发布时间 : 星期五 文章计量经济学导论第四版答案中文版更新完毕开始阅读
计量经济学导论第四版答案中文版
【篇一：计量经济学导论(伍德里奇第三版)课后习题答
案 chapter 1】
>solutions to problems
1.1 (i) ideally, we could randomly assign students to classes of different sizes. that is, each student is assigned a different class size without regard to any student characteristics such as ability and family background. for reasons we will see in chapter 2, we would like substantial variation in class sizes (subject, of course, to ethical considerations and resource constraints).
(ii) a negative correlation means that larger class size is
associated with lower performance. we might find a negative correlation because larger class size actually hurts performance.
however, with observational data, there are other reasons we might find a negative relationship. for example, children from more affluent families might be more likely to attend schools with smaller class sizes, and affluent children generally score better on standardized tests. another possibility is that, within a school, a principal might assign the better students to smaller classes. or, some parents might insist their children are in the smaller classes, and these same parents tend to be more involved in their children’s education.
(iii) given the potential for confounding factors – some of which are listed in (ii) – finding a negative correlation would not be strong evidence that smaller class sizes actually lead to better performance. some way of controlling for the
confounding factors is needed, and this is the subject of multiple regression analysis.
1.2 (i) here is one way to pose the question: if two firms, say a and b, are identical in all
respects except that firm a supplies job training one hour per worker more than firm b, by how much would firm a’s output differ from firm b’s?
(ii) firms are likely to choose job training depending on the characteristics of workers. some observed characteristics are years of schooling, years in the workforce, and experience in a
particular job. firms might even discriminate based on age, gender, or race. perhaps firms choose to offer training to more or less able workers, where ―ability‖ might be difficult to quantify but where a manager has some idea about the
relative abilities of different employees. moreover, different kinds of workers might be attracted to firms that offer more job training on average, and this might not be evident to employers.
(iii) the amount of capital and technology available to workers would also affect output. so, two firms with exactly the same kinds of employees would generally have different outputs if they use different amounts of capital or technology. the quality of managers would also have an effect.
(iv) no, unless the amount of training is randomly assigned. the many factors listed in parts (ii) and (iii) can contribute to finding a positive correlation between output and training even if job training does not improve worker productivity.
1.3 it does not make sense to pose the question in terms of causality. economists would assume that students choose a mix of studying and working (and other activities, such as attending class,
leisure, and sleeping) based on rational behavior, such as maximizing utility subject to the constraint that there are only 168 hours in a week. we can then use statistical methods to measure the association between studying and working,
including regression analysis that we cover starting in chapter 2. but we would not be claiming that one variable ―causes‖ the other. they are both choice variables of the student. chapter 2
solutions to problems
2.1 (i) income, age, and family background (such as number of siblings) are just a few
possibilities. it seems that each of these could be correlated with years of education. (income and education are probably positively correlated; age and education may be negatively correlated because women in more recent cohorts have, on average, more education; and number of siblings and education are probably negatively correlated.)
(ii) not if the factors we listed in part (i) are correlated with educ. because we would like to hold these factors fixed, they
are part of the error term. but if u is correlated with educ then e(u|educ) ? 0, and so slr.4 fails.
2.2 in the equation y = ?0 + ?1x + u, add and subtract ?0 from the right hand side to get y = (?0 + ?0) + ?1x + (u ? ?0). call the new error e = u ? ?0, so that e(e) = 0. the new intercept is ?0 + ?0, but the slope is still ?1.
2.3 (i) let yi = gpai, xi = acti, and n = 8. then = 25.875, = 3.2125, ?(xi – )(yi – ) = i?1n
?= 5.8125, and ?(xi – )2 = 56.875. from equation (2.9), we obtain the slope as ?1 i?1 n
? = – 5.8125/56.875 ? .1022, rounded to four places after the decimal. from (2.17), ?0
? ? 3.2125 – (.1022)25.875 ? .5681. so we can write ? 1
? = .5681 + .1022 act gpan = 8.
the intercept does not have a useful interpretation because act is not close to zero for the
? increases by .1022(5) = .511. population of interest. if act is 5 points higher, gpa
(ii) the fitted values and residuals — rounded to four decimal places — are given along with the observation number i and gpa in the following table:
you can verify that the residuals, as reported in the table, sum to ?.0002, which is pretty close to zero given the inherent rounding error.
?= .5681 + .1022(20) ? 2.61. (iii) when act = 20, gpa
?i2, is about .4347 (rounded to four decimal places), (iv) the sum of squared residuals, ?u i?1 n n
and the total sum of squares, ?(yi – )2, is about 1.0288. so the r-squared from the i?1
regression is
r2 = 1 – ssr/sst ? 1 – (.4347/1.0288) ? .577.
therefore, about 57.7% of the variation in gpa is explained by act in this small sample of students.
?2.4 (i) when cigs = 0, predicted birth weight is 119.77 ounces. when cigs = 20, bwght = 109.49. this is about an 8.6% drop.
(ii) not necessarily. there are many other factors that can
affect birth weight, particularly overall health of the mother and quality of prenatal care. these could be correlated with cigarette smoking during birth. also, something such as caffeine consumption can affect birth weight, and might also be correlated with cigarette smoking.
(iii) if we want a predicted bwght of 125, then cigs = (125 – 119.77)/( –.524) ?–10.18, or about –10 cigarettes! this is
nonsense, of course, and it shows what happens when we are trying to predict something as complicated as birth weight with only a single explanatory variable. the largest predicted birth weight is necessarily 119.77. yet almost 700 of the births in the sample had a birth weight higher than 119.77.
(iv) 1,176 out of 1,388 women did not smoke while pregnant, or about 84.7%. because we are using only cigs to explain birth weight, we have only one predicted birth weight at cigs = 0. the predicted birth weight is necessarily roughly in the
middle of the observed birth weights at cigs = 0, and so we will under predict high birth rates.
2.5 (i) the intercept implies that when inc = 0, cons is predicted to be negative $124.84. this, of course, cannot be true, and reflects that fact that this consumption function might be a poor predictor of consumption at very low-income levels. on the other hand, on an annual basis, $124.84 is not so far from zero.
? = –124.84 + .853(30,000) = 25,465.16 dollars. (ii) just plug 30,000 into the equation: cons
(iii) the mpc and the apc are shown in the following graph. even though the intercept is negative, the smallest apc in the sample is positive. the graph starts at an annual income level increases housing prices.
(ii) if the city chose to locate the incinerator in an area away from more expensive