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About 833 results. 1294 free access solutions
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| m78576 | 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 share of property taxes in total tax revenue, share1 is the share of income tax revenues, and shareS is the share of sales tax revenues. All of these variables are measured in 1980. The omitted share, shareF, includes fees and miscellaneous taxes. By definition, the four shares add up to one. Other factors would include expenditures on education, infrastructure, and so on (all measured in 1980).
(i) Why must we omit one of the tax share variables from the equation?
(ii) Give a careful interpretation of (1. |
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| m78577 | 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. |
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| m78578 | The following equations were estimated using the data in BWGHT.RAW:
And
The 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 coefficient on the variable cigs. In particular, what is the effect on birth weight from smoking 10 more cigarettes per day?
(ii) How much more is a white child predicted to weigh than a nonwhite child, holding the other factors in the first equation fixed? Is the difference statistically significant?
(iii) Comment on the estimated effect and statistical significance of motheduc.
(iv) From the given information, why are you unable to compute the F statistic for joint significance of motheduc and fatheducl what would you have to do to compute the F statistic? |
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| m78600 | The following is a simple model to measure the effect of a school choice program on standardized test performance [see Rouse (1998) for motivation]:
Score = β0 + β1 choice + β2 faminc + u1,
where score is the score on a statewide test, choice is a binary variable indicating whether a student attended a choice school in the last year, and famine is family income. The IV for choice is grant, the dollar amount granted to students to use for tuition at choice schools. The grant amount differed by family income level, which is why we control for famine in the equation.
(i) Even with famine in the equation, why might choice be correlated with u1?
(ii) If within each income class, the grant amounts were assigned randomly, is grant uncorrelated with «,?
(iii) Write the reduced form equation for choice. What is needed for grant to be partially correlated with choice?
(iv) Write the reduced form equation for score. Explain why this is useful. |
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| m78604 | 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 is
log(wage) / (educ = (1 + (2 pareduc.
What sign do you expect for (2? Why?
(ii) Using the data in WAGE2.RAW, the estimated equation is
Does the estimated return to education now depend positively on parent education? Test the null hypothesis that the return to education does not depend on parent education. |
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| m78605 | 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, and prtystrA is a measure of party strength for Candidate A (the percentage of the most recent presidential vote that went to A s party).
(i) What is the interpretation of (1?
(ii) In terms of the parameters, state the null hypothesis that a 1% increase in A s expenditures is offset by a 1% increase in B s expenditures.
(iii) Estimate the given model using the data in VOTE 1.RAW and report the results in usual form. Do A s expenditures affect the outcome? What about B s expenditures? Can you use these results to test the hypothesis in part (ii)?
(iv) Estimate a model that directly gives the t statistic for testing the hypothesis in part (ii). What do you conclude? (Use a two sided alternative). |
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| m78606 | 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) are measured in minutes per week and educ and age are measured in years. (See also Compute Exercise C2.3.)
(i) If adults trade off sleep for work, what is the sign of (1?
(ii) What signs do you think (2 and (3 will have?
(iii) Using the data in SLEEP75.RAW, the estimated equation is
If someone works five more hours per week, by how many minutes is sleep predicted to fail? Is this a large tradeoff?
(iv) Discuss the sign and magnitude of the estimated coefficient on educ.
(v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk? |
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| m78616 | 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 intercept and slope estimates in the equation.
Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points?
(ii) Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero.
(iii) What is the predicted value of GPA when ACT = 20?
(iv) How much of the variation in GPA for these eight students is explained by ACT? Explain. |
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| m78630 | 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 salary?
(ii) Does market value have a significant effect? Explain.
(iii) Interpret the coefficients on ceoten and comten. Are these explanatory variables statistically significant? |
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| m78631 | The following three equations were estimated using the 1,534 observations in 401K.RAW:
Which of these three models do you prefer? Way? |
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| m78720 | The median starting salary for new law school graduates is determined by
Log (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 the law school library, cost is the annual cost of attending law school, and rank is a law school ranking (with rank = 1 being the best).
(i) Explain why we expect (5 ( 0.
(ii) What signs do you expect for the other slope parameters? Justify your answers.
(iii) Using the data in LAWSCH85.RAW, the estimated equation is
+ .038 log (cost) - .0033 rank
n = 136, R2 = .842.
What is the predicated ceteris paribus difference in salary for schools with a median GPA different by one point? (Report your answer as a percentage).
(iv) Interpret the coefficient on the variable log(libvol).
(v) Would you say it is better to attend a higher ranked law school? How much is a difference in ranking of 20 worth in terms of predicted starting salary? |
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| m78965 | The purpose of this exercise is to compare the estimates and standard errors obtained by correctly using 2SLS with those obtained using inappropriate procedures. Use the data file WAGE2.RAW.
(i) Use a 2SLS routine to estimate the equation
log(wage) = β0 + β1 educ + β2 exper + β3 tenure + β4plack + u,
where sibs is the IV for educ. Report the results in the usual form. |
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| m79128 | 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 estimated:
(i) Interpret the coefficient on log(sales). In particular, if sales increases by 10%, what is the estimated percentage point change in rdintensl Is this an economically large effect?
(ii) Test the hypothesis that R&D intensity does not change with sales against the alternative that it does increase with sales. Do the test at the 5% and 10% levels.
(iii) Interpret the coefficient on profmarg. Is it economically large?
(iv) Does profmarg have a statistically significant effect on rdintens? |
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| m79129 | The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. Using the data in SMOKE.RAW, we estimate a linear probability model for smokes:
The variable white equals one if the respondent is white, and zero otherwise; the other in dependent variables are defined in Example 8.7. Both the usual and heteroskedasticity-robust standard errors are reported.
(i) Are there any important differences between the two sets of standard errors?
(ii) Holding other factors fixed, if education increases by four years, what happens to the estimated probability of smoking?
(iii) At what point does another year of age reduce the probability of smoking?
(iv) Interpret the coefficient on the binary variable restaurn (a dummy variable equal to one if the person lives in a state with restaurant smoking restrictions).
(v) Person number 206 in the data set has the following characteristics: cigpric = 67.44, income = 6,500, educ = 16, age = 77, restaurn = 0, white = 0, and smokes = 0. Compute the predicted probability of smoking for this person and comment on the result. |
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| m79167 | 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 xi1, xi2, ...., xik, ŷ2i, i = 1,...., n,
where the u. are the OLS residuals and the ŷi. are the OLS fitted values. Then, we would test joint significance of xi1, xi2, ....., xik and ŷ2i. (Of course, we always include an intercept in this regression.)
(i) What are the df associated with the proposed F test for heteroskedasticity?
(ii) Explain why the R-squared from the regression above will always be at least as large as the R-squareds for the BP regression and the special case of the White test.
(iii) Does part (ii) imply that the new test always delivers a smaller p-value than cither the BP or special case of the White statistic? Explain.
(iv) Suppose someone suggests also adding ŷi to the newly proposed test. What do you think of this idea? |
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| m79176 | 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 contains information on net financial assets (nettfa), family income (inc), a binary variable for eligibility in a 401(k) plan (e401k), and several other variables.
(i) What fraction of the families in the sample are eligible for participation in a 401 (k) plan?
(ii) Estimate a linear probability model explaining 401(k) eligibility in terms of income, age, and gender. Include income and age in quadratic form, and report the results in the usual form.
(iii) Would you say that 401(k) eligibility is independent of income and age? What about gender? Explain.
(iv) Obtain the fitted values from the linear probability model estimated in part (ii). Are any fitted values negative or greater than one?
(vii) The overall percent correctly predicted is about 64.9%. Do you think this is a complete description of how well the model does, given your answers in part (vi)?
(viii) Add the variable pira as an explanatory variable to the linear probability model. Other things equal, if a family has someone with an individual retirement account, how much higher is the estimated probability that the family is eligible for a 401 (k) plan? Is it statistically different from zero at the 10% level? |
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| m79188 | This exercise also uses the data from VOLAT.RAW. Computer Exercise 18.11 studies the long-run relationship between stock prices and industrial production. Here, you will study the question of Granger causality using the percentage changes.
(i) Estimate an AR(3) model for pcipt the percentage change in industrial production (reported at an annualized rate). Show that the second and third lags are jointly significant at the 2.5% level.
(ii) Add one lag of pcspt to the equation estimated in part (i). Is the lag statistically significant? What does this tell you about Granger causality between the growth in industrial production and the growth in stock prices?
(iii) Redo part (ii) but obtain a heteroskedasticity-robust t statistic. Does the robust test change your conclusions from part (ii)? |
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| m79190 | This question assumes that you have access to a statistical package the computes standard errors robust to arbitrary serial correlation and heteroskedasticity for panel data methods.
(i) For the pooled OLS estimates in Table 14.1, obtain the standard errors that allow for arbitrary serial correlation (in the composite errors, vit = ai + uit) and heteroskedasticity. How do the robust standard errors for educ, married, and union compare with the non robust ones?
(ii) Now obtain the robust standard errors for the fixed effects estimates that allow arbitrary serial correlation and heteroskedasticity in the idiosyncratic errors, uit. How do these compare with the non robust FE standard errors?
(iii) For which method, pooled OLS or FE, is adjusting the standard errors for serial correlation more important? Why? |
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| m79249 | To test the effectiveness of a job training program on the subsequent wages of workers, we specify the model
log(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 worker ability. If less able workers have a greater chance of being selected for the program, and you use an OLS analysis, what can you say about the likely bias in the OLS estimator of (1? |
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| m79255 | True or false: "If the errors in a regression model contain ARCH, they must be serially correlated? |
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