伍德里奇计量经济学第六版答案Chapter 5

CHAPTER 5

TEACHING NOTES

Chapter 5 is short, but it is conceptually more difficult than the earlier chapters, primarily

because it requires some knowledge of asymptotic properties of estimators. In class, I give a

brief, heuristic description of consistency and asymptotic normality before stating the

consistency and asymptotic normality of OLS. (Conveniently, the same assumptions that work

for finite sample analysis work for asymptotic analysis.) More advanced students can follow the

proof of consistency of the slope coefficient in the bivariate regression case. Section E.4 contains

a full matrix treatment of asymptotic analysis appropriate for a master’s level course

.

An explicit illustration of what happens to standard errors as the sample size grows emphasizes

the importance of having a larger sample. I do not usually cover the

LM

statistic in a first-

semester course, and I only briefly mention the asymptotic efficiency result. Without full use of

matrix algebra combined with limit theorems for vectors and matrices, it is difficult to prove

asymptotic efficiency of OLS.

I think the conclusions of this chapter are important for students to know, even though they may

not fully grasp the details. On exams I usually include true-false type questions, with explanation,

to test the students’ understanding of asymptotics. [For example: “In large samples we do not

have to worry about omitted variable bias.” (False). Or “Even if the error term is not normally

distributed, in large samples we can still compute approximately valid confidence intervals under

the Gauss-

Markov assumptions.” (True).]

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