chapter13_s - CHAPTER 13 SOLUTIONS TO PROBLEMS 13.1 Without...

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CHAPTER 13 SOLUTIONS TO PROBLEMS 13.1 Without changes in the averages of any explanatory variables, the average fertility rate fell by .545 between 1972 and 1984; this is simply the coefficient on y84 . To account for the increase in average education levels, we obtain an additional effect: –.128(13.3 – 12.2) –.141. So the drop in average fertility if the average education level increased by 1.1 is .545 + .141 = .686, or roughly two-thirds of a child per woman. 13.3 We do not have repeated observations on the same cross-sectional units in each time period, and so it makes no sense to look for pairs to difference. For example, in Example 13.1, it is very unlikely that the same woman appears in more than one year, as new random samples are obtained in each year. In Example 13.3, some houses may appear in the sample for both 1978 and 1981, but the overlap is usually too small to do a true panel data analysis. 13.5 No, we cannot include age as an explanatory variable in the original model. Each person in the panel data set is exactly two years older on January 31, 1992 than on January 31, 1990. This means that age i = 2 for all i . But the equation we would estimate is of the form Δ saving i = δ 0 + β 1 Δ age i + , where 0 is the coefficient the year dummy for 1992 in the original model. As we know, when we have an intercept in the model we cannot include an explanatory variable that is constant across i; this violates Assumption MLR.3. Intuitively, since age changes by the same amount for everyone, we cannot distinguish the effect of age from the aggregate time effect. 13.7 (i) It is not surprising that the coefficient on the interaction term changes little when afchnge is dropped from the equation because the coefficient on afchnge in (3.12) is only .0077 (and its t statistic is very small). The increase from .191 to .198 is easily explained by sampling error. (ii) If highearn is dropped from the equation [so that 1 0 = in (3.10)], then we are assuming that, prior to the change in policy, there is no difference in average duration between high earners and low earners. But the very large (.256), highly statistically significant estimate on highearn in (3.12) shows this presumption to be false. Prior to the policy change, the high earning group spent about 29.2% [ exp( ] longer on unemployment compensation than the low earning group. By dropping highearn from the regression, we attribute to the policy change the difference between the two groups that would be observed without any intervention. .256) 1 .292 −≈ 71
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SOLUTIONS TO COMPUTER EXERCISES C13.1 (i) The F statistic (with 4 and 1,111 df ) is about 1.16 and p -value .328, which shows that the living environment variables are jointly insignificant. (ii) The F statistic (with 3 and 1,111 df ) is about 3.01 and p -value .029, and so the region dummy variables are jointly significant at the 5% level.
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chapter13_s - CHAPTER 13 SOLUTIONS TO PROBLEMS 13.1 Without...

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