我國糧食生產(chǎn)與相關(guān)投入計量經(jīng)濟學(xué)模型分析.doc

我國糧食生產(chǎn)與相關(guān)投入計量經(jīng)濟學(xué)模型分析一， 引言著名經(jīng)濟學(xué)家李子奈教授在曾對我國19831995年糧食生產(chǎn)數(shù)據(jù)進行過研究分析,他選取的影響因素數(shù)據(jù)是:農(nóng)用化肥施用量,糧食播種面積,成災(zāi)面積,農(nóng)業(yè)機械動力和農(nóng)業(yè)勞力,并擬合出了關(guān)于我國糧食生產(chǎn)的線性回歸模型.在本文中,我們將運用計量經(jīng)濟學(xué)的方法對上述模型問題進行研究.對于糧食產(chǎn)量的影響,除了選取上述影響因素外,還把農(nóng)村用電量、國家財政用于農(nóng)業(yè)的支出和灌溉面積的影響因素數(shù)據(jù)也加到了模型中去.二，變量的確定與C-D生產(chǎn)函數(shù)模型i. 被解釋變量與解釋變量的確定最終確定的模型的被解釋變量為:糧食總產(chǎn)量;解釋變量為:播種面積、成災(zāi)面積、化肥施用量、農(nóng)業(yè)機械動力、國家財政用于農(nóng)業(yè)的支出、灌溉面積和農(nóng)業(yè)勞動力.由初步的分析知,糧食產(chǎn)量與成災(zāi)面積是負(fù)相關(guān)的,而與其它變量則是正相關(guān)的.ii. C-D生產(chǎn)函數(shù)模型我們選擇在經(jīng)濟領(lǐng)域應(yīng)用最廣泛的一種生產(chǎn)函數(shù)模型C-D生產(chǎn)函數(shù)模型來進行研究.即Y=f(A,K,L,)其中Y為產(chǎn)出量,A,K,L分別為技術(shù)、資本、勞動的投入要素.生產(chǎn)要素對生產(chǎn)函數(shù)的作用與影響,主要是由一定的技術(shù)條件決定的,從本質(zhì)上講,生產(chǎn)函數(shù)反映了生產(chǎn)過程中投入要素與產(chǎn)出量之間的技術(shù)關(guān)系.2數(shù)據(jù)收集根據(jù)上面的所確定的模型的變量,我們收集到了1980年2004年主要糧食生產(chǎn)數(shù)據(jù)(表一)。iii. 模型的估計 設(shè)定:糧食總產(chǎn)量為Y播種面積為X1成災(zāi)面積為X2,化肥施用量為X3,灌溉面積為X4,國家財政用于農(nóng)業(yè)資金為X5,農(nóng)機動力為X6,農(nóng)村勞動力為X7.由C-D生產(chǎn)函數(shù)模型,得模型形式如下:Yt=AXitbit(i=1,2,7)(1)兩邊取對數(shù)并進行變換,得:log Yt =b0+bilogXit+t(i=1,2,7)(2)其中b0=logA,t=logt.運用Eviews軟件對模型(2)進行OLS估計,我們得到估計結(jié)果Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/10/09 Time: 03:55Sample: 1980 2004Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C3.3758955.5021110.6135640.5476LOG(X1)0.9587450.2795123.4300650.0032LOG(X2)-0.1037040.040353-2.5699500.0199LOG(X3)0.4948670.1044504.7378190.0002LOG(X4)-0.5649730.462026-1.2228180.2381LOG(X5)-0.0143810.074375-0.1933540.8490LOG(X6)0.0183880.1192590.1541820.8793LOG(X7)-0.0694990.137533-0.5053240.6198R-squared0.963763 Mean dependent var10.66170Adjusted R-squared0.948842 S.D. dependent var0.127561S.E. of regression0.028852 Akaike info criterion-3.998937Sum squared resid0.014151 Schwarz criterion-3.608897Log likelihood57.98671 F-statistic64.59068Durbin-Watson stat1.245744 Prob(F-statistic)0.000000從表2可以看出,回歸估計的判決系數(shù)R2很高,方程很顯著,但是8個參數(shù)的t檢驗值中，卻只有兩個略微顯著.顯然,出現(xiàn)了嚴(yán)重的多重共線性。iv. 模型的檢驗1）多重共線性的檢驗與消除1相關(guān)系數(shù)法.從各解釋變量之間的相關(guān)系數(shù)(表3)也能初步看出各變量之間存在著多重共線性:檢驗簡單相關(guān)系數(shù)：2修正的Frish方法.下面我們用修正的Frish方法來消除該模型的多重共線性。首先,做出被解釋變量logY關(guān)于解釋變量logXi的每一個回歸方程,得各判決系數(shù)R2i依次為:R12=0.098512;R22=0.154683;R32=0.825167;R42=0.586538;R52=0.629207;R62=0.687181;R72= 0.581854.從上面我們知道判決系數(shù)R2最大的為R32,從而可選取X3作為模型的出發(fā)點進行估計,Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/10/09 Time: 04:51Sample: 1980 2004Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C8.4718850.21045940.254320.0000LOG(X3)0.2767310.02656010.418940.0000R-squared0.825167 Mean dependent var10.66170Adjusted R-squared0.817566 S.D. dependent var0.127561S.E. of regression0.054484 Akaike info criterion-2.905185Sum squared resid0.068277 Schwarz criterion-2.807675Log likelihood38.31482 F-statistic108.5543Durbin-Watson stat0.733968 Prob(F-statistic)0.000000在Y, X3中加入解釋變量X1進行估計,常數(shù)項不顯著,在去掉常數(shù)項后再一次估計VariableCoefficientStd. Errort-StatisticProb. LOG(X1)0.7044220.01355751.961760.0000LOG(X3)0.3135990.01986815.784330.0000R-squared0.894484 Mean dependent var10.66170Adjusted R-squared0.889897 S.D. dependent var0.127561S.E. of regression0.042327 Akaike info criterion-3.410155Sum squared resid0.041207 Schwarz criterion-3.312645Log likelihood44.62693 Durbin-Watson stat0.783868從結(jié)果可以看出在加入解釋變量X1之后,其判決系數(shù)R2的值有了明顯的變化,并且對X3的系數(shù)值和t檢驗值沒有多大影響,因此可以加入變量X1.同理,在Y,X1,X3中加入解釋變量X2進行估計得常數(shù)項不顯著,在去掉常數(shù)項后,得下表logY對logXt(t=1,2,3)的回歸VariableCoefficientStd. Errort-StatisticProb. LOG(X1)0.7913390.02214635.732830.0000LOG(X2)-0.1491430.033820-4.4099140.0002LOG(X3)0.3763580.02053218.330150.0000R-squared0.943993 Mean dependent var10.66170Adjusted R-squared0.938901 S.D. dependent var0.127561S.E. of regression0.031531 Akaike info criterion-3.963536Sum squared resid0.021872 Schwarz criterion-3.817271Log likelihood52.54420 Durbin-Watson stat0.855241從結(jié)果可以看出:在加入變量X2之后,其判決系數(shù)R2的值有了明顯變化,并且對X1, X3的系數(shù)值和t檢驗值沒有多大影響,并且X2的估計系數(shù)是負(fù)值,符合經(jīng)濟意義,加入變量X2.在Y, X1, X2, X3中加入變量X4進行估計得常數(shù)項不顯著,去掉常數(shù)項后,再一次估計得下表.從結(jié)果可以看出加入解釋變量X4之后,其判決系數(shù)R2的值雖然有變化,但對X2的系數(shù)值和t檢驗值有較大影響,且X4的估計系數(shù)是負(fù)值,不符合經(jīng)濟意義.它的t檢驗值也不太顯著,因此暫時不考慮加入變量X4VariableCoefficientStd. Errort-StatisticProb. LOG(X1)1.1221880.1135989.8785990.0000LOG(X2)-0.1035570.032933-3.1445050.0049LOG(X3)0.4612170.03372013.677790.0000LOG(X4)-0.4611060.156080-2.9543010.0076R-squared0.960436 Mean dependent var10.66170Adjusted R-squared0.954784 S.D. dependent var0.127561S.E. of regression0.027125 Akaike info criterion-4.231099Sum squared resid0.015451 Schwarz criterion-4.036079Log likelihood56.88874 Durbin-Watson stat0.947940運用同樣的方法逐個加入變量X5, X6進行估計知,加入的變量對表7的判決系數(shù)R2沒有多大影響,但對t檢驗值有較大影響,因此暫時不考慮加入上述變量.在Y, X1, X2, X3中加入解釋變量X7進行估計得下表：VariableCoefficientStd. Errort-StatisticProb. C-2.2993632.950548-0.7793000.4449LOG(X1)0.9742660.2277764.2772970.0004LOG(X2)-0.1378920.037783-3.6496210.0016LOG(X3)0.3824680.03317811.527730.0000LOG(X7)0.0012580.1259820.0099840.9921R-squared0.945786 Mean dependent var10.66170Adjusted R-squared0.934943 S.D. dependent var0.127561S.E. of regression0.032536 Akaike info criterion-3.836071Sum squared resid0.021172 Schwarz criterion-3.592296Log likelihood52.95089 F-statistic87.22663Durbin-Watson stat0.770568 Prob(F-statistic)0.000000從結(jié)果可以看出,在加入解釋變量X7之后,其判決系數(shù)R2的值有較大變化,況且它對其余解釋變量的t檢驗值和系數(shù)沒有多大影響,因此可以加入該變量.最終,我們確定模型的形式為:log Yt =b0+b1logX1t+ b2logX2t+ b3logX3t + b4logX7t +t從而我們有如下的回歸模型:log(Y) =0.974266log(X1) -0.137892log（X2) +0.382468log(X3) +0.001258log(X7)- 2.299363 (0.227776)(0.037783) (0.033178) (0.125982) (2.950548) (4.277297)(-3.649621) (13.67779) （0.009984） (-0.779300)R2=0.945786SE=0.032536DW=0.770568F=87.22663從報告可以看出, X1, X7和常數(shù)項的t檢驗值并不太顯著,模型擬合得并不是太好,且常數(shù)項為負(fù)值,這也不符合經(jīng)濟含義.從DW表中可以看到,對于n=25,k=4,在5%的顯著水平下,有dL=0.953和dU=1.886,而表中的DW值僅為d=0.770568,明顯比dL值要小,這說明模型存在嚴(yán)重的序列自相關(guān)性,這有可能是導(dǎo)致上述t檢驗值并不顯著的重要原因.因此,為了使模型更具有價值,我們首先必須消除模型的自相關(guān).自相關(guān)的消除下面試著用迭代法來消除自相關(guān).經(jīng)過多次反復(fù)擬合,得較理想的回歸結(jié)果 VariableCoefficientStd. Errort-StatisticProb. LOG(X1)0.8038200.02386433.683510.0000LOG(X2)-0.1085590.033016-3.2880490.0041LOG(X3)0.2821770.0356007.9263580.0000Y(-1)5.78E-062.66E-062.1725680.0434Y(-2)-1.16E-063.00E-06-0.3879450.7026R-squared0.954228 Mean dependent var10.68601Adjusted R-squared0.944057 S.D. dependent var0.100122S.E. of regression0.023681 Akaike info criterion-4.458614Sum squared resid0.010094 Schwarz criterion-4.211767Log likelihood56.27406 Durbin-Watson stat1.415754從表可以看出,添入Y(-1)和Y(-2)項后,DW值由0.770568提高到了1.415754,自相關(guān)得到了消除,且各統(tǒng)計量均能顯著通過.下面再來看表9的異方差檢驗.異方差的檢驗采用懷特檢驗法，輔助回歸模型的估計結(jié)果如下：White Heteroskedasticity Test:F-statistic6.446908 Probability0.001765Obs*R-squared19.39070 Probability0.035572Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/11/09 Time: 00:44Sample: 1982 2004Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C0.69446510.704310.0648770.9493LOG(X1)0.0163161.8525080.0088080.9931(LOG(X1)2-0.0004920.079981-0.0061570.9952LOG(X2)-0.1222230.043327-2.8209250.0154(LOG(X2)20.0061120.0021352.8630900.0143LOG(X3)-0.0542750.032070-1.6923930.1164(LOG(X3)20.0034750.0020301.7117620.1126Y(-1)-9.25E-075.87E-07-1.5768410.1408Y(-1)28.46E-126.79E-121.2456550.2367Y(-2)1.27E-065.34E-072.3853180.0344Y(-2)2-1.38E-115.88E-12-2.3370470.0376R-squared0.843074 Mean dependent var0.000439Adjusted R-squared0.712302 S.D. dependent var0.000718S.E. of regression0.000385 Akaike info criterion-12.58009Sum squared resid1.78E-06 Schwarz criterion-12.03703Log likelihood155.6710 F-statistic6.446908Durbin-Watson stat2.441613 Prob(F-statistic)0.001765在同方差的條件下：n，h=3,為解釋變量的個數(shù)從上圖可知n19.390702，在顯著水平0.05的情況下，7.82，由于n7.82,故存在異方差性?？朔惙讲?，采用加權(quán)最小二乘法（WLS）,以為權(quán)數(shù)進行WLS估計，得估計結(jié)果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/11/09 Time: 01:30Sample(adjusted): 1982 2004Included observations: 23 after adjusting endpointsWeighting series: 1/ABS(RESID)White Heteroskedasticity-Consistent Standard Errors & CovarianceVariableCoefficientStd. Errort-StatisticProb. LOG(X1)0.8102180.004790169.16200.0000LOG(X2)-0.1092530.005836-18.720180.0000LOG(X3)0.2684210.01691515.868420.0000Y(-1)1.020 9920.200 1010.961870.0000Y(-2)-0.498 950.216 003-0.3980640.6953Weighted StatisticsR-squared1.000000 Mean dependent var10.72762Adjusted R-squared1.000000 S.D. dependent var31.92350S.E. of regression0.001570 Akaike info criterion-9.885525Sum squared resid4.44E-05 Schwarz criterion-9.638679Log likelihood118.6835 Durbin-Watson stat1.776039Unweighted StatisticsR-squared0.953685 Mean dependent var10.68601Adjusted R-squared0.943392 S.D. dependent var0.100122S.E. of regression0.023821 Sum squared resid0.010214Durbin-Watson stat1.409905最終擬合的回歸方程為log(Y)= 0.810218log(X1)- 0.109253log(X2)+ 0.268421log(X3)(0.004790)(0.005836) (0.016915) (169.1620)(-18.72018) (15.86842)+1.020 992log Yt-1-0.498 95log Yt-2(10.96187)(-0.398064)(0.200 10) (0.216 003)R2=1.000000SE=0.001570DW=1.776039和初始方程比較，無論是擬合優(yōu)度還是個參數(shù)的t值都有顯著的改善。擬合結(jié)果可以由下圖形象的看出：三，經(jīng)濟意義檢驗對于方程,經(jīng)濟含義上logX1的系數(shù)為0.810218,logX2的系數(shù)為-0.109253,logX3的系數(shù)為0.268421.三者之和為0.969386,約等于1,這說明該模型是規(guī)模報酬不變的,符合預(yù)測值四，模型預(yù)測檢驗根據(jù)方程,我們可以推出序列Yt的預(yù)測公式為:log(Y)= 0.810218log(X1)- 0.109253log(X2)+ 0.268421log(X3)(0.004790)(0.005836) (0.016915) (169.1620)(-18.72018) (15.86842)+1.020 992log Yt-1