Prob(F-statistic)0.0000002)财政预算总收入用万元(Y2)表示,全省生产总值用万元(X2)表示的回归: 回归结果为：可曲Dependent Variable: Y2 Fvlethod: Least SquaresDate: 03/16/18 Time: 20:57Sample: 1978 2016Included observations: 39VariableCoefficientStd. Error t-StatisticProb.C-2270518.463471.3-4.8989400.0000X20.1917650.00259873.800830.0000R-squared0.993253Mean dependent var19031059Adjusted R-squared0.993070S.D. dependent var27203599S.E. of regression2264575.Akaike info criterion32.15359Sum squared resid1.90E+14Schwarz criterion32.23890Log likelihood-624.9951Hannan-Quinn criter.32,18420F-statistic5446.562Durbin-Watson stat0.276451Prob(F-statistic)0.0000003)财政预算总收入用万元(丫2)表示,全省生产总值用亿元(XI)表示的回归:Dependent Variable: Y2 fvlethod: Least SquaresDate: 03/16/18 Time: 20:59 Sample: 1978 2016Included observations: 39VariableCoefficientStd. Error t-StatisticProb.C-2270518.463471.3-4.8989400.0000X11917.65325.9841773.800830.0000R-squared0.993253Mean dependent var19031059Adjusted R-squared0.993070S.D. dependent var27203599S.E. of regression2264575.Akaike info criterion32.15359Sum squared resid1.90E+14Schwarz criterion32.23890Log likelihood-624.9951Hannan-Quinn criter.32.18420F-statistic5446.562Durbin-Watson stat0.276451Prob(F-statistic)0.0000004)财政预算总收入用亿元(Y1)表示,全省生产总值用万元(X2)表示的回归:Dependent Variable: Y1 Method: Least SquaresDate: 03/16/18 Time: 21:00 Sample: 1978 2016Included observations: 39VariableCoefficientStd. Error t-StatisticProb.C-227.051846.34713-4.8989400.0000X21.92E-052.60E-0773.800830.0000R-squared0.993253Mean dependent var1903.106Adjusted R-squared0.993070S.D. dependent var2720.360S.E. of regression226.4575Akaike info criterion13.73291Sum squared resid1897471.Schwarz criterion13.81822Log likelihood-265.7918Hannan-Quinn criter.13.76352F-statistic5446.562Durbin-Watson stat0.276451Prob(F-statistic)0.0000007.=-3228.02+ 0.05XDependent Variable: Y Method: Least Squares Date: 03/12/18 Time: 22:32 Sample: 1994 2016 Included observations: 23VariableCoefficientStd. Error t-StatisticProb.C-3228.021834.3202-3.8690430.0009X10.0501310.00231221.679810.0000R-squared0.957231Mean dependent var11003.76Adjusted R-squared0.955195S.D.dependentvar11666.83S.E. of regression2469.548Akaike info criterion18.54440Sum squared resid1.28E+08Schwarz criterion18.64314Log likelihood-211.2606Hannan-Quinn criter.18.56923F-statistic470.0140Durbin-Watson stat0.215776Prob(F-statistic)0.000000建立y与x2的数量关系如下:y.=-39438.73 + 6165.25XnDependent Variable: Y Method: Least SquaresDate: 03/12/18 Time: 22:35Sample: 1994 2016 Included observations: 23VariableCoefficientStd. Error t-StatisticProb.C-39438.731950.462-20.220200.0000X26165.253232.682026.496470.0000R-squared0.970957Mean dependent var11003.76Adjusted R-squared0.969574S.D.dependentvar11666.83S.E. of regression2035.056Akaike info criterion18.15738Sum squared resid86970504Schwarz criterion18.25611Log likelihood-206.8098Hannan-Quinn criter.18.18221F-statistic702.0629Durbin-Watson stat0.699706Prob(F-statistic)0.000000建立y与x3的数量关系如下:7.=-9106.17 + 71.64Xn对比几种回归的回归结果:释变量 解释变量财政预算总收入以亿元计Y1以万元计Y2全省生产总值以亿元计XI常数项-227.0518-2270518斜率系数0.1917651917.65以万元计X2常数项-227.0518-2270518斜率系数0.00001920.191765变动的规律性：1 ）被解释变量计量单位变化扩大（或缩 /倍,解释变量计量单位不变时:常数项将缩小（或扩大）K倍；斜率系数将缩 '（或扩大）K倍2）被解释变量计量单位不变，解释变量计量单位扩大（或缩力）K倍时: 常数项将不变；斜率系数将缩小（或扩大）K倍3）被解释变量计量单位与解释变量计量单位同时扩大（或缩小）K倍时: 常数项将缩 '（或扩大）K倍；斜率系数不变4）变量计量单位的变化对t检验和F检验的统计量没有影响。2.8 联系自己所学的专业选择一个实际问题，设定一个简单线性模型，并自己去收集样 本数据，用本章的方法估计和检验这个模型，你如何评价自己所做的这项研究？【练习题2.8参考解答】本题无参考解答Dependent Variable: Y Method: Least SquaresDate: 03/12/18 Time: 22:35Sample: 1994 2016 Included observations: 23VariableCoefficientStd. Error t-StatisticProb.C-9106.1663170.972-2.8717270.0091X371.6393810.203027.0213880.0000R-squared0.701280Mean dependent var11003.76Adjusted R-squared0.687055S.D.dependent var11666.83S.E. of regression6526.601Akaike info criterion20.48810Sum squared resid8.95E+08Schwarz criterion20.58684Log likelihood-233.6132Hannan-Quinn criter.20.51293F-statistic49.29989Durbin-Watson stat0.219452Prob(F-statistic)0.000001（2）对所建立的回归模型进行检验，对几个模型估计检验结果进行比较。2关于中国国内旅游总花费与国内生产总值模型，由上可知，R =0987,说明所建模型整体 上对样档搪以合翎b对于回归麴赃1通佥1侬）=21-68>£0,025（21） = 2.08,对斜率系数的显著组播表阻GDP 对中国国内旅游总花费有显著影响O2同理：关于中国国内旅游总花费与铁路里程模型，由上可知，R =0971,说明所建模型整 体上对样本数据拟合物子。对于回归系数的"翎佥KBD = 26.50 >%02式21） = 2.08,对斜率检的显著的士明，铁 路里不翎中国国内旅游总花费有显著影响。2关于中国国内旅游总花费与公路里程模型，由上可知，R =。701,说明所建模型整体上对 样档螂哈较感对于回归系数的t逸佥t（BD = 7. 02 > t0.025（21）= 2.08,对斜率系数的显著性检验表明，公路 里程对中国国内旅游总花费有显著影响。2.2为了研究浙江省一般预算总收入与地区生产总值的关系，由浙江省统计年鉴得到如 表2.8所示的数据。表2.8浙江省财政预算收入与地区生产总值数据年份一般预算总收入 （亿元）地区生产总值 （亿元）年份一般预算总收入 （亿元）地区生产总值 （亿元）YXYX197827.45123.721998401.805052.62197925.87157.751999477.405443.92198031.13179.922000658.426141.03198134.34204.862001917.766898.34198236.64234.0120021166.588003.67198341.79257.0920031468.899705.02198446.67323.2520041805.1611648.70198558.25429.1620052115.3613417.68198668.61502.4720062567.6615718.47198776.36606.9920073239.8918753.73198885.55