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Unformatted text preview: CHAPTER 16 TEACHING NOTES I spend some time in Section 16.1 trying to distinguish between good and inappropriate uses of SEMs. Naturally, this is partly determined by my taste, and many applications fall into a gray area. But students who are going to learn about SEMS should know that just because two (or more) variables are jointly determined does not mean that it is appropriate to specify and estimate an SEM. I have seen many bad applications of SEMs where no equation in the system can stand on its own with an interesting ceteris paribus interpretation. In most cases, the researcher either wanted to estimate a tradeoff between two variables, controlling for other factors – in which case OLS is appropriate – or should have been estimating what is (often pejoratively) called the “reduced form.” The identification of a two-equation SEM in Section 16.3 is fairly standard except that I emphasize that identification is a feature of the population. (The early work on SEMs also had this emphasis.) Given the treatment of 2SLS in Chapter 15, the rank condition is easy to state (and test). Romer’s (1993) inflation and openness example is a nice example of using aggregate cross- sectional data. Purists may not like the labor supply example, but it has become common to view labor supply as being a two-tier decision. While there are different ways to model the two tiers, specifying a standard labor supply function conditional on working is not outside the realm of reasonable models. Section 16.5 begins by expressing doubts of the usefulness of SEMs for aggregate models such as those that are specified based on standard macroeconomic models. Such models raise all kinds of thorny issues; these are ignored in virtually all texts, where such models are still used to illustrate SEM applications. SEMs with panel data, which are covered in Section 16.6, are not covered in any other introductory text. Presumably, if you are teaching this material, it is to more advanced students in a second semester, perhaps even in a more applied course. Once students have seen first differencing or the within transformation, along with IV methods, they will find specifying and estimating models of the sort contained in Example 16.8 straightforward. Levitt’s example concerning prison populations is especially convincing because his instruments seem to be truly exogenous. 183 SOLUTIONS TO PROBLEMS 16.1 (i) If α 1 = 0 then y 1 = β 1 z 1 + u 1 , and so the right-hand-side depends only on the exogenous variable z 1 and the error term u 1 . This then is the reduced form for y 1 . If α 1 = 0, the reduced form for y 1 is y 1 = β 2 z 2 + u 2 . (Note that having both α 1 and α 2 equal zero is not interesting as it implies the bizarre condition u 2 – u 1 = β 1 z 1 − β 2 z 2 .) If α 1 ≠ 0 and α 2 = 0, we can plug y 1 = β 2 z 2 + u 2 into the first equation and solve for y 2 : β 2 z 2 + u 2 = α 1 y 2 + β 1 z 1 + u 1 or α 1 y 2 = β 1 z 1 − β 2 z 2 + u 1 –...
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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.
- Spring '10