Econometrics-I-14

# 2 1 2 3 1 1 1 1 1 ρ ρ ρ ρ ρ ρ σ σ ρ ρ ρ ρ

This preview shows pages 33–40. Sign up to view the full content.

2 1 2 3 1 1 1 1 1 - - - - - - ρ ρ ρ ρ ρ ρ σ σ = ρ ρ ρ ÷ ρ ρ ρ Ω L L L M M M O M L T T u T T T T

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Part 14: Generalized Regression Estimated AR(1) Model ---------------------------------------------------------------------- AR(1) Model: e(t) = rho * e(t-1) + u(t) Initial value of rho = .87566 Maximum iterations = 1 Method = Prais - Winsten Iter= 1, SS= .022, Log-L= 127.593 Final value of Rho = .959411 Std. Deviation: e(t) = .076512 Std. Deviation: u(t) = .021577 Autocorrelation: u(t) = .253173 N[0,1] used for significance levels --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------------------- Constant| -20.3373*** .69623 -29.211 .0000 FGLS LP| -.11379*** .03296 -3.453 .0006 3.72930 LY| .87040*** .08827 9.860 .0000 9.67215 LPNC| .05426 .12392 .438 .6615 4.38037 LPUC| -.04028 .06193 -.650 .5154 4.10545 RHO| .95941*** .03949 24.295 .0000 --------+------------------------------------------------------------------------- Constant| -21.2111*** .75322 -28.160 .0000 OLS LP| -.02121 .04377 -.485 .6303 3.72930 LY| 1.09587*** .07771 14.102 .0000 9.67215 LPNC| -.37361** .15707 -2.379 .0215 4.38037 LPUC| .02003 .10330 .194 .8471 4.10545 ™  33/44
Part 14: Generalized Regression Two Step Estimation The general result for estimation when is estimated. GLS uses [ X-1X ] X -1 y which converges in probability to . We seek a vector which converges to the same thing that this does. Call it “Feasible GLS” or FGLS, based on [ X X ] X y The object is to find a set of parameters such that [ X X ] X y - [ X -1 X ] X -1 y 0 ™  34/44 ˆ -1 Ω ˆ -1 Ω ˆ -1 Ω ˆ -1 Ω

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Part 14: Generalized Regression Feasible GLS ™  35/44 For FGLS estimation, we do not seek an estimator of  such that ˆ                      ˆ This makes no sense, since   is nxn and does not "converge" to anything.  We seek a matrix  such that            Ω - 0 Ω Ω Ω   Ω ˆ  (1/n) (1/n) For the asymptotic properties, we will require that ˆ             (1/ n) (1/n) Note in this case, these are two random vectors, which we require to converge ε ε → -1 -1 -1 -1 X' X -   X' 0 Ω Ω X'  -   X'   0 Ω Ω  to the same random vector.
Part 14: Generalized Regression Two Step FGLS VVIR (Theorem 9.6) To achieve full efficiency, we do not need an efficient estimate of the parameters in , only a consistent one. ™  36/44

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Part 14: Generalized Regression Harvey’s Model Examine Harvey’s model once again. Methods of estimation: Two step FGLS: Use the least squares residuals to estimate , then use Full maximum likelihood estimation. Estimate all parameters simultaneously. A handy result due to Oberhofer and Kmenta - the “zig-zag” approach. Iterate back and forth between and . ™  37/44 ( 29 { } ( 29 1 1 1 ˆ ˆ ˆ ˆ - - - X X X y β = Ω θ Ω θ
Part 14: Generalized Regression Harvey’s Model for Groupwise Heteroscedasticity Groupwise sample, yig, xig,… N groups, each with Ng observations. Var[εig] = σg2 Let dig = 1 if observation i,g is in group g, 0 else. = group dummy variable. Var[εig] = σg2 exp(θ2d2 + … θGdG) Var1 = σg2 , Var2 = σg2 exp(θ2) and so on.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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