計(jì)量經(jīng)濟(jì)學(xué)案例作業(yè).doc

2013級(jí)統(tǒng)計(jì)學(xué)專業(yè)計(jì)量經(jīng)濟(jì)學(xué)案例作業(yè)學(xué)號(hào)： 130702060 姓名：葉豪特1.下表是消費(fèi)Y與收入X的數(shù)據(jù)，試根據(jù)所給數(shù)據(jù)資料完成以下問(wèn)題：（1）估計(jì)回歸模型中的未知參數(shù)和，并寫(xiě)出樣本回歸模型的書(shū)寫(xiě)格式；（2）試用Goldfeld-Quandt法和White法檢驗(yàn)?zāi)Ｐ偷漠惙讲钚?；?）選用合適的方法修正異方差。（1）eview結(jié)果Method: Least SquaresDate: 06/08/15 Time: 10:20Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb.C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423Mean dependent var119.6667Adjusted R-squared0.945500S.D. dependent var38.68984S.E. of regression9.032255Akaike info criterion7.272246Sum squared resid4731.735Schwarz criterion7.342058Log likelihood-216.1674Hannan-Quinn criter.7.299553F-statistic1024.564Durbin-Watson stat1.790431Prob(F-statistic)0.000000，樣本回歸模型書(shū)寫(xiě)格式： （2）首先，用Goldfeld-Quandt法進(jìn)行檢驗(yàn)。 a.將樣本按遞增順序排序，去掉1/4，再分為兩個(gè)部分的樣本，即。 b.分別對(duì)兩個(gè)部分的樣本求最小二乘估計(jì)，得到兩個(gè)部分的殘差平方和，即求F統(tǒng)計(jì)量為給定，查F分布表，得臨界值為。c.比較臨界值與F統(tǒng)計(jì)量值，有=4.1390，說(shuō)明該模型的隨機(jī)誤差項(xiàng)存在異方差。用White法進(jìn)行檢驗(yàn)White Heteroskedasticity Test:F-statistic6.301373 Probability0.003370Obs*R-squared10.86401 Probability0.004374Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/08/15 Time: 12:25Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C-10.03614131.1424-0.0765290.9393X0.1659771.6198560.1024640.9187X20.0018000.0045870.3924690.6962R-squared0.181067 Mean dependent var78.86225Adjusted R-squared0.152332 S.D. dependent var111.1375S.E. of regression102.3231 Akaike info criterion12.14285Sum squared resid596790.5 Schwarz criterion12.24757Log likelihood-361.2856 F-statistic6.301373Durbin-Watson stat0.937366 Prob(F-statistic)0.003370，在自由度為2下查卡方分布表，得。比較臨界值與卡方統(tǒng)計(jì)量值，即，說(shuō)明模型中的隨機(jī)誤差項(xiàng)存在異方差。 （2）用加權(quán)最小二乘估計(jì)，得如下結(jié)果 Dependent Variable: YMethod: Least SquaresDate: 06/08/15 Time: 13:10Sample: 1 60Included observations: 60Weighting series: W1VariableCoefficientStd. Errort-StatisticProb. C10.370512.6297163.9435870.0002X0.6309500.01853234.046670.0000Weighted StatisticsR-squared0.211441 Mean dependent var106.2101Adjusted R-squared0.197845 S.D. dependent var8.685376S.E. of regression7.778892 Akaike info criterion6.973470Sum squared resid3509.647 Schwarz criterion7.043282Log likelihood-207.2041 F-statistic1159.176Durbin-Watson stat0.958467 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.946335 Mean dependent var119.6667Adjusted R-squared0.945410 S.D. dependent var38.68984S.E. of regression9.039689 Sum squared resid4739.526Durbin-Watson stat0.800564其估計(jì)的書(shū)寫(xiě)形式為2. 下表給出了日本工薪家庭實(shí)際消費(fèi)支出與可支配收入數(shù)據(jù)日本工薪家庭實(shí)際消費(fèi)支出與實(shí)際可支配收入單位：1000日元年份個(gè)人實(shí)際可支配收入X個(gè)人實(shí)際消費(fèi)支出Y年份個(gè)人實(shí)際可支配收入X個(gè)人實(shí)際消費(fèi)支出Y1970197119721973197419751976197719781979198019811982239248258272268280279282285293291294302300311329351354364360366370378374371381198319841985198619871988198919901991199219931994304308310312314324326332334336334330384392400403411428434441449451449449要求：（1）建立日本工薪家庭的收入消費(fèi)函數(shù)； （2）檢驗(yàn)?zāi)Ｐ椭写嬖诘膯?wèn)題，并采取適當(dāng)?shù)难a(bǔ)救措施預(yù)以處理； （3）對(duì)模型結(jié)果進(jìn)行經(jīng)濟(jì)解釋。要求：（1）檢測(cè)進(jìn)口需求模型的自相關(guān)性； （2）采用科克倫奧克特迭代法處理模型中的自相關(guān)問(wèn)題。（1）由eviews一元線性回歸結(jié)果可得：Dependent Variable: YMethod: Least SquaresDate: 06/09/15 Time: 20:20Sample: 1970 1994Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C-68.1602615.26513-4.4650960.0002X1.5297120.05097630.008460.0000R-squared0.975095Mean dependent var388.0000Adjusted R-squared0.974012S.D. dependent var43.33397S.E. of regression6.985763Akaike info criterion6.802244Sum squared resid1122.420Schwarz criterion6.899754Log likelihood-83.02805Hannan-Quinn criter.6.829289F-statistic900.5078Durbin-Watson stat0.348288Prob(F-statistic)0.000000Y=-68.16+1.53X （1）（2）Dependent Variable: YMethod: Least SquaresDate: 06/09/15 Time: 20:58Sample: 1970 1994Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C18.3314429.515180.6210850.5409X1.2022390.10938210.991210.0000TIME20.0505020.0155223.2536110.0036R-squared0.983186Mean dependent var388.0000Adjusted R-squared0.981657S.D. dependent var43.33397S.E. of regression5.868976Akaike info criterion6.489404Sum squared resid757.7875Schwarz criterion6.635669Log likelihood-78.11755Hannan-Quinn criter.6.529972F-statistic643.2046Durbin-Watson stat0.403640Prob(F-statistic)0.000000D.W.檢驗(yàn)結(jié)果表明，在5%顯著性水平下，n=25，k=2（包含常數(shù)項(xiàng)），查表得，由于D.W.=0.35,故（1）存在正自相關(guān)。引入時(shí)間變量T（T=1，2，25）以平方的形式出現(xiàn)，回歸函數(shù)變化為：（2），這里，D.W.值仍然比較低，沒(méi)有通過(guò)5%顯著性水平下的D.W.檢驗(yàn)，因此判斷（2）式仍然存在正自相關(guān)性。再對(duì)（2）式進(jìn)行序列相關(guān)性的拉格朗日乘數(shù)檢驗(yàn)。含一階滯后殘差項(xiàng)的輔助回歸為：于是，LM=24=18，該值大于顯著性水平為5%，自由度為1的分布的臨界值，由此判斷原模型存在1階序列相關(guān)性。含2階滯后殘差項(xiàng)的輔助回歸為：Dependent Variable: AMethod: Least SquaresDate: 06/09/15 Time: 22:00Sample: 1970 1994Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C-0.62016619.49328-0.0318140.9749X0.0018950.0722250.0262390.9793TIME20.0014470.0102400.1413110.8890RE0.9176810.2108534.3522280.0003RE2-0.1974030.213975-0.9225500.3672R-squared0.604654Mean dependent var1.98E-14Adjusted R-squared0.525585S.D. dependent var5.619117S.E. of regression3.870322Akaike info criterion5.721409Sum squared resid299.5879Schwarz criterion5.965184Log likelihood-66.51761Hannan-Quinn criter.5.789022F-statistic7.647165Durbin-Watson stat1.826752Prob(F-statistic)0.000657（RE2為）采用科克倫奧克特兩步法處理模型中的自相關(guān)問(wèn)題根據(jù)，eviews運(yùn)行結(jié)果如下：最終的消費(fèi)模型為 Y t = 93.7518+0.5351 X t （3）模型說(shuō)明日本工薪居民的邊際消費(fèi)傾向?yàn)?.5351，即收入每增加1元，平均說(shuō)來(lái)消費(fèi)增加0.54元。3. 下表給出了中國(guó)商品進(jìn)口額Y、國(guó)內(nèi)生產(chǎn)總值GDP、居民消費(fèi)價(jià)格指數(shù)CPI。中國(guó)商品進(jìn)口額、國(guó)內(nèi)生產(chǎn)總值、居民消費(fèi)價(jià)格指數(shù)年份商品進(jìn)口額(億元)國(guó)內(nèi)生產(chǎn)總值(億元)居民消費(fèi)價(jià)格指數(shù)(1985=100)19851257.89016.0100.019861498.310275.2106.519871614.212058.6114.319882055.115042.8135.819892199.916992.3160.219902574.318667.8165.219913398.721781.5170.819924443.326923.5181.719935986.235333.9208.419949960.148197.9258.6199511048.160793.7302.8199611557.471176.6327.9199711806.578973.0337.1199811626.184402.3334.4199913736.489677.1329.7200018638.899214.6331.0200120159.2109655.2333.3200224430.3120332.7330.6200334195.6135822.8334.6200446435.8159878.3347.7200554273.7183084.8353.9200663376.9 211923.5359.2200773284.6 249529.9376.5請(qǐng)考慮下列模型：1)利用表中數(shù)據(jù)估計(jì)此模型的參數(shù)。2)根據(jù)所學(xué)知識(shí)判斷數(shù)據(jù)中有多重共線性嗎？ 3)若存在多重共線性，利用逐步回歸克服多重共線性。解：（1) Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/10/15 Time: 14:34Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb.C-3.0601490.337427-9.0690590.0000LOG(X1)1.6566740.09220617.967030.0000LOG(X2)-1.0570530.214647-4.9246180.0001R-squared0.992218Mean