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econometric

Introductory Econometrics A Modern Approach 4th edition Jeffrey M. Wooldridge - Solutions

Use the data in WAGE 1 .RAW for this exercise.(i) Find the average education level in the sample. What are the lowest and highest years of education?(ii) Find the average hourly wage in the sample. Does it seem high or low?(iii) The wage data are reported in 1976 dollars. Using the Economic Report
Use the data in BWGHT.RAW to answer this question. (i) How many women are in the sample, and how many report smoking during pregnancy? (ii) What is the average number of cigarettes smoked per day? Is the average a good measure of the "typical" woman in this case? Explain. (iii) Among women who
The data MEAP01.RAW are for the state of Michigan in the year 2001. Use these data to answer the following question. (i) Find the largest and smallest values of math4. Does the range make sense? Explain. (ii) How many schools have perfect pas rate on the math test? What percentage is this of the
The data in JTRAIN2.RAW come form a job training experiment conducted for low income men during 1976 - 1977; See Lalonde (1986). (i) Use the indicator variable train to determine the fraction of men receiving job training. (ii) The variable re78 is earnings from 1978, measured in thousands of 1982
Let kids denote the number of children over born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = (0 + (1 educ + u, where u is the unobserved error. (i) What kinds of factors are contained in u? Are these likely to
(v) Do the algebra to simplify the expression in part (iv) to equation.
Suppose you are interested in estimating the effect of hours spent in an SAT preparation course (hours) on total SAT score (sat). The population is all college-bound high school seniors for a particular year. (i) Suppose you are given a grant to run a controlled experiment. Explain how you would
In the simple linear regression model y = (0 + (1x + u. Suppose that E(u) ( 0. Letting a0 = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value?
The following table contains the ACT scores and the GPA (grade point average) for eidght college students. Grade point average is based on a four point scale and has been rounded to one digit after the decimal.(i) Estimate the relationship between GPA and ACT using ULS; that is, obtain the
The data set BWGHT.RAW contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variables, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following
In the linear consumption functionThe (estimated) marginal propensity to consume (MPC) out of income is simply the slope, , while the average propensity to consume (APC) is Using observations for 100 families on annul income and consumption (both measured in dollars), the following equation is
Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and McClain (1995), the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist):n = 135, R2 = 0.162. (i) Interpret the coefficient on log (dist). Is the sign of this
Consider the savings functionWhere e is a random variable with E(e) = 0 and Var(e) = (2e, Assume that e is independent of inc.(i) Show that E(u|inc) = 0, so that the key zero conditional mean assumption (Assumption SLR.4) is satisfied. [if e is independent of inc, then E(e|inc) = E(e).](ii) Show
Consider the standard simple regression model y = (0 + (1x + u under the Gauss Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators unbiased for their respective population parameters. Let be the estimator of obtained by assuming the intercept zero (see Section 2.6).(i) Find E() in
(i) Let and be the intercept and slope from the regression of yi on xi, using n observations. Let c1 and c2, with c2 ( 0, be constants. Let and be the intercept and slope from the regression of c1.yi on c2.xi. Show that = (c1/c2) and = c1, thereby verifying the claims on units of measurement
The data in 40IK.RAW are a subset of data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan. The variable prate is the percentage of eligible workers with an active account; this is the variable we would like to explain.
The data set in CEOSAL2.RAW contains information on chief executive officers for U.S. corporations. The variable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years as company CEO.(i) Find the average salary and the average tenure in the sample.(ii) How many
Use the data in SLEEP75.RAW from Biddle and Hamermesh (1990) to study whether there is a tradeoff between the time spent sleeping per week and the time spent in paid work. We could use either variable as the dependent variable. For concreteness, estimate the modelSleep = (0 + (1 totwrk + u,Where
Use the data in WAGE2.RAW to estimate a simple regression explaining monthly salary (wage) in terms of IQ score (IQ).(i) Find the average salary and average IQ in the sample. What is the sample standard deviation of IQ? (IQ scores are standardized so that the average in the population is 100 with a
For the population of firms in the chemical industry, let rd denote annual expenditures on research and development, and let sales denote annual sales (both are in millions of dollars).(i) Write down a model (not an estimated equation) that implies a constant elasticity between rd and sales. Which
We used the data in MEAP93.RAW for Example 2.12. Now we want to explore the relationship between the math pass rate (math10) and spending per student (expend).(i) Do you think each additional dollar spent has the same effect on the pass rate, or does a diminishing effect seem more appropriate?
Use the data in CHARITY.RAW [obtained from Franses and Paap (2001)] to answer the following questions: (i) What is the average gift in the sample of 4,268 people (in Dutch guilders)? What percentage of people gave no gift? (ii) What is the average mailings per year? What are the minimum and maximum
Using the data in GPA2.RAW on 4,137 college students, the following equation was estimated by OLS:Where colgpa is measured on a four-point scale, hsperc s the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top 5% of the calss),(i) Why does it make
Suppose that you are interested in estimating the ceteris paribus relationship between y and xi. For this purpose, you can collect data on two control variables, x2 and x3 (For concreteness, you might think of y as final exam score, x1 as class attendance, x2 as GPA up through the previous
Suppose that the population model determining y isy = (0 + (1x1 + (2x2 + (3x3 + u,
The following equation represents the effects of tax revenue mix on subsequent employment growth for the population of counties in the United State. growth = (0 + (1shareP + (2share1 + (3shareS + other factors,where growth is the percentage change in employment from 1980 to 1990, shareP is the
(i) Consider the simple regression model y = (0 +(1x + u under the first four Gauss-Markov assumptions. For some function g(x), for example g(x) = x2 or g(x) = log(1 + x2), define zi = g(xi). Define a slope estimator as(ii) Add the homoskedasticity assumption, MLR.5. Show thatnotice that we can
The data in WAGE2.RAW on working men was used to estimate the following equation:Where educ is years of schooling, sibs is number of siblings, meduc is mother's years of schooling, and feduc is father's years of schooling.(i) Does sibs have the expected effect? Explain. Holding meduc and feduc
The following model is simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spend sleeping and working and to look at other factors affecting sleep:Sleep = (0 + (1 totwrk + (2 edu + (3 age + u,Where sleep and totwrk (total work)
The median starting salary for new law school graduates is determined byLog (salary) = (0 + (1. LSAT + (2 GPA + ((3 log (libvol) + (4log (cost)+ (5 rank + u,Where LSAT is the median LSAT score for the graduating class, GPA is the median college GPA for the class, libvol is the number of volumes in
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
Which of the following can cause OLS estimators to be biased?(i) Heteroskedasticity.(ii) Omitting and important variable.(iii) A sample correlation coefficient of .95 between two independent variables both included in the model?
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 + (1 avgtrain + (2 avgabil + u.Assume that this equation satisfies the Gauss-Markov assumptions. If grants have
The following equation describes the media 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 + (1 log (nox) + (2 rooms + u.(i) What are the probable signs of (1 and (2? What is the
A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various illnesses. Since factors other than
Use the data in HPRICE1 .RAW to estimate the modelPrice = (0 + (1 sqrft + (2 bdrms + u,where price is the house price measured in thousands of dollars.(i) Write out the results in equation form.(ii) What is the estimated increase in price for a house with one more bedroom, holding square footage
The file CEOSAL2.RAW contains data on 177 chief executive officers and can be used to examine the effects of firm performance on CEO salary.(i) Estimate a model relating annual salary to firm sales and market value. Make the model of the constant elasticity variety for both independent variables.
Use the data in ATTEND.RAW this exercise(i) Obtain the minimum, maximum, and average values for the variables atndrte, priGPA, and ACT.(ii) Estimate the modelatndrte = (0 + (1priGPA + (2ACT + u,and write the results in equation form. Interpret the intercept. Does it have a useful meaning?(iii)
Confirm the partialling out interpretation of the OLS estimates by explicitly doing the partialling out for Example 3.2. This first requires regressing educ on exper and tenure and saving the residuals, / Then, regress log(wage) on /. Compare the coefficient on/with the coefficient on educ in the
Use the data set in WAGE2.RAW for this problem. As usual, be sure all of the following regressions contain an intercept.
Use the data in MEAP93.RAW to answer this question.(i) Estimate the modelmath10 = (0 + (1 log (expend) + (2 lnchprg + u,and report the results in the usual form, including the sample size and R-squared. Are the signs of the slope coefficients what you expedited? Explain.(ii) What do you make of the
Use the data in DISCRIM.RAW to answer this question. These are ZIP code-level data on prices for various items at fast-food restaurants, along with characteristics of the zip code population, in New Jersey and Pennsylvania. The idea is to see whether fast-food restaurants charge higher prices in
Use the data in CHARITY.RAW to answer the following questions: (i) Estimate the equation gift = (0 + (1 mailsyear + (2 giftlast + (3 propresp + u by OLS and report the results in the usual way, including the sample size and R-squared. How does the R-squared compare with that from the simple
Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H0)? (i) Heteroskedasticity. (ii) A sample correlation coefficient of .95 between two independent variables that are in the model. (iii) Omitting an important explanatory variables.
Regression analysis can be used to test whether the market efficiently uses information in valuing stocks. For concreteness, let return be the total return from holding a firm's stock over the four-year period from the end of 1990 to the end of 1994. The efficient markets hypothesis says that these
The following table was created using the data in CEOSAL2.RAW:The variable mktval is market value of the firm, profmarg is profit as a percentage of sales, ceoten is years as CEO with the current company, and comtenis total years with the company.(i) Comment on the effect of profmarg on CEO
Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equality (roe, in percentage form), and return on the firm's stock (ros, in percentage form):log (salary) = (0 + (1 log (sales) + (2roe + (3ros + u.(i) In terms of the model parameters, state the null
The variable rdintens is expenditures on research and development (R&D) as a percentage of sales. Sales are measured in millions of dollars. The variables profmarg is profits as a percentage of sales.Using the data in RDCHEM.RAW for 32 firms in the chemical industry, the following equation is
Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percentage of the
In Section 4.5, we used as an example testing the rationality of assessments of housing prices. There, we used a log-log model in price and assess [see equation (4.47)]. Here, we use a level-level formulation,(i) In the simple regression modelprice = (0 + (1 possess + u,the assessment is rational
In Example 4.7, we used data on nonunionized manufacturing firms to estimate the relationship between the scrap rate and other firm characteristics. We now look at this example more closely and use all available firms.(i) The population model estimated in Example 4.7 can be written aslog(scrap) =
Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR. 1 through MLR.6:y = (0 + (1x1 + (2x2 + (3x3 + u.You would like to test the null hypothesis H0: (1 - 3(2 = 1.(ii) Write the t statistic for testing H0: (1 - 3(2 = 1.(iii) Define
In Problem 3.3, we estimated the equationwhere we now report standard errors along with the estimates.(i) Is either educ or age individually significant at the 5% level against a two-sided alternative? Show your work.(ii) Dropping educ and age from the equation givesAre educ and age jointly
The following model can be used to study whether campaign expenditures affect election outcomes:voteA = (0 + (1 log(expendA) + (2 log(expendB) + (3 prtystrA + u,where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign expenditures by Candidates A and B,
Use the data in ELEM94_95 to answer this question. The findings can be compared with those in Table 4.1. The dependent variable lavgsal is the log of average teacher salary and bs is the ratio of average benefits to average salary (by school).(i) Run the simple regression of lavgsal on bs. Is the
Use the data in LAWSCH85.RAW for this exercise.(i) Using the same model as Problem 3.4, state and test the null hypothesis that the rank of law schools has no ceteris paribus effect on median starting salary.(ii) Are features of the incoming class of students-namely, LSAT and GPA- individually or
Refer to Problem 3.14. Now, use the log of the housing price as the dependent variable:log(price) = (0 + (1 sqrft + bdrms + u.(i) You are interested in estimating and obtaining a confidence interval for the percentage change in price when a 150-square-foot bedroom is added to a house. In decimal
In Example 4.9, the restricted version of the model can be estimated using all 1,388 observations in the sample. Compute the R-squared from the regression of bwght on cigs, parity, and famine using all observations. Compare this to the fl-squared reported for the restricted model in Example 4.9.
Use the data in MLB 1 .RAW for this exercise.(i) Use the model estimated in equation (4.31) and drop the variable rbisyr. What happens to the statistical significance of hrunsyr? What about the size of the coefficient on hrunsyrl?(ii) Add the variables runsyr (runs per year), fldperc (fielding
Use the data in WAGE2.RAW for this exercise.(i) Consider the standard wage equationlog(wage) = (0 + (1educ + (2exper + (3 tenure + u.State the null hypothesis that another year of general workforce experience has the same effect on log(wage) as another year of tenure with the current employer.(ii)
Refer to the example used in Section 4.4. You will use the data set TWOYEAR.RAW.(i) The variable phsrank is the person's high school percentile. (A higher number is better. For example, 90 means you are ranked better than 90 percent of your graduating class.) Find the smallest, largest, and average
The data set 401KSUBS.RAW contains information on net financial wealth (nettfa), age of the survey respondent (age), annual family income (inc), family size (fsize), and participation in certain pension plans for people in the United States. The wealth and income variables are both recorded in
Use the data in DISCRIM.RAW to answer this question. (See also Computer Exercise C3.8 in Chapter 3.)(i) Use OLS to estimate the modellog(psoda) = (0 + (1 rpblck + (2 log(income) + fiiprppov + u,(ii) What is the correlation between log(income) and prppov? Is each variable statistically significant
In the simple regression model under MLR. 1 through MLR.4, we argued that the slope estimator, is consistent for (1. Using = - , show that plim = (0. [You need to use the consistency of , and the law of large numbers, along with the fact that (0 = E(y) - (1E(x1).]
Suppose that the modelpctstck = (0 + (1 funds + (2 risktol + u
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? Explain.
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 = - Show that plim = (0?
Use the data in WAGE 1 .RAW for this exercise.(i) Estimate the equationwage = (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 satisfied for
Use the data in GPA2.RAW for this exercise.(i) Using all 4,137 observations, estimate the equationcolgpa = (0 + (0 hsperc + (2 sat + uand 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 errors on
In equation (4.42) of Chapter 4, compute the LM statistic for testing whether motheduc and fatheduc are jointly significant. In obtaining the residuals for the restricted model, be sure that the restricted model is estimated using only those observations for which all variables in the unrestricted
(i) First use the data set 401KSUBS.RAW, keeping only observations with fsize = 1. Find the skewness measure for inc. Do the same for log(mc). Which variable has more skewness and therefore seems less likely to be normally distributed?(ii) Next use BWGHT2.RAW. Find the skewness measures for bwght
The following equation was estimated using the data in CEOSALI.RAW:This equation allows roe to have a dimming effect on log (salary). Is this generality necessary? Explain why or why not.
[Use the fact that the j solve the first order conditions in (3.13), and the j must solve the first order conditions involving the rescaled dependent and independent variables.]
Using the data in RDCHEM.RAW, the following equation was obtained by OLS:(i) At what point does the marginal effect of sales on rdintens become negative?(ii) Would you keep the quadratic term in the model? Explain.(iii) Define salesbil as sales measured in billions of dollars: salesbil =
The following model allows the return to education to depend upon the total amount of both parents' education, called pareduc:log(wage) = (0 + (1 educ + (2 educ(pareduc + (3 exper + (4 tenure + u.(i) Show that, in decimal form, the return to another year of education in this model islog(wage) /
In Example 4.2, where the percentage of students receiving a passing score on a tenth - grade math exam (math10) is the deponent variable, does it make sense to include sci11 - the percentage of eleventh graders passing a science exam - as an additional explanatory variables?
When atndrte2 and ACT. atndrte 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?
The following three equations were estimated using the 1,534 observations in 401K.RAW:Which of these three models do you prefer? Way?
Suppose we want to estimate the effects of alcohol consumption (alcohol) on college grade point average (colGPA). In addition to collecting information on grade point averages and alcohol usage, we also obtain attendance information (say, percentage of lectures attended, called attend). A
(i) For what values of will the point prediction be in the 95% prediction interval? Does this condition seem likely to hold in most applications?(ii) Verify that the condition from part (i) is satisfied in the CEO salary example.
Use the data in KIELMC.RAW, only for the year 1981, to answer the following questions. The data are for houses that sold during 1981 in North Andover, Massachusetts: 1981 was the year construction began on a local garbage incinerator.(i) To study the effects of the incinerator location on housing
Use the data in BWGHT2.RAW for this exercise.(i) Estimate the equationlog(bwght) = (0 + (1 npvis + (2 npvis2 + uby 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 maximizes
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 magnitudes.(ii)
Use the 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 modelnettfa = (0 + (1 jnc + (2 age + (3 age2 + u,what is the
Use the data in MEAP00_01 to answer this question.(i) Estimate the modelmathA = (0 + (2 lexppp + (2 lenroIl + (3 lunch + uby OLS, and report the results in the usual form. Is each explanatory variable statistically significant at the 5% level?(ii) Obtain the fitted values from the regression in
Use the data in WAGE 1 .RAW for this exercise,(i) Use OLS to estimate the equationlog(wage) = (0 + (1 educ + (2 exper + (3 exper2 + uand report the results using the usual format.(ii) is exper2 statistically significant at the 1% level?(iii) Using the approximationFind the approximation return to
Consider a model where the return to education depends upon the amount of work experience (and vice versa):log(wage) = (0 + (1educ + (2 exper + (3 educ exper + u.(i) Show that the return to another year of education (in decimal form), holding exper fixed, is (1 + (3 exper.(ii) State the null
Use the data in GPA2.RAW for this exercise, (i) Estimate the modelsat = (0 + (1 hsize + (2 hsize2 + 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 part
Use the housing price data in HPRICE1.RAW for this exercise.(i) Estimate the modellog(price) = (0 + (1 log(lotsize) + (2 log(sqrft) + (3 bdrms + uand report the result in the usual OLS format.(ii) Find the predicated value of log(price), when lotsize = 20,000, sqrft = 2,500, and bdrms = 4. Using
Use the data in VOTE1.RAW for this exercise.(i) Consider a model with an interaction between expenditures:voteA = (0 + (1 prtystrA + (2 expendA + (3 expendB + (4 expendA-expendB + u.What is the partial effect of expendB on voteA, holding prtystrA and expendA fixed? What is the partial effect of
Use the data in ATTEND.RAW for this exercise.(i) In the model of Example 6.3, argue thatUse 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 asWhere (2 = (2 + 2(4 (2.59) + (6 (82.) (The intercept
Use the data in HPRICE1.RAW for this exercise.(i) Estimate the modelprice = (0 + (1 lotsize + (2 sqrft + (3 bdrms + uand report the results in the usual form, including the standard error of the regression. Obtain predicated price, when we plug in lotsize = 10,000, sqrft = 2,300, and bdrms = 4;
The data set NBASAL.RAW contains salary information and career statistics for 269 players in the National Basketball Association (NBA).(i) 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
Using the data in SLEEP75.RAW (see also Problem 3.3), we obtain the estimated equationThe variable sleep is total minutes per week spent sleeping at night, totwrk is total weekly minutes spent working, educ and age are measured in years, and male is a gender dummy.(i) All other factors being equal,
For a child i living in a particular a school district, let voucheri be a dummy variable equal to one if a child is selected to participate in a school voucher program, and let scorei be that child's score on a subsequent standardized exam. Suppose that the participation variable, voucheri, is
The following equations were estimated using the data in BWGHT.RAW:AndThe variables are defined as in Example 4.9, but we have added a dummy variable for whether the child is male and a dummy variable indicating whether the child is classified as white.(i) In the first equation, interpret the
Using the data in GPA2.RAW, the following equation was estimated:The variable sat is the combined SAT score, hsize is size of the student's high school graduating class, in hundreds, female is a gender dummy variable, and black is a race dummy variable equal to one for blacks and zero otherwise.(i)
An equation explaining chief executive officer salary isThe data used are in CEOSALI.RAW, where finance, consprod, and utility are binary variables indicating the financial, consumer products, and utilities industries. The omitted industry is transportation.(i) Compute the approximate percentage
In Example 7.2, let noPC be a dummy variable equal to one if the student does not own a PC, and zero otherwise.(ii) What will happen to the R-squared if noPC is used in place of PC?(iii) Should PC and noPC both be included as independent variables in the model? Explain.
To test the effectiveness of a job training program on the subsequent wages of workers, we specify the modellog(wage) - (0 + (1 Strain + (2 educ + (3 exper + 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

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