計量經濟學案例作業(yè).doc

2013級統(tǒng)計學專業(yè)計量經濟學案例作業(yè)學號： 130702060 姓名：葉豪特1.下表是消費Y與收入X的數據，試根據所給數據資料完成以下問題：（1）估計回歸模型中的未知參數和，并寫出樣本回歸模型的書寫格式；（2）試用Goldfeld-Quandt法和White法檢驗模型的異方差性；（3）選用合適的方法修正異方差。（1）eview結果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，樣本回歸模型書寫格式： （2）首先，用Goldfeld-Quandt法進行檢驗。 a.將樣本按遞增順序排序，去掉1/4，再分為兩個部分的樣本，即。 b.分別對兩個部分的樣本求最小二乘估計，得到兩個部分的殘差平方和，即求F統(tǒng)計量為給定，查F分布表，得臨界值為。c.比較臨界值與F統(tǒng)計量值，有=4.1390，說明該模型的隨機誤差項存在異方差。用White法進行檢驗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)計量值，即，說明模型中的隨機誤差項存在異方差。 （2）用加權最小二乘估計，得如下結果 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其估計的書寫形式為2. 下表給出了日本工薪家庭實際消費支出與可支配收入數據日本工薪家庭實際消費支出與實際可支配收入單位：1000日元年份個人實際可支配收入X個人實際消費支出Y年份個人實際可支配收入X個人實際消費支出Y1970197119721973197419751976197719781979198019811982239248258272268280279282285293291294302300311329351354364360366370378374371381198319841985198619871988198919901991199219931994304308310312314324326332334336334330384392400403411428434441449451449449要求：（1）建立日本工薪家庭的收入消費函數； （2）檢驗模型中存在的問題，并采取適當的補救措施預以處理； （3）對模型結果進行經濟解釋。要求：（1）檢測進口需求模型的自相關性； （2）采用科克倫奧克特迭代法處理模型中的自相關問題。（1）由eviews一元線性回歸結果可得：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.檢驗結果表明，在5%顯著性水平下，n=25，k=2（包含常數項），查表得，由于D.W.=0.35,故（1）存在正自相關。引入時間變量T（T=1，2，25）以平方的形式出現，回歸函數變化為：（2），這里，D.W.值仍然比較低，沒有通過5%顯著性水平下的D.W.檢驗，因此判斷（2）式仍然存在正自相關性。再對（2）式進行序列相關性的拉格朗日乘數檢驗。含一階滯后殘差項的輔助回歸為：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階序列相關性。含2階滯后殘差項的輔助回歸為：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問題根據，eviews運行結果如下：最終的消費模型為 Y t = 93.7518+0.5351 X t （3）模型說明日本工薪居民的邊際消費傾向為0.5351，即收入每增加1元，平均說來消費增加0.54元。3. 下表給出了中國商品進口額Y、國內生產總值GDP、居民消費價格指數CPI。中國商品進口額、國內生產總值、居民消費價格指數年份商品進口額(億元)國內生產總值(億元)居民消費價格指數(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請考慮下列模型：1)利用表中數據估計此模型的參數。2)根據所學知識判斷數據中有多重共線性嗎？ 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