1、Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE Pindyck,R.S.&D.L.Rubinfeld(1991),pp.163-4:“Our discussion of econometrics has relied heavily on the assumption that the model to be estimated is correctly specified.Once the correct specif
2、ication of the model is assumed,model estimation and model testing become relatively straightforward.In reality,however,we can never be sure that a given model is correctly specified.In fact,researchers usually examine more than one possible specification,attempting to find the specification which b
3、est describes the process under study.”Friday,21 Nov.2008CUFE Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEtttuXY10ln)1(1ln1dXYdYdXdYYdXYdFriday,21 Nov.2008CUFEttutGDP10)ln(Friday,21 Nov.2008CUFEtttuXYln10XdXdY11XdXdYdXdYX1XXYXY的相对变动的绝对变动1 XXY11Friday,21 Nov.2008CUFE tttuXY11000Friday,21 Nov.2008CUFE
4、(Mills,T.C.(1993):The reciprocal model has the following properties:(a)(b)(c)The model might be used to model:the relationship between average fixed costs of production and output of a firm;the Philips Curve:relationship between wage changes and unemployment;Engel expenditure curves,having a thresho
5、ld level of income()and a saturation level :with given tastes or preferences,the proportion of income spent on food diminishes as incomes increase.01/0Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2012.ptttpttYXXXuFriday,21 Nov.2008CUFE10tttuXY10的绝对变动的绝对变动XYdXdYtttuXYlnln10的相对变动的相对变动XYXdXYdYtttuXY10ln
6、ttutY10ln的绝对变动的相对变动XYdXYdY的相对变动的绝对变动XYXdXdYtttuXY1102XdXdY00YiPiPiiuXXY10当Xtime时，也叫增长模型(growth model)：当X时，Y ,即Y将无限靠近其渐近线（1tttuXYln10Friday,21 Nov.2008CUFE 模型中遗漏了对因变量有显著影响的解释变量的后果是：将使模型参数估计量不再是无偏估计量模型参数估计量不再是无偏估计量。模型中包括无关的解释变量，参数估计量仍无参数估计量仍无偏，但会增大估计量的方差，即增大误差偏，但会增大估计量的方差，即增大误差。注 有关上述两点结论的说明请参见教科书P101
7、-102。Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2R2RFriday,21 Nov.2008CUFE2RFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2jjjRSSnk2m22Friday,21 Nov.2008CUFE22/()/()(1)2()/()exp2(1)/jjjjjjjmjjjjjppRRSSnkSRSSnknkCRSSkPCRSSnknkAICRSSkn Friday,21 Nov.2008CUFE2R2R222R2R22()jE22()jE22()jEFriday,21 Nov.200
8、8CUFE1()kkfYfY2()ffEYYpCpSFriday,21 Nov.2008CUFEpCpSFriday,21 Nov.2008CUFE2(1)/knR S SA ICen(1)/knRSSSICnnFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE Friday,21 Nov.2008CUFE iiiXXY22110iiiiiiiuYYYXXY45342322110Friday,21 Nov.2008CUFE)1/(/)(knRSSMRSSRSSFMFriday,21 Nov.2008CUFE Friday,21 Nov.2008CUFEFr
9、iday,21 Nov.2008CUFE0110ktktXCXCCnt,2,1Friday,21 Nov.2008CUFE)u()()u()()()(111EXXXXXXXEYXXXEEFriday,21 Nov.2008CUFEttttuXXY22110 ttXXrVar11212211 VarFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE)1(1)(2iiRVIFFriday,21 Nov.2008CUFE5)(iVI
10、FFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE22213Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEu*3210PPXQvPPXQ)(*321Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE22tFriday,21 Nov.2008CUFEFrid
11、ay,21 Nov.2008CUFE21)(XXFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2tFriday,21 Nov.2008CUFE0)()()()()(2222eeXXxeeXeXeeXXeeXXrttttttttttFriday,21 Nov.2008CUFE)12(261nntdrFriday,21 Nov.2008CUFEtXtXtetetetd7.03.0124566116122nndrtFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2t11221kne13223kneFriday,21 N
12、ov.2008CUFE2321232123212123Friday,21 Nov.2008CUFE2123Friday,21 Nov.2008CUFE12233(1)iiiiYXXu222122334253623(2)iiiiiiiieXXXXX Xv Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE222()1,2,.tttVar utn Friday,21 Nov.2008CUFE011.(2)ttKttKtttttYXXu222221)(1)(ttttttuVaruVar22tFriday,21 Nov.2008CUFEFriday,21 Nov.
13、2008CUFE111)(,PPPPuPXPYP111Friday,21 Nov.2008CUFE)()(11*PuuPEuuE)(11PuuEP)(121PP)(112PPPP)(112PPPPI2我们有Friday,21 Nov.2008CUFE这表明，模型（2）中的扰动项u*满足OLS法的基本假设，可直接用OLS估计，估计量向量*1*)(YXXXYPPXXPPX11111)()(YXXX111)(这就是广义最小二乘估计量（GLS估计量）的公式，该估计量是BLUE。从上述证明过程可知，我们可将GLS法应用于为任意正定矩阵的情形。Friday,21 Nov.2008CUFE2)(uuE222
14、212.000.0.000.00nntt,.,2,1,02PPn.000.0.000.0021Friday,21 Nov.2008CUFE)(1.000.0.0100.0011211PPn2222111.000.0.0100.001nFriday,21 Nov.2008CUFE22221.000.0.000.00n2t2t222tt2Friday,21 Nov.2008CUFEnXXX.000.0.000.00212t2Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEteteFriday,21 Nov.2008CUFE.1101010210tjtttjt
15、ttjtttjttuXeuXeuXeuXeteFriday,21 Nov.2008CUFEjttX2jnjjXXX.000.0.000.0021Friday,21 Nov.2008CUFE22221nnP1.11211Friday,21 Nov.2008CUFEtttKtKtttttuXXY110),.,2,1,1(nttFriday,21 Nov.2008CUFE12(1)iiiYXuFriday,21 Nov.2008CUFE)8434.3()1948.0(4783.00319.099.1922RXYiiiiX2iX)2(121iiiiiiXuXXXYFriday,21 Nov.2008C
16、UFE21246.680.03680.6258(0.647)(5.172)iiiiYXRXXFriday,21 Nov.2008CUFE Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEnttnttteeeDW12221)(Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.
17、2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE11122:1,2,.:.ktitititttp t pttAYXutnBuuuu白噪声Friday,21 Nov.2008CUFE012:.0pH111,2,.(3)pktit it iitiieXetnFriday,21 Nov.2008CUFEt ie2P F22()P FPFriday,21 Nov.2008C
18、UFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE1tttYYY1tttXXXFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2112122122212()().()()().()().()().()nnnnnE uE u uE u uE u uE uE u uE uuE u uE u uE u Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFE2n2221 2t2tYXXXGLS111)(Friday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEFriday,21 Nov.2008CUFEi2i 3iiFriday,21 Nov.2008CUFE
