Econometrics-I-14

# 3844 part 14 generalized regression estimating

• Notes
• 45

This preview shows page 39 - 45 out of 45 pages.

™  38/44

Subscribe to view the full document.

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
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

Subscribe to view the full document.

Part 14: Generalized Regression Analysis of Variance ™  41/44
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

Subscribe to view the full document.

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
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

{[ snackBarMessage ]}

###### "Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern