Econometrics-I-18

Estimators of the asymptotic covariance asymptotic

This preview shows pages 22–31. Sign up to view the full content.

Estimators of the Asymptotic Covariance Asymptotic Covariance Matrix ™  21/47 ( 29 1 1 1 1 1 1 1 Conventional Estimator - Inverse of the information matrix "Usual" "Berndt, Hall, Hall, Hausman" (BHHH) [( ) ][( ) ] n i i i i n n i i i i i i i i i i y y - - = - - = = λ = = - λ - λ x x XΛX g g x x 1 2 1 ( ) n i i i i i y - = = - λ x x

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

View Full Document
Part 18: Maximum Likelihood Estimation Robust Estimation p Sandwich Estimator p H-1 (GG) H-1 p Is this appropriate? Why do we do this? ™  22/47 ( 29 ( 29 1 1 2 1 ( ) n i i i i i y - - = - λ XΛX x x X ΛX
Part 18: Maximum Likelihood Estimation Newton’s Method ™  23/47

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

View Full Document
Part 18: Maximum Likelihood Estimation Newton’s Method for Poisson Regression ™  24/47
Part 18: Maximum Likelihood Estimation Poisson Regression Iterations Poisson ; lhs = doctor ; rhs = one,female,hhninc,educ;mar;output=3\$ Method=Newton; Maximum iterations=100 Convergence criteria: gtHg .1000D-05 chg.F .0000D+00 max|db| .0000D+00 Start values: .00000D+00 .00000D+00 .00000D+00 .00000D+00 1st derivs. -.13214D+06 -.61899D+05 -.43338D+05 -.14596D+07 Parameters: .28002D+01 .72374D-01 -.65451D+00 -.47608D-01 Itr 2 F= -.1587D+06 gtHg= .2832D+03 chg.F= .1587D+06 max|db|= .1346D+01 1st derivs. -.33055D+05 -.14401D+05 -.10804D+05 -.36592D+06 Parameters: .21404D+01 .16980D+00 -.60181D+00 -.48527D-01 Itr 3 F= -.1115D+06 gtHg= .9725D+02 chg.F= .4716D+05 max|db|= .6348D+00 1st derivs. -.42953D+04 -.15074D+04 -.13927D+04 -.47823D+05 Parameters: .17997D+01 .27758D+00 -.54519D+00 -.49513D-01 Itr 4 F= -.1063D+06 gtHg= .1545D+02 chg.F= .5162D+04 max|db|= .1437D+00 1st derivs. -.11692D+03 -.22248D+02 -.37525D+02 -.13159D+04 Parameters: .17276D+01 .31746D+00 -.52565D+00 -.49852D-01 Itr 5 F= -.1062D+06 gtHg= .5006D+00 chg.F= .1218D+03 max|db|= .6542D-02 1st derivs. -.12522D+00 -.54690D-02 -.40254D-01 -.14232D+01 Parameters: .17249D+01 .31954D+00 -.52476D+00 -.49867D-01 Itr 6 F= -.1062D+06 gtHg= .6215D-03 chg.F= .1254D+00 max|db|= .9678D-05 1st derivs. -.19317D-06 -.94936D-09 -.62872D-07 -.22029D-05 Parameters: .17249D+01 .31954D+00 -.52476D+00 -.49867D-01 Itr 7 F= -.1062D+06 gtHg= .9957D-09 chg.F= .1941D-06 max|db|= .1602D-10 * Converged ™  25/47

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

View Full Document
Part 18: Maximum Likelihood Estimation Regression and Partial Effects +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ Constant| 1.72492985 .02000568 86.222 .0000 FEMALE | .31954440 .00696870 45.854 .0000 .47877479 HHNINC | -.52475878 .02197021 -23.885 .0000 .35208362 EDUC | -.04986696 .00172872 -28.846 .0000 11.3206310 +-------------------------------------------+ | Partial derivatives of expected val. with | | respect to the vector of characteristics. | | Effects are averaged over individuals. | | Observations used for means are All Obs. | | Conditional Mean at Sample Point 3.1835 | | Scale Factor for Marginal Effects 3.1835 | +-------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ Constant| 5.49135704 .07890083 69.598 .0000 FEMALE | 1.01727755 .02427607 41.905 .0000 .47877479 HHNINC | -1.67058263 .07312900 -22.844 .0000 .35208362 EDUC | -.15875271 .00579668 -27.387 .0000 11.3206310 ™  26/47
Part 18: Maximum Likelihood Estimation Comparison of Standard Errors Negative Inverse of Second Derivatives +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ Constant| 1.72492985 .02000568 86.222 .0000 FEMALE | .31954440 .00696870 45.854 .0000 .47877479 HHNINC | -.52475878 .02197021 -23.885 .0000 .35208362 EDUC | -.04986696 .00172872 -28.846 .0000 11.3206310 BHHH +--------+--------------+----------------+--------+--------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| +--------+--------------+----------------+--------+--------+ Constant| 1.72492985 .00677787 254.495 .0000 FEMALE | .31954440 .00217499 146.918 .0000 HHNINC | -.52475878 .00733328 -71.559 .0000 EDUC | -.04986696 .00062283 -80.065 .0000 Why are they so different?  Model failure. This is a panel. There is autocorrelation. ™  27/47

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

View Full Document
Part 18: Maximum Likelihood Estimation MLE vs. Nonlinear LS ™  28/47
Part 18: Maximum Likelihood Estimation Testing Hypotheses – A Trinity of Tests The likelihood ratio test: Based on the proposition (Greene’s) that restrictions always “make life worse” Is the reduction in the criterion (log-likelihood) large?

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