Econ140A_Chap6_Sol

# Econ140A_Chap6_Sol - CHAPTER 6 TEACHING NOTES I cover most...

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CHAPTER 6 TEACHING NOTES I cover most of Chapter 6, but not all of the 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, I briefly mention beta coefficients; if students have a need for them, they can read this subsection. The functional form material is important, and I spend some time on more complicated models involving logarithms, quadratics, and interactions. An important point for models with quadratics, and especially interactions, is that we need to evaluate the partial effect at interesting values of the explanatory variables. Often, zero is not an interesting value for an explanatory variable and is well outside the range in the sample. Using the methods from Chapter 4, it is easy to obtain confidence intervals for the effects at interesting x values. As far as goodness-of-fit, I only introduce the adjusted R -squared, as I think using a slew of goodness-of-fit measures to choose a model can be confusing to novices (and does not reflect empirical practice). It is important to discuss how, if we fixate on a high R -squared, we may wind up with a model that has no interesting ceteris paribus interpretation. I often have students and colleagues ask if there is a simple way to predict y when log( y ) has been used as the dependent variable, and to obtain a goodness-of-fit measure for the log( y ) model that can be compared with the usual R -squared obtained when y is the dependent variable. The methods described in Section 6.4 are easy to implement and, unlike other approaches, do not require normality. The section on prediction and residual analysis contains several important topics, including constructing prediction intervals. It is useful to see how much wider the prediction intervals are than the confidence interval for the conditional mean. I usually discuss some of the residual- analysis examples, as they have real-world applicability. 46

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SOLUTIONS TO PROBLEMS 6.1 The generality is not necessary. The t statistic on roe 2 is only about .30, which shows that roe 2 is very statistically insignificant. Plus, having the squared term has only a minor effect on the slope even for large values of roe . (The approximate slope is .0215 .00016 roe , and even when roe = 25 – about one standard deviation above the average roe in the sample – the slope is .211, as compared with .215 at roe = 0.) 6.2 By definition of the OLS regression of c 0 y i on c 1 x i 1 , , c k x ik , i = 2, , n , the j β ± solve 00 1 1 1 1 11 0 0 1 11 1 1 1 1 1 [( ) ( ) ( )] 0 ( )[( ) ( ) ( )] 0 ( )[( ) ( ) ... ( )] 0. n ii k k i k i n i k k i k i n ki k i i k ki k i cy cx c y ββ = = = −− = = ±± ± ± # ± = [We obtain these from equations (3.13), where we plug in the scaled dependent and independent variables.] We now show that if 0 ± = ˆ c and j ± = 0 (/) j cc j ± j , j = 1,…, k , then these k + 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.

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Econ140A_Chap6_Sol - CHAPTER 6 TEACHING NOTES I cover most...

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