龐皓計量經(jīng)濟學練習題及參考解答第四版

1、練習題2.1表2.9中是中國歷年國內(nèi)旅游總花費（Y）、國內(nèi)生產(chǎn)總值（XI）、鐵路里程（X2）、公路里程數(shù)據(jù)（X3）的數(shù)據(jù)。表2.7中國歷年國內(nèi)旅游總花費、國內(nèi)生產(chǎn)總值、鐵路里程、公路里程數(shù)據(jù)年份國內(nèi)旅游總花費（億元）國內(nèi)生產(chǎn)總值（億元）鐵路里程（萬公里）公路里程（萬公里）19941023.54S637.55.9111.7819951375.761339.96.24115.719961638.471813.66.19118.5819972112.7797156.6122.6419982391.285195.56.64127.8519992831.990564.4O.：1135.172000317

2、5.5100280.16.87167.9820013522.4110863.17.01169.820023878.4121717.47.19176.5220033442.31374227.3180.9820044710.7161840.27.44187.0720055285.9187318.97.54334.5220066229.7219438.57.71345.720077770.6270232.37.8358.3720088749.3319515.57.97373.02200910183.7349081.48.55386.08201012579.8413030.39.12100.82201

3、119305.4189300.69.32410.64201222706.2540367.49.76423.75201326276.1595244.410.31435.62201430311.964397411.18446.39201534195.1689052.112.1457.73201639390743585.512.1469.63資料來源：中國統(tǒng)計年鑒（1）分別建立線性回歸模型，分析中國國內(nèi)旅游總花費與國內(nèi)生產(chǎn)總值、鐵路里程、公路里程數(shù)據(jù)的數(shù)最關系。（2）對所建立的回歸模型進行檢驗，對幾個模型估計檢驗結果進行比較?！揪毩曨}2.1參考解答】（1）分別建立億元線性回歸模型建立y與xl的數(shù)最關

4、系如卜:Yt=-3228.02+0.05XnDependentVariable:YMethod:LeastSquaresDate:03/12/18Time:22:32Sample:19942016Includedobservations:23VariableCoedentStd.Errort-StatisticProb.C-3228.021834.3232-3.8690430.0009X10.0501310.00231221.679810.0000R-squared0.957231Meandependentvar11003.76AdjustedR-squared0.955195S.D.depe

5、ndentvar11666.83S.E.ofregression2469.548Akaikenocriterion18.54440Sumsquaredresid1.28E*08Schwarzcriterion18.64314Loglikelihood-211.2606Hannan-Quinncriter.18.56923F-statistic470.0140Durbin-Watsonstat0.215776Prob(F-statistic)0.030000建立y與x2的數(shù)量關系如下：z=-39438.73+6165.25*打DependentVariable:/Method:LeastSqua

6、resDate:03/12/18Time:22:35Sample:19942016Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C39433.731950.462-20.220200.0000X26165253232.662026.496470.0000R-squared0.970957Meandependentvar11003.76AdjustedR-squared0.969574S.D.dependentvar11666.83S.E.ofregression2035056Akaikeirfocriter

7、ion18.15738sumsquaredresia86970504scnwarzcriterion18.25611Loglikelihood-206.8098Hannan-Quinncriter.18.18221F-statistic702.0629Durbin-V/atsonstat0.699706Prob(F-statistic)o.oocooo建立y與工3的數(shù)最關系如卜：Z=-9106.17+71.64X1DependentVariable:YMethod:LeastSquaresDate:03/12/18Time:22:35Sample:19942016Indudodobcorvat

8、ions:23VariableCoefficientStd.Errort-StatisticProb.C-9106.1663170.972-2.8717270.0091X371.6393810.203027.0213880.0000R-squared0701280dpendntvar1100376AdjustedR-squared0687055SD.dependentvar11666.83S.E.ofregression6526.601Aoikeirfocriterion20.43810Sumsquaredresid895E+08Schwarzcriterion20.58684Loglikel

9、ihood-233.6132Hannan-Quinnenter20.51293F-MatiAtic4929989Oirbin-WAtAonAtatO219452Prob(F-stdtistic)0000001（2）對所建立的回歸模型進行檢臉，對幾個模型估計檢驗結果進行比較。關于中國國內(nèi)旅游總花費與國內(nèi)生產(chǎn)總值模型，由上可知，/?2=0.987,說明所建模型整體上對W本數(shù)據(jù)擬合較好。對于回歸系數(shù)的t檢）金t（pi）=21.68t0.025（21）=2.08,對斜率系數(shù)的顯劑I檢驗表明,P對中國國內(nèi)旅游總花費有顯著影響。同理：關于中國國內(nèi)旅游總花費與鐵路里程模型，由上可知，R2=0.971,說明所

10、建模型腳上對樣本數(shù)據(jù)擬合較好。X打回力1系數(shù)的t檢會t（pl）=26.50t0.025（21）=2.08,對斜率系數(shù)的顯著性檢驗衣明，鐵路里程對中國國內(nèi)旅游總花費有顯著影響。關于中國國內(nèi)旅游總花費與公路里程模型，由上口J知，/?2=0.701,說明所建模型整體匕寸樣本數(shù)據(jù)擬合較好。對于4訓I系數(shù)的t悒金t（pi）=7.02r0.025（21）=2.08,對斜率系數(shù)的顯相槍臉表明，公路里程對111國國內(nèi)旅游總花費右顯著影響。2.2為了研究浙江省一般預算總收入與地區(qū)生產(chǎn)總值的關系，由浙江省統(tǒng)計年鑒得到如表28所示的數(shù)據(jù)。表2.8浙江省財政預算收入與地區(qū)生產(chǎn)總值數(shù)據(jù)年份一般預算總收入（億元）地區(qū)生產(chǎn)

11、總值年份一般預算總收入（億元）地區(qū)生產(chǎn)總值（億元）（億元）YXYX197827.45123.721998401.805052.62197925.87157.751999477.405443.92198031.13179.922000658.426141.03198134.34204.862001917.766898.34198236.64234.0120021166.588003.6719834179257.0920031468.899705.021984466323.2520041805.1611648.70198558.25429.16200521153613417.68198668.61

12、502.4720062567.6615718.47198776.366069920073239.8918753.73198885.55770.25200837300621462.6919899821849.4420094122.0422998.241990101.59904.6920104895.4127747.651991108.941089.3320115925.0032363.381992118361375.7020126408.4934739.131993166641925.9120136908.4137756.581994209392689.2820147421.7040173.03

13、1995248.503557.5520158549.4742886.491996291.754188.5320169225.0747251.361997340.524686.11(1)建立浙江省一般預算收入與全行地區(qū)生產(chǎn)總值的計量經(jīng)濟模型，估計模型的參數(shù)，檢驗模型的顯著性，用規(guī)范的形式寫出估計檢驗結果，并解釋所估計參數(shù)的經(jīng)濟意義(2)如果2017年，浙江省地區(qū)生產(chǎn)總值為52000億元,比上年增長10%,利用計量經(jīng)濟模型對浙江省2017年的一股預算收入做出點預測和區(qū)間預測(3)建立浙江省-般預算收入的對數(shù)與地區(qū)生產(chǎn)總值對數(shù)的計量經(jīng)濟模型，估計模型的參數(shù)檢驗模型的顯著性，并解釋所估計參數(shù)的經(jīng)濟意義

14、?！揪毩曨}2.2參考解答】(1)建立浙江省一般預算收入與全省地區(qū)生產(chǎn)總值的計量經(jīng)濟模型，估計模型的參數(shù)，檢驗模型的顯著性，用規(guī)范的形式寫出估計檢驗結果，并解釋所估計參數(shù)的經(jīng)濟意義作X與Y的散點圖圖形近似于線性關系，可建立線性回歸模型:丫=4+網(wǎng)區(qū)+4用EXiews估計檢驗結果為DependentVariable-YMethod:LeastSquaresDate:03/19.18Time:154519782016inauocaot30taiio(i539VariableCo而dentStdEriexkSMistkProbCX-22705180.1917654634713-48989490W259

15、87383083000000.0000RsquargAcjusioaR-squarcdS.E.orregressionSumsquaredresidLeglikeliioodF-stahsticProWF-statistc)0.9032530.993070226.45751897471-2657918SM65620.000000MeanacpccidontvarS.D.oororoorwgrAoieinfoalle(lonScfinarioitenonHannan-CuvincriterDcrbir-Wateonstat1003.1062720.360137329113818221378352

16、0276451(DI可歸結果的規(guī)范形式:Yt=-227.0518+0.191765Xj(46.34713)(0.002598)t=(-4.89894)(73.80083)R2=0.993253R2=0.99307F=5446.562n=39擬介優(yōu)度：由回歸結果可知R2=0.993253,產(chǎn)=0.99307,說明整體上模型擬合較好。t檢驗：分別針對地區(qū)生產(chǎn)總值參數(shù)為0的原假設，給定顯著性水平以=0.05,查t分布表中自由度為八一2=37的臨界值匕.025(37)=2.021。由回歸結果可知，參數(shù)的t值的絕對值均大于臨界值，這說明在顯著性水平a=0.053應該拒原假設，解釋變量地區(qū)生產(chǎn)總值對財政收

17、入有顯著影響。參數(shù)經(jīng)濟意義：浙江全省生產(chǎn)總值每增長1億元，平均說來財政預算收入將增長01918億元.(2)如果2017年，浙江省地區(qū)生產(chǎn)總值為52000億元，比上年增長10%,利用計量經(jīng)濟模型對浙江省2017年的一般預算收入做出點預測和區(qū)間預測xYMean11108.151933.105Median4586.110340.5203Maximum47251.369225.070Minimum123.72002587003Std.Dev14137.942720.363Skewress12519611.399702Kulosis32339773.647243Jarque-Bera10.2771100

18、3586613415340001222ProbabilitySum433217774?2113SumSqDe/.7631092.61E-08Observations3939將52000億元帶入回歸方程得到,般預算收入的點預測：Yf=-227.0518+0.191765X52000=9744.746一般預算收入的平均值預測：E0力(ri-1)=14137.942X(39-1)=7595491202.8568-X)2=(52000-11108.15)2=1672143396.4225當&=52000時，S025(37)=2.021,代入計算可得:9744.746+2.021X226.4575X11

19、672143396.4225FJ397595491202.8568=9744.746+226.901即：當?shù)貐^(qū)生產(chǎn)總值達到52000億元時，財政收入9平均值置信度95%的預測區(qū)間為(9517.845,9971.647)o一般預算收入的個別值預測區(qū)間為9744.746+2.021x226.4575x11672143396.42251+1397595491202.8568=9744.746+510.829即：當?shù)貐^(qū)生產(chǎn)總值達到52000億元時，財政收入V個別值置信度95%的預測區(qū)間為(9233.917,10255.575)o(3)建立浙江省一般預算收入的對數(shù)與地區(qū)生產(chǎn)總值對數(shù)的計最經(jīng)濟模型，估計模

20、型的參數(shù)，檢驗模型的顯著性，并解釋所估計參數(shù)的經(jīng)濟意義。DopondontVariGbloLOCtY)Method:LeastSquaresDate03/19J18Tine1609Sarrpl9(adusted)19782016Includedooser/ations:39afteradjustmentsvdfladleCoefTIcivitSidErrcrl-StattscP(obC225709102364859.5442980.0DO3LOG(X)1030813002848336.19114O.OODOR-squaroc0972527Meandependentvar6.084647Adju

21、stedR-squared0971785S.D.dependentvar1.957031SE.ofregression0330417Akaikeinfocriterion0.672999Sumsqua飛drsic4039493senwarzcnterion0.758310Loglitolhood-11.12347HannanQuinrcrilor0.703607F-statistc1309.799Dtrbin-Wasonstat0.085302ProUF-stalistlc)0000000回歸結果的規(guī)范形式：logTX)=-2.257091+1.0308161og(%)(0.236486)(0

22、.028483)t=(-9.544298)(36.19114)R2=0.972527R2=0.971785F=1309.799n=39擬合優(yōu)度：由回歸結果可知”=0.972527,產(chǎn)=0.972527,說明整體上模型擬合較好。參數(shù)顯著性檢驗:分別針對地區(qū)生產(chǎn)總值參數(shù)為0的原假設，給定顯著性水平a=0.05,杳t分布表中自由度為n2=37的臨界值玷.025(37)=2.021。由歸I歸結果可知，參數(shù)的e值的絕對值均大于臨界值，這說明在顯著性水平a=0.05卜，應該拒原假設，對數(shù)化的地區(qū)生產(chǎn)總值對對數(shù)化的財政收入有顯著影響。經(jīng)濟意義：地區(qū)生產(chǎn)總值每增長1%,財政收入平均而言增長1.030816%。

23、2.3在線性消費函數(shù)中，C是消費支HLY是可.支配收入，收入的邊際消費傾向(MPC)是斜率A，而平均消費傾向(APC)為/X。由中國統(tǒng)計年鑒得到2016午中國各地區(qū)居民人均消費支出和居民人均可支配收入數(shù)據(jù)：表2,92016年中國居民消費支出與可支配收入數(shù)據(jù)地區(qū)居民消費支出(元)居民可支配收入(元)地區(qū)居民消費支出(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廣東23448.430295.8lil西12682.919048.9廣西12295.218305.1

24、內(nèi)蒙古18072.324126.6海南14275.420653.4遼寧19852.826039.7慶16384.822034.1吉林14772.619967.0四川14838.518808.3黑龍江14445.819838.5貴州11931.615121.1上海37458.354305.3云南11768.816719.9江蘇22129.932070.1西減9318.713639.2浙江25526.638529.0陜西13943.018873.7安徽14711.519998.1甘肅12254.214670.3福建20167.527607.9青海14774.717301.8江西13258.6201

25、09.6寧夏14965.418832.3ill東15926.424685.3新商14066.518354.7河南12712.318443.1（1）在95%的置信度3求夕2的置信區(qū)間。（2）以可支配收入為x軸，畫出估計的MPC和APC圖。（3）當居民人均可支配收入為60000元時，預計人均消費支出C的點預測值。（4）在95%的置信度卜人均消費支出C平均值的預測區(qū)間。（5）在95%的置信度卜，人均消費支出C個別值的預測區(qū)間?！揪毩曨}2.3參考解答】（1）在95%的置信概率下，A的區(qū)間估計是多少？P庇-*SE（fiz）工傷工質(zhì)+越*SEG52）=0.9522得到：魚一2SE（ft）V為W62+德.S

26、E（/?2）220.66-t0.025（29）*0.02p20.66+t0.025（29）*0.020.66-2.0450.02ft0.66+t0.025（29）0.020.6191cProb.C227.051846.34713-4.8989400.0000X10.1917650.00259873.800830.0000R-squared0.993253Meandependentvar1903.106AdjustedR-squared0993070SDdependentvar2720360SEofregression226.4575Akaikeinfocriterion1373291Sumsq

27、uaredresid1897471.Schwarzcritenon1381822Loglikelihood2657918Hannan-Quinnenter.1376352F-statistic5446.562Durbin-Watsonstat0.276451ProtKF-statistic)00000002)財政預算總收入用萬元(Y2)表示,全省生產(chǎn)總值用萬元(X2)表示的回歸:回歸結果為：DependentVariableY2Method:LeastSquaresDate:03/16/18Time20:57Sample.19782016Includedobservations:39Varia

28、bleCoefficientStd.Errort-StatisticProbIC-2270518.463471.3-4.89894000000X201917650.00259873.8008300000R-squared0993253Meandependentvar19031059AdjustedR-squared0993070SDdependentvar27203599SE.ofregression2264575.Akaikeinfoenterion32.15359Sumsquaredresid1.90E*14Schwarzenterion32.23890Loglikelihood-6249

29、951Hannan-Ouinnenter.32.18420Fstatistic5446562DurDin-Watsonstat0276451Prob(F-statistic)00000003)財政預算總收入用萬元(Y2)表示,全省生產(chǎn)總值用億元(XI)表示的回歸:DependentVanable:Y2Method:LeastSquaresDate:03/16/18Time2059Sample:19782016Includedobservations39VariableCoefficientStdErrorbStatisticProb.C-2270518463471.3-4.8989400000

30、0X11917.65325.9841773800830.0000R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)0.99325309930702264575.1.90E*14-624.995154465620.000000MeandependentvarS.D.dependentvarAKaikeinfocriterionSchwarzcriterionHannan-QuinnenterDurbin-Watsonstat1903105927203599