伍德里奇计量经济学导论第四版习题答案1 大学课件

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1、CHAPTER 1TEACHING NOTESYou have substantial latitude about what to emphasize in Chapter 1. I find it useful to talk aboutthe economics of crime example Example 1.1 and the wage example Example 1.2 so thatstudents see at the outset that econometrics is linked to economic reasoning even if theeconomic

2、s is not complicated theory.I like to familiarize students with the important data structures that empirical economists usefocusing primarily on cross-sectional and time series data sets as these are what I cover in afirst-semester course. It is probably a good idea to mention the growing importance

3、 of data setsthat have both a cross-sectional and time dimension.I spend almost an entire lecture talking about the problems inherent in drawing causal inferencesin the social sciences. I do this mostly through the agricultural yield return to education andcrime examples. These examples also contras

4、t experimental and nonexperimentalobservational data. Students studying business and finance tend to find the term structure ofinterest rates example more relevant although the issue there is testing the implication of asimple theory as opposed to inferring causality. I have found that spending time

5、 talking aboutthese examples in place of a formal review of probability and statistics is more successful andmore enjoyable for the students and me. 1This edition is intended for use outside of the U.S. only with content that may be different from the U.S. Edition. This may not be resold copied or d

6、istributed without the prior consent of the publisher.SOLUTIONS TO PROBLEMS1.1 It does not make sense to pose the question in terms of causality. Economists would assumethat students choose a mix of studying and working and other activities such as attending classleisure and sleeping based on ration

7、al behavior such as maximizing utility subject to theconstraint that there are only 168 hours in a week. We can then use statistical methods tomeasure the association between studying and working including regression analysis that wecover starting in Chapter 2. But we would not be claiming that one

8、variable “causes the other.They are both choice variables of the student.1.2 i Ideally we could randomly assign students to classes of different sizes. That is eachstudent is assigned a different class size without regard to any student characteristics such asability and family background. For reaso

9、ns we will see in Chapter 2 we would like substantialvariation 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 si

10、ze 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 withsmaller class sizes and affluent children generally score better on standardized tes

11、ts. Anotherpossibility 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 parentstend to be more involved in their childrens education. iii Given the potential for confounding f

12、actors some of which are listed in ii finding anegative correlation would not be strong evidence that smaller class sizes actually lead to betterperformance. Some way of controlling for the confounding factors is needed and this is thesubject of multiple regression analysis.1.3 i Here is one way to

13、pose the question: If two firms say A and B are identical in allrespects except that firm A supplies job training one hour per worker more than firm B by howmuch would firm As output differ from firm Bs ii Firms are likely to choose job training depending on the characteristics of workers. Someobser

14、ved characteristics are years of schooling years in the workforce and experience in aparticular job. Firms might even discriminate based on age gender or race. Perhaps firmschoose to offer training to more or less able workers where “ability might be difficult toquantify but where a manager has some

15、 idea about the relative abilities of different employees.Moreover different kinds of workers might be attracted to firms that offer more job training onaverage and this might not be evident to employers. iii The amount of capital and technology available to workers would also affect output. Sotwo f

16、irms with exactly the same kinds of employees would generally have different outputs ifthey use different amounts of capital or technology. The quality of managers would also have aneffect. 2This edition is intended for use outside of the U.S. only with content that may be different from the U.S. Ed

17、ition. This may not be resold copied or distributed without the prior consent of the publisher. iv No unless the amount of training is randomly assigned. The many factors listed in partsii and iii can contribute to finding a positive correlation between output and training even ifjob training does n

18、ot improve worker productivity.SOLUTIONS TO COMPUTER EXERCISESC1.1 i The average of educ is about 12.6 years. There are two people reporting zero years ofeducation and 19 people reporting 18 years of education. ii The average of wage is about 5.90 which seems low in the year 2021. iii Using Table B-

19、60 in the 2004 Economic Report of the President the CPI was 56.9 in1976 and 184.0 in 2003. iv To convert 1976 dollars into 2003 dollars we use the ratio of the CPIs which is184 / 56.9 3.23 . Therefore the average hourly wage in 2003 dollars is roughly3.235.90 19.06 which is a reasonable figure. v Th

20、e sample contains 252 women the number of observations with female 1 and 274men.C1.2 i There are 1388 observations in the sample. Tabulating the variable cigs shows that 212women have cigs gt 0. ii The average of cigs is about 2.09 but this includes the 1176 women who did notsmoke. Reporting just th

21、e average masks the fact that almost 85 percent of the women did notsmoke. It makes more sense to say that the “typical woman does not smoke during pregnancyindeed the median number of cigarettes smoked is zero. iii The average of cigs over the women with cigs gt 0 is about 13.7. Of course this ismu

22、ch higher than the average over the entire sample because we are excluding 1176 zeros. iv The average of fatheduc is about 13.2. There are 196 observations with a missingvalue for fatheduc and those observations are necessarily excluded in computing the average. v The average and standard deviation

23、of faminc are about 29.027 and 18.739respectively but faminc is measured in thousands of dollars. So in dollars the average andstandard deviation are 29027 and 18739.C1.3 i The largest is 100 the smallest is 0. ii 38 out of 1823 or about 2.1 percent of the sample. 3This edition is intended for use o

24、utside of the U.S. only with content that may be different from the U.S. Edition. This may not be resold copied or distributed without the prior consent of the publisher. iii 17 iv The average of math4 is about 71.9 and the average of read4 is about 60.1. So at leastin 2001 the reading test was hard

25、er to pass. v The sample correlation between math4 and read4 is about .843 which is a very highdegree of linear association. Not surprisingly schools that have high pass rates on one testhave a strong tendency to have high pass rates on the other test. vi The average of exppp is about 5194.87. The s

26、tandard deviation is 1091.89 whichshows rather wide variation in spending per pupil. The minimum is 1206.88 and themaximum is 11957.64.C1.4 i 185/445 .416 is the fraction of men receiving job training or about 41.6. ii For men receiving job training the average of re78 is about 6.35 or 6350. For men

27、 notreceiving job training the average of re78 is about 4.55 or 4550. The difference is 1800which is very large. On average the men receiving the job training had earnings about 40higher than those not receiving training. iii About 24.3 of the men who received training were unemployed in 1978 the fi

28、gure is35.4 for men not receiving training. This too is a big difference. iv The differences in earnings and unemployment rates suggest the training program hadstrong positive effects. Our conclusions about economic significance would be stronger if wecould also establish statistical significance wh

29、ich is done in Computer Exercise C9.10 inChapter 9. 4This edition is intended for use outside of the U.S. only with content that may be different from the U.S. Edition. This may not be resold copied or distributed without the prior consent of the publisher. CHAPTER 2TEACHING NOTESThis is the chapter

30、 where I expect students to follow most if not all of the algebraic derivations.In class I like to derive at least the unbiasedness of the OLS slope coefficient and usually Iderive the variance. At a minimum I talk about the factors affecting the variance. To simplifythe notation after I emphasize t

31、he assumptions in the population model and assume randomsampling I just condition on the values of the explanatory variables in the sample. Technicallythis is justified by random sampling because for example Euix1x2xn Euixi byindependent sampling. I find that students are able to focus on the key as

32、sumption SLR.4 andsubsequently take my word about how conditioning on the independent variables in the sample isharmless. If you prefer the appendix to Chapter 3 does the conditioning argument carefully.Because statistical inference is no more difficult in multiple regression than in simple regressi

33、onI postpone inference until Chapter 4. This reduces redundancy and allows you to focus on theinterpretive differences between simple and multiple regression.You might notice how compared with most other texts I use relatively few assumptions toderive the unbiasedness of the OLS slope estimator foll

34、owed by the formula for its variance.This is because I do not introduce redundant or unnecessary assumptions. For example onceSLR.4 is assumed nothing further about the relationship between u and x is needed to obtain theunbiasedness of OLS under random sampling. 5This edition is intended for use ou

35、tside of the U.S. only with content that may be different from the U.S. Edition. This may not be resold copied or distributed without the prior consent of the publisher.SOLUTIONS TO PROBLEMS2.1 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 err

36、or e u 0 so that Ee 0. The new intercept is 0 0 but the slope is still 1. n2.2 i Let yi GPAi xi ACTi and n 8. Then x 25.875 y 3.2125 xi x yi y i1 n5.8125 and xi x 2 56.875. From equation 2.9 we obtain the slope as 1 i15.8125/56.875 .1022 rounded to four places after the decimal. From 2.17 0 y x 3.21

37、25 .102225.875 .5681. So we can write 1 GPA .5681 .1022 ACT n 8.The intercept does not have a useful interpretation because ACT is not close to zero for thepopulation of interest. If ACT is 5 points higher GPA increases by .10225 .511. ii The fitted values and residuals rounded to four decimal place

38、s are given along withthe observation number i and GPA in the following table: i GPA GPA u 1 2.8 2.7143 .0857 2 3.4 3.0209 .3791 3 3.0 3.2253 .2253 4 3.5 3.3275 .1725 5 3.6 3.5319 .0681 6 3.0 3.1231 .1231 7 2.7 3.1231 .4231 8 3.7 3.6341 .0659You can verify that the residuals as reported in the table

39、 sum to .0002 which is pretty close tozero given the inherent rounding error. iii When ACT 20 GPA .5681 .102220 2.61. 6This edition is intended for use outside of the U.S. only with content that may be different from the U.S. Edition. This may not be resold copied or distributed without the prior co

40、nsent of the publisher. n iv The sum of squared residuals u i 1 2 i is about .4347 rounded to four decimal places nand the total sum of squares yi i1 y 2 is about 1.0288. So the R-squared from theregression is R2 1 SSR/SST 1 .4347/1.0288 .577.Therefore about 57.7 of the variation in GPA is explained

41、 by ACT in this small sample ofstudents.2.3 i Income age and family background such as number of siblings are just a fewpossibilities. It seems that each of these could be correlated with years of education. Incomeand education are probably positively correlated age and education may be negatively c

42、orrelatedbecause women in more recent cohorts have on average more education and number of siblingsand education are probably negatively correlated. ii Not if the factors we listed in part i are correlated with educ. Because we would like tohold these factors fixed they are part of the error term. B

43、ut if u is correlated with educ thenEueduc 0 and so SLR.4 fails.2.4 i We would want to randomly assign the number of hours in the preparation course so thathours is independent of other factors that affect performance on the SAT. Then we wouldcollect information on SAT score for each student in the experiment yielding a data set sati hoursi : i 1. n where n is the number of students we can afford to have in the study.From equation 2.7 we should try to get as much variation in hoursi as is feasible. .