Introductory Econometrics A Modern Approach 6th Edition Jeffrey M. Wooldridge - Solutions

Discover a comprehensive resource for "Introductory Econometrics: A Modern Approach, 6th Edition" by Jeffrey M. Wooldridge. Access online answers key and solutions pdf for all your textbook needs. Whether you're seeking solved problems, chapter solutions, or step-by-step answers, our solution manual and instructor manual provide detailed guidance. Enhance your learning with our questions and answers section, featuring a test bank for thorough preparation. Enjoy the convenience of free download options to support your econometrics studies and achieve academic success.

C9.10 You need to use two data sets for this exercise, JTRAIN2.RAW and JTRAIN3.RAW. The former is the outcome of a job training experiment. The file JTRAIN3.RAW contains observational data, where individuals themselves largely determine whether they partici- pate in job training. The data sets
C9.9 In this exercise, you are to compare OLS and I plan eligibility on net financial assets. The model nettfa = B+ Binc+ Binc + Bage O estimates of the effects of 401(k) Brage + Bmale + e401k + u. (i) Use the data in 401KSUBS.RAW to estimate the equation by OLS and report the results in the usual
C9.8 Use the data in TWOYEAR.RAW for this exercise. (i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and stan- dard deviation of stotal. (ii) Run simple regressions of jc and univ on stotal. Are both college
9.7 Use the data in LOANAPP.RAW for this exercise. (i) How many observations have obrat > 40, that is, other debt obligations more than 40% of total income? (ii) Reestimate the model in part (iii) of Computer Exercise C7.8, exclud- ing observations with obrat > 40. What happens to the estimate and
C9.6 Redo Example 4.10 by dropping schools where teacher benefits are less than 1% of salary. How many observations are lost? Does dropping these observations have any important effects on the estimated tradeoff?
C9.5 Use the data in RDCHEM.RAW to further examine the effects of outliers on OLS estimates and to see how LAD is less sensiti OHM rdintens B+ Bsale Bsales+Baprofmarg + u, where you should first change sales to be in billions of dollars to make the estimates eas- ier to interpret. (i) Estimate the
C9.4 Use the data for the year 1990 in INFMRT.RAW for this exercis IN (i) Reestimate equation (9.37), but now include a dummy variable for the observation on the District of Columbia (called DC). Interpret the coefficient on DC and comment on its size and significance. (ii) Compare the estimates
C9.3 Use the data from JTRAIN.RAW for this exercise. (i) Consider the simple regression model log(scrap) 0 1grant u, where scrap is the firm scrap rate and grant is a dummy variable indicating whether a firm received a job training grant. Can you think of some reasons why the unobserved
C9.2 Use the data set WAGE2.RAW for this exercise. (i) Use the variable KWW (the “knowledge of the world of work” test score) as a proxy for ability in place of IQ in Example 9.3. What is the estimated return to education in this case? (ii) Now, use IQ and KWW together as proxy variables. What
C9.1 (i) Apply RESET from equation (9.3) to the model estimated in Computer Exercise C7.5. Is there evidence of functional form misspecification in the equation? (ii) Compute a heteroskedasticity-robust form of RESET. Does your conclusion from part (i) change?
9.5 In Example 4.4, we estimated a model relating number of campus crimes to student enrollment for a sample of colleges. The sample we used was not a random sample of col- leges in the United States, because many schools in 1992 did not report campus crimes. Do you think that college failure to
9.4 The following equation explains weekly hours of television viewing by a child in terms of the child’s age, mother’s education, father’s education, and number of siblings: tvhours* 0 1age 2age2 3motheduc 4 fatheduc 5sibs u.We are worried that tvhours* is measured with
9.3 Let math 10 denote the percentage of students at a Michigan high school receiving a passing score on a standardized math test (see also Example 4.2). We are interested in estimating the effect of per student spending on math performance. A simple model is math 10 = Bo+ Blog(expend) +
9.2 Let us modify Computer Exercise C8.4 by using voting outcomes in 1990 for incumbents who were elected in 1988. Candidate A was elected in 1988 and was seeking reelection in 1990; voteA90 is Candidate A's share of the two-party vote in 1990. The 1988 voting share of Candidate A is used as a
9.1 In Problem 4.11, the R-squared from estimating the model log(salary) = Blog(sales) + Blog(mktval) + B3profmarg + Baceoten + B-comten + u, are using the data in CEOSAL2.RAW, was R2 = .353 (n = 177). When ceoten? and comten an added, R2 = .375. Is there evidence of functional form
C8.11 Use the data in 401KSUBS.RAW to answer this question, restricting attention to single-person households (fsize = 1). PRO =VIEW&oa nettfa = o + Binc + Bage + Bage + Bmale + Be401k OLS. Report the usual standard errors as well as the heteroskedasticity- robust standard errors. Comment on any
C8.10 Use the data set 401KSUBS.RAW for this exercise. NIN (i) Using OLS, estimate a linear probability model for e401k, using as explanatory variables inc, inc, age, age, and male. Obtain both the usual OLS standard errors and the heteroskedasticity-robust versions. Are there any important
C8.9 In Example 8.7, we computed the OLS and a set of WLS estimates in a cigarette demand equation. (i) Obtain the OLS estimates in equation (8.35). (ii) Obtain the h, used in the WLS estimation of equation (8.36) and repro- duce equation (8.36). From this equation, obtain the unweighted residu-
C8.8 Use the data set GPA1 RAW for this exercise. (i) Use OLS to estimate a model relating colGPA to hsGPA, ACT, skipped, and PC. Obtain the OLS residuals. (ii) Compute the special case of the White test for heteroskedasticity. In the regression of on colGPA, colGPA, obtain the fitted values, say
C8.7 Use the data in LOANAPP.RAW for this exerc (i) Estimate the equation in part (iii) of Computer Exercise C7.8, comput- ing the heteroskedasticity-robust standard errors. Compare the 95% con- fidence interval on white with the nonrobust confidence interval. (ii) Obtain the fitted values from the
C8.6 In Example 7.12, we estimated a linear probability model for whether a young man was arrested during 1986: arr86 = B+ Bpcnv + Bavgsen + tottime + Baptime86 + Bgempe (i) Estimate this model by OLS and verify that all fitted values OSSR between zero and one. What are the smallest and largest
C8.5 Use the data in PNTSPRD.RAW for this exercise. EVIEW The variable sprdcvr is a binary variable equal to one if the Las Vegas point spread for a college basketball game was covered. The expected value of sprdcvr, say , is the probability that the spread is covered in a randomly selected game.
C8.4 Use VOTE1.RAW for this exercise. (i) Estimate a model with voteA as the dependent variable and prtystrA, democA, log(expendA), and log(expendB) as independent variables. Obtain the OLS residuals, , and regress these on all of the independent (ii) Now, compute the Breusch-Pagan test for
C8.3 Apply the full White test for heteroskedasticity [see equation (8.19)] to equation (8.18). Using the chi-square form of the statistic, obtain the p-value. What do you conclude?
C8.2 (i) Use the data in HPRICE1.RAW to obtain the heteroskedasticity-robust standard errors for equation (8.17). Discuss any important differences with the usual standard errors. (ii) Repeat part (i) for equation (8.18). ERSSO (iii) What does this example suggest about heteroskedasticity and the
C8.1 Consider the following model to explain sleeping behavior: sleep = B+ Btotwrk + Beduc + Bage + Bage + Byngkid + B male + u. (i) Write down a model that allows the variance of u to differ between men and women. The variance should not depend on other factors. (ii) Use the data in SLEEP75.RAW to
8.7 Consider a model at the employee level, Yie Bo+Biel + Bx2 + + Briek + fi + Vie where the unobserved variable f; is a "firm effect" to each employee at a given firm i. The error term vie is specific to employee e at firm i. The composite error is ue = fi + Vie such as in equation (8.28). SRRI
8.6 There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedasticity. One possibility not covered in the text is to run the regression on xxx, i = 1,.. where the , are the OLS residuals and the , are the OLS fitted values. Then, we would test joint
8.5 The variable smokes is a binary variable equal to one if a person smokes, and zero oth- erwise. Using the data in SMOKE.RAW, we estimate a linear probability model for smokes: smokes = .656.069 log(cigpric) + .012 log(income) -.029 educ (.006) [.006] (.855) (.204) [.856] [.207] (.026) [.026] +
8.4 Using the data in GPA3.RAW, the following equation was estimate second semester students: trmgpa-2.12 + .900 crsgpa + .193 cumgpa (.55) (.175) [.55] [.166] (.064) [.074] [.0012] + .0018 sat .0039 hsperc +351 female - .157 season (.0002) [.0002] (.0018) [.0019] (.098) [.080] and e of overall GPA
8.2 Consider a linear model to explain monthly beer consumption: beer = Bo+ Binc+ Bprice + Beduc + Bfemale + u E(ulinc,price,educ,female) = 0 Var(u inc,price,educ,female) = oinc. Write the transformed equation that has a homoskedastic error term.
8.1 Which of the following are consequences of heteroskedasticity? (i) The OLS estimators, , are inconsistent. (ii) The usual F statistic no longer has an F distribution. (iii) The OLS estimators are no longer BLUE.
8.5 The variable smokes is a binary variable equal to one if a person smokes, and zero oth- erwise. Using the data in SMOKE.RAW, we estimate a linear probability model for smokes: smokes = .656.069 log(cigpric) + .012 log(income) -.029 educ (.006) [.006] (.855) (.204) [.856] [.207] (.026) [.026]
8.4 Using the data in GPA3.RAW, the following equation was estimated for the fall and second semester students: (trmgpa 2.12)(.900)crsgpa (.193)cumgpa (.0014)tothrs 2trmgpa (.55)(.175)crsgpa (.064)cumgpa (.0012)tothrs 2trmgpa [.55][.166]crsgpa [.074]cumgpa [.0012]tothrs
8.3 True or False: WLS is preferred to OLS, when an important variable has been omitted from the model.
8.2 Consider a linear model to explain monthly beer consumption: beer=B+ Binc + Bprice + Beduc + female + u E(ulinc,price,educ,female) = 0 Var(ulinc,price,educ female) =inc. Write the transformed equation that has a homoskedastic error term.
8.1 Which of the following are consequences of heteroskedasticity? (i) The OLS estimators, , are inconsistent. (ii) The usual F statistic no longer has an F distribution. (iii) The OLS estimators are no longer BLUE.
C7.13 Use the data in APPLE.RAW to answer this question. (i) Define a binary variable as ecobuy = 1 if ecolbs 0 and ecobuy = 0 if ecolbs 0. In other words, ecobuy indicates whether, at the prices given, a family would buy any ecologically friendly apples. What fraction of families claim they would
C7.12 Use the data set in BEAUTY.RAW, which contains a subset of the variables (but more usable observations than in the regressions) reported by Hamermesh and Biddle (1994). (i) Find the separate fractions of men and women that are classified as having above average looks. Are more people rated as
C7.11 Use the data in 401KSUBS.RAW for this exercise. (i) Compute the average, standard deviation, minimum, and maximum val- ues of nettfa in the sample. (ii) Test the hypothesis that average nettfa does not differ by 401(k) eligi- bility status; use a two-sided alternative. What is the dollar
C7.10 Use the data in NBASAL.RAW for this exercise. (i) Estimate a linear regression model relating points per game to experi- ence in the league and position (guard, forward, or center). Include experience in quadratic form and use centers as the base group. Report the results in the usual form.
C7.9 There has been much interest in whether the presence of 401(k) pension plans, available to many U.S. workers, increases net savings. The data set 401KSUBS.RAW con- tains information on net financial assets (nettfa), family income (inc), a binary variable for eligibility in a 401(k) plan
C7.8 Use the data in LOANAPP.RAW for this exercise. The binary variable to be explained is approve, which is equal to one if a mortgage loan to an individual was approved. The key explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants in the
C7.7 Use the data in WAGE1.RAW for this exercise. NING SRO (i) Use equation (7.18) to estimate the gender differential when educ 12.5. Compare this with the estimated differential when educ = 0. (ii) Run the regression used to obtain (7.18), but with female-(educ - 12.5) replacing female educ. How
C7.6 Use the data in SLEEP75.RAW for this exercise. The equation of interest is sleep = Bo+ Btotwrk + Breduc + Bage + Bage + Bayngkid + u. (i) Estimate this equation separately for men and women and report the results in the usual form. Are there notable differences in the two esti- mated
C7.5 In Problem 4.2, we added the return on the firm's stock, ros, to a model explain- ing CEO salary; ros turned out to be insignificant. Now, define a dummy variable, rosneg, which is equal to one if ros
C7.4 Use the data in GPA2.RAW for this exercise. (i) Consider the equation CLASSE LEARNING colgpa = B+ Bhsize + Bhsize + Bahsperc + + sfemale + Bathlete + u, where colgpa is cumulative college grade point average, hsize is size of high school graduating class, in hundreds, hsperc is academic per-
C7.3 A model that allows major league baseball player salary to differ by position is = log(salary) Bo+ B years + Bgamesyr + Bbavg + Bhrunsyr + Berbisyr + Brunsyr + B-fldperc + Ballstar + Bofrstbase + Bioscndbase + Bthrdbase + Bshrtstop + Bcatcher + u, where outfield is the base group. (i) State
C7.2 Use the data in WAGE2.RAW (i) Estimate the model decide whether this gener- Bexper+Batenure + Bmarried PP REVIEW OYO FOR SPECL + Bsblack + Besouth + B-urban + u and report the results in the usual form. Holding other factors fixed, what is the approximate difference in monthly salary between
C7.1 Use the data in GPA1.RAW for this exercise. (i) Add the variables mothcoll and fathcoll to the equation estimated in (7.6) and report the results in the usual form. What happens to the estimated effect of PC ownership? Is PC still statistically significant? (ii) Test for joint significance of
7.9 Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model his is PR R REWOR y=B+8d+ Bz +8d+z+u version of a model with an interaction between a dummy variable and a quantitative variable. [An example is in equation (7.17).] Since it changes nothing important,
7.8 Suppose you collect data from a survey on wages, education, experiING and gen ONING der. In addition, you ask for information about marijuana usage. The original question is: "On how many separate occasions last month did you smoke marijuana?" (i) Write an equation that would allow you to
7.7 In the example in equation (7.29), suppose that we define outlf to be one if the woman is out of the labor force, and zero otherwise. (i) If we regress outlf on all of the independent variables in equation (7.29), what will happen to the intercept and slope estimates? (Hint: inlf = 1 outlf.
7.6 To test the effectiveness of a job training program on the subsequent wages of work- ers, we specify the model log(wage) B+ Btrain + Beduc + Bzexper + u, where train is a binary variable equal to unity if a worker participated in the program. Think of the error term u as containing unobserved
7.5 In Example 7.2, let noPC be a dummy variable equal to one if the student does not own a PC, and zero otherwise. (i) noPC is used in place of PC in equation (7.6), what happens to the inter- cept in the estimated equation? What will be the coefficient on noPC? (Hint: Write PC = 1-noPC and plug
7.4 An equation explaining chief executive officer salary is log(salary) 4.59 + .257 log(sales) + .011 roe+.158 find = (.30) (.032) (.004) LEARNING CLASSRO +.181 consprod - .283 utility (.085) (.099) n = 209, R = .357. The data used are in CEOSAL1.RAW, where finance, c ables indicating the
7.3 Using the data in GPAZ RAW, the following equation was estimated: PR SREVIEW 1,028.10 (6.29) 19.30 hsize - 2.19 hsize - 45.09 female (3.83) (.53) (4.29) 169.81 black + 62.31 female-black (12.71) (18.15) n 4,137, R2 .0858. The variable sat is the combined SAT score, hsize is size of the
7.2 The following equations were estimated using the data in BWGHT.RAW: 4.66.0044 cigs + .0093 log(faminc) + .016 parity log(bwght) (.22) (.0009) (.0059) +.027 male + .055 white (.010) (.013) n 1,388, R2 .0472 (.006) and log(bwght) = 4.65 .0052 cigs + .0110 log(faminc) + .017 par (.0010) (.0085)
7.1 Using the data equat P SLEEP75.RAW (see also Problem 3.3), we obtain the estimated sleep 3,840.83.163 totwrk - 11.71 educ - 8.70 age REVIEW N (235.11) (.018) (5.86) +.128 age + 87.75 male (.134) (34.33) n = 706, R2 = .123, R = .117. (11.21) The variable sleep is total minutes per week spent
C6.12 Use subset of 401KSUBS.RAW with fsize 1; this restricts the analysis to single person households; see also Computer Exercise C4.8. (i) What is the youngest age of people in this sample? How many people are at that age? (ii) In the model nettfa 0 1inc 2age 3age2 u, what is the
C6.11 Use APPLE.RAW to verify some of the claims made in Section 6.3. (i) Run the regression ecolbs on ecoprc, regprc and report the results in the usual form, including the R-squared and adjusted R-squared. Interpret the coefficients on the price variables and comment on their signs and
C6.10 Use the data in BWGHT2.RAW for this exercise. (i) Estimate the equation log(bwght) 0 1npvis 2npvis2 u by OLS, and report the results in the usual way. Is the quadratic term significant? (ii) Show that, based on the equation from part (i), the number of prenatal visits that
C6.9 The data set NBASAL.RAW contains salary information and career statistics 269 players in the National Basketball Association (NBA). Estimate a model relating points-per-game (points) to years in the league (exper), age, and years played in college (coll). Include a quadratic in exper; the
C6.8 Use the data in HPRICE1.RAW this exercise. (i) Estimate the model price = Bo+ Blotsize + Basqrft + B,bdrms + u and report the results in the usual form, including the standard error of the regression. Obtain predicted price, when we plug in lotsize = 10,000, sqrft 2,300, and bdrms = 4; round
C6.7 Use the data in ATTEND.RAW for this exercise. (i) In the model of Example 6.3, argue that stndfnl/ priGPA 2 24priGPA 6atndrte.Use equation (6.19) to estimate the partial effect when priGPA 2.59 and atndrte 82. Interpret your estimate. (ii) Show that the equation can be written as
C6.6 Use the data in VOTE1.RAW for this exercise. (i) Consider a model with an interaction between expenditures: voteA 0 1prtystrA 2expendA 3expendB 4expendAexpendB u. What is the partial effect of expendB on voteA, holding prtystrA and expendA fixed? What is the partial effect of
C6.5 Use the housing price data in HPRICE1.RAW for this exercise. (i) Estimate the model log(price) 0 1log(lotsize) 2log(sqrft) 3bdrms u and report the results in the usual OLS format. (ii) Find the predicted value of log(price), when lotsize 20,000, sqrft 2,500, and bdrms 4.
C6.4 Use the data in GPA2.RAW for this exercise. (i) Estimate the model sat 0 1hsize 2hsize2 u where hsize is the size of the graduating class (in hundreds), and write the results in the usual form. Is the quadratic term statistically significant? (ii) Using the estimated equation from
C6.2 Use the data in WAGE1.RAW for this exercise (i) Use OLS to estimate the equation PRARTS SALE LO Bexper + B,exper + u (ii) is exper statistically significant at the 1% level? %Awage=100(B+2 exper) Aexper, approximate return to the fifth year of experience. What is the approximate return to the
6.6 When atndrte2 and ACTatndrte are added to the equation estimated in (6.19), the R-squared becomes .232. Are these additional terms jointly significant at the 10% level? Would you include them in the model?
6.5 In Example 4.2, where the percentage of students receiving a passing score on a tenthgrade math exam (math10) is the dependent variable, does it make sense to include sci11— the percentage of eleventh graders passing a science exam—as an additional explanatory variable?
6.4 The following model allows the return to education to depend upon the total amount of both parents’ education, called pareduc: log(wage) 0 1educ 2educpareduc 3exper 4tenure u. (i) Show that, in decimal form, the return to another year of education in this model is log(wage)/
6.2 Let ˆ 0, ˆ 1, ..., ˆ k be the OLS estimates from the regression of yi on xi1, ..., xik, i 1, 2, ..., n. For nonzero constants c1, ..., ck, argue that the OLS intercept and slopes from the regression of c0yi on c1xi1, ..., ckxik, i 1, 2, ..., n, are given by ˜ 0 c0ˆ 0, ˜ 1
6.1 The following equation was estimated using the data in CEOSAL1.RAW: log(salary) (4.322) (.276) log(sales) (.0215) roe (.00008) roe2 log(saˆ lary) (.324) (.033) log(sales) (.0129) roe (.00026) roe2 n 209, R2 .282. This equation allows roe to have a diminishing effect on
C5.2 Use the data in GPA2.RAW for this exercise. (i) Using all 4,137 observations, estimate the equation colgpa 0 1hsperc 2sat u and report the results in standard form. (ii) Reestimate the equation in part (i), using the first 2,070 observations. (iii) Find the ratio of the standard
C5.1 Use the data in WAGE1.RAW for this exercise. (i) Estimate the equation wage 0 1educ 2exper 3tenure u. Save the residuals and plot a histogram. (ii) Repeat part (i), but with log(wage) as the dependent variable. (iii) Would you say that Assumption MLR.6 is closer to being
5.4 In the simple regression model (5.16), under the first four Gauss-Markov assumptions, we showed that estimators of the form (5.17) are consistent for the slope, 1. Given such an estimator, define an estimator of 0 by ˜ 0 y¯ ˜ 1x¯. Show that plim ˜ 0 0.
5.3 The data set SMOKE.RAW contains information on smoking behavior and other variables for a random sample of single adults from the United States. The variable cigs is the (average) number of cigarettes smoked per day. Do you think cigs has a normal distribution in the U.S. adult population?
5.2 Suppose that the model pctstck 0 1funds 2risktol u satisfies the first four Gauss-Markov assumptions, where pctstck is the percentage of a worker’s pension invested in the stock market, funds is the number of mutual funds that the worker can choose from, and risktol is some measure
5.1 In the simple regression model under MLR.1 through MLR.4, we argued that the slope estimator, ˆ 1, is consistent for 1. Using ˆ 0 y¯ ˆ 1x¯1, show that plim ˆ 0 0. [You need to use the consistency of ˆ 1 and the law of large numbers, along with the fact that 0 E(y)
C3.6 Use the data set in WAGE2.RAW for this problem. As usual, be sure all of the following regressions contain an intercept. (i) Run a simple regression of IQ on educ to obtain the slope coefficient, say, 5. (ii) Run the simple regression of log(wage) on educ, and obtain the slope coefficient, B-
C3.4 Use the data in ATTEND.RAW for t (i) Obtain the minimum, maximum, and atndrte, priGPA, and ACT PROTAMS RSEARC (ii) Estimate the model values for the variables + BACT + u. and write the results in equation form. Interpret the intercept. Does it (iii) Discuss the estimated slope coefficients.
3.13 (i) Consider the simple regression model y = B+ Bx + u under the first four Gauss-Markov assumptions. For some function g(x), for example g(x) EV = x or g(x) = log(1 + r), define z = g(x). Define a slope estimator as B -(2-3)/(22-3x). Show that B, is linear and unbiased. Remember, because
3.12 The following equation represents the effects of tax revenue mix on subsequent employment growth for the population of counties in the United States: growth B+ B share,+Bashare,+Bashare,+ other factors, where growth is the percentage change in employment from 1980 to 1990, sharep is the share
3.11 Suppose that the population model determining y is y=B+ Bx + Bxy + Bzxz + u and this model satisifies Assumptions MLR.1 through MLR.4. M= MS LENING LE OR CROC model that omits x3. Let B. B, and B, be the OLS estimators from the regression of y on x, and x. Show that the expected value of B,
3.9 The following equation describes the median housing price in a community in terms of amount of pollution (nox for nitrous oxide) and the average number of rooms in houses in the community (rooms): log(price) 0 1log(nox) 2rooms u. (i) What are the probable signs of 1 and 2? What is
3.8 Suppose that average worker productivity at manufacturing firms (avgprod) depends on two factors, average hours of training (avgtrain) and average worker ability (avgabil): avgprod 0 1avgtrain 2avgabil u. Assume that this equation satisfies the Gauss-Markov assumptions. If grants
3.6 Consider the multiple regression model containing three independent variables, under Assumptions MLR.1 through MLR.4: y = B+ Bx + Bx2 + B3x3 + u. You are interested in estimating the sum of the parameters on x and x2; call this = + B. (i) Show that + B is an unbiased estimator of (ii) Find
3.5 In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four
3.4 The median starting salary for new law school graduates is determined by log(salary) = B+ B, LSAT + BGPA + Blog(libvol) + Blog(cost) + Brank + u, where LSAT is the median LSAT score for the graduating class, GPA is the median col- lege GPA for the class, libvol is the number of volumes in the
3.3 The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep: Bo+B,totwrk + Beduc + Bage + u, where sleep and totwrk (total work) are
3.2 The data in WAGE2.RAW on working men was used to estimat equation: SON LEANING OR CLASSRO educ = 10.36 - .094 sibs + .131 meduc + 210, n = 722, R = .214, where educ is years of schooling, sibs is number of siblin schooling, and feduc is father's years of schooling. meduc is mother's years of
3.1 Using the data in GPA2.RAW on 4,137 college students, the following equation was estimated by OLS: colgpa 1.392 .0135 hsperc+.00148 sat - n = 4,137, R2 = .273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for
Suppose that the linear model, written in matrix notation, y 5 Xb 1 u satisfies Assumptions E.1, E.2, and E.3. Partition the model as y 5 X1b1 1 X2b2 1 u, where X1 is n 3 1k1 1 12 and X2 is n 3 k2.(i) Consider the following proposal for estimating b2. First, regress y on X1 and obtain the
Assume that the model y 5 Xb 1 u satisfies the Gauss-Markov assumptions and let b^ be the OLS estimator ofb. Let Z 5 G1X2 be an n 3 1k 1 12 matrix function of X and assume that ZrX3a 1k 1 12 3 1k 1 12 matrix4 is nonsingular. Define a new estimator of b by b| 5 1ZrX2 21 Zry.(i) Show that E1b|0X2 5b,
Assume that the model y 5 Xb 1 u satisfies the Gauss-Markov assumptions, let G be a 1k 1 12 3 1k 1 12 nonsingular, nonrandom matrix, and define d 5 Gb, so that d is also a 1k 1 12 3 1 vector. Let b^ be the 1k 1 12 3 1 vector of OLS estimators and define d^ 5 Gb^ as the OLS estimator of d.(i) Show
Let b^ be the OLS estimate from the regression of y on X. Let A be a 1k 1 12 3 1k 1 12 nonsingular matrix and define zt ; xt A, t 5 1, p, n. Therefore, zt is 1 3 1k 1 12 and is a nonsingular linear combination of xt. Let Z be the n 3 1k 1 12 matrix with rows zt. Let b^ denote the OLS estimate from
Let b^ be the 1k 1 12 3 1 vector of OLS estimates.(i) Show that for any 1k 1 12 3 1 vectorb, we can write the sum of squared residuals as SSR1b2 5 u^ ru^ 1 1b^ 2 b2 rXrX1b^ 2 b2.{Hint: Write 1y 2 Xb2 r 1y 2 Xb2 5 3u^ 1 X1b^ 2 b2 4 r 3u^ 1 X1b^ 2 b2 4 and use the fact that Xru^ 5 0.}
Let xt be the 1 3 1k 1 12 vector of explanatory variables for observation t. Show that the OLS estimator b^ can be written as b^ 5 a a nt51 xt rxtb 21 a a nt51 xt rytb.Dividing each summation by n shows that b^ is a function of sample averages.
Let X be an n 3 k matrix partitioned as X 5 1X1 X2 2, where X1 is n 3 k1 and X2 is n 3 k2.(i) Show that XrX 5 a Xr 1X1 Xr 1X2 Xr 2X1 Xr 2X2 b.

Showing 1900 - 2000 of 4105

First
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Last

Introductory Econometrics A Modern Approach 6th Edition Jeffrey M. Wooldridge - Solutions

Step by Step Answers