20XX年复习资料
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CHAPTER 20XXXX
TEACHING NOTES
I spend some time in Section 20XXXX.1 trying to distinguish between good and inappropriate us 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 becau two (or more) variables are jointly determined does not mean that it is appropriate to specify and estimate an SEM. I have en many bad applications of SEMs where no equation in the system can stand on its own with an interesting ceteris paribus interpretation. In most cas, the rearcher either wanted to estimate a tradeoff between two variables, controlling for other factors – in which ca 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 20XXXX.3 is fairly standard except th
at 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 20XXXX, the rank condition is easy to state (and test).
Romer’s (20XXXX0XX3) inflation and openness example is a nice example of using aggregate cross-ctional 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 20XXXX.5 begins by expressing doubts of the ufulness of SEMs for aggregate models such as tho that are specified bad on standard macroeconomic models. Such models rai all kinds of thorny issues; the are ignored in virtually all texts, where such models are still ud to illustrate SEM applications.
SEMs with panel data, which are covered in Section 20XXXX.6, are not covered in any other introductory text. Presumably, if you are teaching this material, it is to more advanc
ed students in a cond mester, perhaps even in a more applied cour. Once students have en first differencing or the within transformation, along with IV methods, they will find specifying and estimating models of the sort contained in Example 20XXXX.8 straightforward. Levitt’s example concerning prison populations is especially convincing becau his instruments em to be truly exogenous.
SOLUTIONS TO PROBLEMS
20XXXX.1 (i) If 关于春天的成语 1 = 0 then y1 = 1z1 + u1, and so the right-hand-side depends only on the exogenous variable z1 and the error term u1. This then is the reduced form for y1. If 1 = 0, the reduced form for y1 is y1 = 2z2 + u2. (Note that having both 1 and 2 equal zero is not interesting as it implies the bizarre condition u2 – u1 = 1z1 2z2.)
If 1 0 and 2 = 0, we can plug y1 = 2z2 + u2 into the first equation and solve for y2:
2z2 + u2 = 1南美对虾y2 + 1z1 + u1
or
1y2 = 1z1 2z2 + u1 – u2.
Dividing by 1 (becau 1 0) gives
y2 = ( 1/ 1)z1 – ( 2/ 1)z2 + (u1 – u2)/ 1
21z1超宽带技术 + 22z2 + v2,
where 21 = 1/ 1, 22 = 2/ 1, and v2 = (u1 – u2)/ 1. Note that the reduced form for y2 generally depends on 三大改造的时间z1 and z2 (as well as on u1 and u2).
(ii) If we multiply the cond structural equation by ( 一应俱全1/ 2) and subtract it from the first structural equation, we obtain
y1 – ( 1/ 2)y1 = 1y2 1y2 + 1z1 – ( 1/ 2) 2z2 + u1 – ( 1/ 2)u2
= 1z1 – (长期均衡 1/ 2) 2z2 + u家风传承1 – ( 1/ 2)u2
or
[1 – ( 1/ 2)]y1 = 1z1 – ( 1/ 2) 2z2 + u1 – ( 1/ 2)u2.
Becau 1 2, 1 – ( 1/ 2) 0, and so we can divide the equation by 1 – ( 1/ 2) to obtain the reduced form for y1: y1 = 20XXXXz1 + 20XXXXz2 + v1, where 20XXXX = 1/[1 – ( 1/ 2)], 20XXXX = ( 1/ 2) 2/[1 – ( 1/ 2)], and v1 = [u1 – ( 1/ 2)u2]/[1 – ( 1/ 2)].
