Econ140A_Chap4_Sol

Econ140A_Chap4_Sol - CHAPTER 4 TEACHING NOTES At the start...

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CHAPTER 4 TEACHING NOTES At the start of this chapter is good time to remind students that a specific error distribution 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 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 perspective, students still need to know where the t distribution comes from because virtually all regression packages report t statistics 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 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 will be punished if they write something like H 0 : 1 ˆ β = 0 on an exam or, even worse, H 0 : .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 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 packages 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 needed 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 interactions (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 practice, 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.
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This note was uploaded on 08/05/2010 for the course ECON Econ 140 taught by Professor Jack during the Spring '10 term at UCSB.

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Econ140A_Chap4_Sol - CHAPTER 4 TEACHING NOTES At the start...

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