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1、CHAPTER 1 TEACHING NOTES You have substantial latitude about what to emphasize in Chapter 1.I find it useful to talk about the economics of crime example(Example 1.1)and the wage example(Example 1.2)so that students see,at the outset,that econometrics is linked to economic reasoning,even if the econ
2、omics is not complicated theory.I like to familiarize students with the important data structures that empirical economists use,focusing primarily on cross-sectional and time series data sets,as these are what I cover in a first-semester course.It is probably a good idea to mention the growing impor
3、tance of data sets that have both a cross-sectional and time dimension.I spend almost an entire lecture talking about the problems inherent in drawing causal inferences in the social sciences.I do this mostly through the agricultural yield,return to education,and crime examples.These examples also c
4、ontrast experimental and nonexperimental(observational)data.Students studying business and finance tend to find the term structure of interest rates example more relevant,although the issue there is testing the implication of a simple theory,as opposed to inferring causality.I have found that spendi
5、ng time talking about these examples,in place of a formal review of probability and statistics,is more successful(and more enjoyable for the students and me).CHAPTER 2 TEACHING NOTES This is the chapter where I expect students to follow most,if not all,of the algebraic derivations.In class I like to
6、 derive at least the unbiasedness of the OLS slope coefficient,and usually I derive the variance.At a minimum,I talk about the factors affecting the variance.To simplify the notation,after I emphasize the assumptions in the population model,and assume random sampling,I just condition on the values o
7、f the explanatory variables in the sample.Technically,this is justified by random sampling because,for example,E(ui|x1,x2,xn)=E(ui|xi)by independent sampling.I find that students are able to focus on the key assumption SLR.4 and subsequently take my word about how conditioning on the independent var
8、iables in the sample is harmless.(If you prefer,the appendix to Chapter 3 does the conditioning argument carefully.)Because statistical inference is no more difficult in multiple regression than in simple regression,I postpone inference until Chapter 4.(This reduces redundancy and allows you to focu
9、s on the interpretive differences between simple and multiple regression.)You might notice how,compared with most other texts,I use relatively few assumptions to derive the unbiasedness of the OLS slope estimator,followed by the formula for its variance.This is because I do not introduce redundant o
10、r unnecessary assumptions.For example,once SLR.4 is assumed,nothing further about the relationship between u and x is needed to obtain the unbiasedness of OLS under random sampling.CHAPTER 3 TEACHING NOTES For undergraduates,I do not work through most of the derivations in this chapter,at least not
11、in detail.Rather,I focus on interpreting the assumptions,which mostly concern the population.Other than random sampling,the only assumption that involves more than population considerations is the assumption about no perfect collinearity,where the possibility of perfect collinearity in the sample(ev
12、en if it does not occur in the population)should be touched on.The more important issue is perfect collinearity in the population,but this is fairly easy to dispense with via examples.These come from my experiences with the kinds of model specification issues that beginners have trouble with.The com
13、parison of simple and multiple regression estimates based on the particular sample at hand,as opposed to their statistical properties usually makes a strong impression.Sometimes I do not bother with the“partialling out”interpretation of multiple regression.As far as statistical properties,notice how
14、 I treat the problem of including an irrelevant variable:no separate derivation is needed,as the result follows form Theorem 3.1.I do like to derive the omitted variable bias in the simple case.This is not much more difficult than showing unbiasedness of OLS in the simple regression case under the f
15、irst four Gauss-Markov assumptions.It is important to get the students thinking about this problem early on,and before too many additional(unnecessary)assumptions have been introduced.I have intentionally kept the discussion of multicollinearity to a minimum.This partly indicates my bias,but it also
16、 reflects reality.It is,of course,very important for students to understand the potential consequences of having highly correlated independent variables.But this is often beyond our control,except that we can ask less of our multiple regression analysis.If two or more explanatory variables are highl
17、y correlated in the sample,we should not expect to precisely estimate their ceteris paribus effects in the population.I find extensive treatments of multicollinearity,where one“tests”or somehow“solves”the multicollinearity problem,to be misleading,at best.Even the organization of some texts gives th
18、e impression that imperfect multicollinearity is somehow a violation of the Gauss-Markov assumptions:they include multicollinearity in a chapter or part of the book devoted to“violation of the basic assumptions,”or something like that.I have noticed that masters students who have had some undergradu
19、ate econometrics are often confused on the multicollinearity issue.It is very important that students not confuse multicollinearity among the included explanatory variables in a regression model with the bias caused by omitting an important variable.I do not prove the Gauss-Markov theorem.Instead,I
20、emphasize its implications.Sometimes,and certainly for advanced beginners,I put a special case of Problem 3.12 on a midterm exam,where I make a particular choice for the function g(x).Rather than have the students directly compare the variances,they should 文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编
21、码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E
22、8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编
23、码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E
24、8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编
25、码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E
26、8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编
27、码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6appeal to the Gauss-Markov theorem for the superiority of OLS over any other linear,unbiased estimator.CHAPTER 4 TEACHING NOTESAt the start of this chapter is good time to remind students that a specific error distribution
28、played no role in the results of Chapter 3.That is because only the first two moments were derived under the full set of Gauss-Markov assumptions.Nevertheless,normality is needed to obtain exact normal sampling distributions(conditional on the explanatory variables).I emphasize that the full set of
29、CLM assumptions are used in this chapter,but that in Chapter 5 we relax the normality assumption and still perform approximately valid inference.One could argue that the classical linear model results could be skipped entirely,and that only large-sample analysis is needed.But,from a practical perspe
30、ctive,students still need to know where the t distribution comes from because virtually all regression packages report tstatistics and obtain p-values off of the t distribution.I then find it very easy to cover Chapter 5 quickly,by just saying we can drop normality and still use t statistics and the
31、 associated p-values as being approximately valid.Besides,occasionally students will have to analyze smaller data sets,especially if they do their own small surveys for a term project.It is crucial to emphasize that we test hypotheses about unknown population parameters.I tell my students that they
32、will be punished if they write something like H0:1?=0 on an exam or,even worse,H0:.632=0.One useful feature of Chapter 4 is its illustration of how to rewrite a population model so that it contains the parameter of interest in testing a single restriction.I find this is easier,both theoretically and
33、 practically,than computing variances that can,in some cases,depend on numerous covariance terms.The example of testing equality of the return to two-and four-year colleges illustrates the basic method,and shows that the respecified model can have a useful interpretation.Of course,some statistical p
34、ackages now provide a standard error for linear combinations of estimates with a simple command,and that should be taught,too.One can use an F test for single linear restrictions on multiple parameters,but this is less transparent than a t test and does not immediately produce the standard error nee
35、ded for a confidence interval or for testing a one-sided alternative.The trick of rewriting the population model is useful in several instances,including obtaining confidence intervals for predictions in Chapter 6,as well as for obtaining confidence intervals for marginal effects in models with inte
36、ractions(also in Chapter 6).The major league baseball player salary example illustrates the difference between individual and joint significance when explanatory variables(rbisyr and hrunsyr in this case)are highly correlated.I tend to emphasize the R-squared form of the F statistic because,in pract
37、ice,it is applicable a large percentage of the time,and it is much more readily computed.I do regret that this example is biased toward students in countries where baseball is played.Still,it is one of the better examples 文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4
38、C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 H
39、F5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4
40、C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 H
41、F5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4
42、C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 H
43、F5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4
44、C6文档编码:CG3K6Y9X1K2 HF5T7E8T3W3 ZO2B8Q6R4C6of multicollinearity that I have come across,and students of all backgrounds seem to get the point.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 asy
45、mptotic 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 st
46、udents 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 masters level course.An explicit illustration of what happens to standard errors as the sample size grows emphasi
47、zes 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 very difficult to prove asymptoti
48、c 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
49、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).CHAPTER6 TEACHING NOTES I cover most of Chapter 6,but not all of the
50、material in great detail.I use the example in Table 6.1 to quickly run through the effects of data scaling on the important OLS statistics.(Students should already have a feel for the effects of data scaling on the coefficients,fitting values,and R-squared because it is covered in Chapter 2.)At most