Questions and Answers of Econometric

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.
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 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?
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
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 +
(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
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 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 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
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
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
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
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.
(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
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
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
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
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
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
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
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
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
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
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 +
(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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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,
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
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
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
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) =
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
(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
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
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)
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
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 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
(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
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
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)
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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

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