3844 part 14 generalized regression estimating

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Part 14: Generalized Regression Estimating Variance Components p OLS is still consistent: p Est.Var1 = e1’e1/N1 estimates σg2 p Est.Var2 = e2’e2/N2 estimates σg2 exp(θ2) p Estimator of θ2 is ln[(e2’e2/N2)/(e1’e1/N1)] p (1) Now use FGLS – weighted least squares p Recompute residuals using WLS slopes p (2) Recompute variance estimators p Iterate to a solution… between (1) and (2) ™  39/44
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Part 14: Generalized Regression Baltagi and Griffin’s Gasoline Data World Gasoline Demand Data, 18 OECD Countries, 19 years Variables in the file are COUNTRY = name of country  YEAR = year, 1960-1978 LGASPCAR = log of consumption per car LINCOMEP = log of per capita income LRPMG = log of real price of gasoline  LCARPCAP = log of per capita number of cars  See Baltagi (2001, p. 24) for analysis of these data. The article on which the  analysis is based is Baltagi, B. and Griffin, J., "Gasolne Demand in the OECD: An  Application of Pooling and Testing Procedures," European Economic Review, 22,  1983, pp. 117-137.  The data were downloaded from the website for Baltagi's text.  ™  40/44
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Part 14: Generalized Regression Analysis of Variance ™  41/44
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Part 14: Generalized Regression Least Squares First Step ---------------------------------------------------------------------- Multiplicative Heteroskedastic Regression Model... Ordinary least squares regression ............ LHS=LGASPCAR Mean = 4.29624 Standard deviation = .54891 Number of observs. = 342 Model size Parameters = 4 Degrees of freedom = 338 Residuals Sum of squares = 14.90436 Wald statistic [17 d.f.] = 699.43 (.0000) (Large) B/P LM statistic [17 d.f.] = 111.55 (.0000) (Large) Cov matrix for b is sigma^2*inv(X'X)(X'WX)inv(X'X) --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Constant| 2.39133*** .20010 11.951 .0000 LINCOMEP| .88996*** .07358 12.094 .0000 -6.13943 LRPMG| -.89180*** .06119 -14.574 .0000 -.52310 LCARPCAP| -.76337*** .03030 -25.190 .0000 -9.04180 --------+------------------------------------------------------------- ™  42/44
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Part 14: Generalized Regression Variance Estimates = log[e(i)’e(i)/T] Sigma| .48196*** .12281 3.924 .0001 D1| -2.60677*** .72073 -3.617 .0003 .05556 D2| -1.52919** .72073 -2.122 .0339 .05556 D3| .47152 .72073 .654 .5130 .05556 D4| -3.15102*** .72073 -4.372 .0000 .05556 D5| -3.26236*** .72073 -4.526 .0000 .05556 D6| -.09099 .72073 -.126 .8995 .05556 D7| -1.88962*** .72073 -2.622 .0087 .05556 D8| .60559 .72073 .840 .4008 .05556 D9| -1.56624** .72073 -2.173 .0298 .05556 D10| -1.53284** .72073 -2.127 .0334 .05556 D11| -2.62835*** .72073 -3.647 .0003 .05556 D12| -2.23638*** .72073 -3.103 .0019 .05556 D13| -.77641 .72073 -1.077 .2814 .05556 D14| -1.27341* .72073 -1.767 .0773 .05556 D15| -.57948 .72073 -.804 .4214 .05556 D16| -1.81723** .72073 -2.521 .0117 .05556 D17| -2.93529*** .72073 -4.073 .0000 .05556 ™  43/44
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Part 14: Generalized Regression OLS vs. Iterative FGLS Looks like a substantial gain in reduced standard errors --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- |Ordinary Least Squares |Cov matrix for b is sigma^2*inv(X'X)(X'WX)inv(X'X) Constant| 2.39133*** .20010 11.951 .0000 LINCOMEP| .88996*** .07358 12.094 .0000 -6.13943 LRPMG| -.89180*** .06119 -14.574 .0000 -.52310 LCARPCAP| -.76337*** .03030 -25.190 .0000 -9.04180 --------+------------------------------------------------------------- |Regression (mean) function Constant| 1.56909*** .06744 23.267 .0000 LINCOMEP| .60853*** .02097 29.019 .0000 -6.13943 LRPMG| -.61698*** .01902 -32.441 .0000 -.52310 LCARPCAP| -.66938*** .01116 -59.994 .0000 -9.04180   44/44
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