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About 833 results. 1294 free access solutions
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| m78260 | Suppose you want to test whether girls who attend a girls high school do better in math than girls who attend coed schools. You have a random sample of senior high school girls from a state in the United States, and score is the score on a standardized math test. Let girlhs be a dummy variable indicating whether a student attends a girls high school.
(i) What other factors would you control for in the equation? (You should be able to reasonably collect data on these factors.)
(ii) Write an equation relating score to girlhs and the other factors you listed in part (i).
(iii) Suppose that parental support and motivation are unmeasured factors in the error term in part (ii). Are these likely to be correlated with girlhs? Explain.
(iv) Discuss the assumptions needed for the number of girls high schools within a 20-mile radius of a girl s home to be a valid IV for girlhs. |
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| m78277 | Suppose yt follows a second order FDL model:
yt = a0 + (0zt + (1zt-1 + (2zt-2 + ut.
Let z* denote the equilibrium value of zt and let y* be the equilibrium value of yt, such that
y* = a0 + (0z* + (1z* + (2z*.
Show that the change in y*, due to a change in z*, equals the long-run propensity times the change in z*:
(y* = LRP((z*.
This gives an alternative way of interpreting the LRP. |
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| m78437 | 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 measure of generosity is the plan match rate, mrate. This variable gives the average amount the firm contributes to each worker s plan for each $1 contribution by the worker. For example, if mrate = 0.50, then a $1 contribution by the worker is matched by a 50ȼ contribution by the firm.
(i) Find the average participation rate and the average match rate in the sample of plans.
(ii) Now, estimate the simple regression equation
and report the results along with the sample size and R-squared.
(iii) Interpret the intercept in your equation. Interpret the coefficient on mrate.
(iv) Find the predicted prate when mrate = 3.5. Is this a reasonable prediction? Explain what is happening here.
(v) How much of the variation in prate is explained by mrate? Is this a lot in your opinion? |
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| m78439 | The data in FERTIL2.RAW includes, for women in Botswana during 1988, information on number of children, years of education, age, and religious and economic status variables.
(i) Estimate the model
children = β0 + β1educ + β2 age + β1 age2 + u
by OLS, and interpret the estimates. In particular, holding age fixed, what is the estimated effect of another year of education on fertility? If 100 women receive another year of education, how many fewer children are they expected to have?
(ii) The variable frsthalf is a dummy variable equal to one if the woman was bom during the first six months of the year. Assuming that frsthalf is uncorrelated with the error term from part (i), show that frsthalf is a reasonable IV candidate for educ.
(iii) Estimate the model from part (i) by using frsthalf as an IV for educ. Compare the estimated effect of education with the OLS estimate from part (i).
(iv) Add the binary variables electric, tv, and bicycle to the model and assume these are exogenous. Estimate the equation by OLS and 2SLS and compare the estimated coefficients on educ. Interpret the coefficient on tv and explain why television ownership has a negative effect on fertility. |
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| m78440 | 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 dollars. Find the average of re78 for the sample of men receiving job training and the sample not receiving job training. Is the difference economically large?
(iii) The variable unem78 is an indicator of whether a man is unemployed or not in 1978. What fraction of the men who received job training? Comment on the difference.
(iv) From parts (ii) and (iii), does it appear that the job training program was effective? What would make our conclusions more convincing? |
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| m78444 | 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 fixed, by how much does sibs have to increase to reduce predicted years of education by one year? (A non-integer answer is acceptable here.)
(ii) Discuss the interpretation of the coefficient on meduc.
(iii) Suppose that Man A has no siblings, and his mother and father each have 12 years of education. Man B has no siblings, and his mother and father each have 16 years of education. What is the predicted difference in years of education between B and A? |
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| m78446 | 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 total sample?
(iii) How many schools have math pass rates of exactly 50 percent?
(iv) Compare are average pass rates for the math and reading scores. Which test is harder to pass?
(v) Find the correlation between math4 and rad4. What do you conclude?
(vi) The variable exppp is expenditure per pupil. Find the average of exppp along with its standard deviation. Would you say there is wide variation in per pupil spending?
(vii) Suppose School A spends $6,000 per student and School B spends $5,500 per student. By what percentage does School A s spending exceed School B s? Compare this to 100. [log(6,000) - log(5,500)], which is the approximation percentage difference based on the difference in the natural logs. (See Section A.4 in Appendix A.) |
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| m78453 | 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 thousands of dollars. For this question, use only the data for single-person households (so fsize = 1).
(i) How many single-person households are there in the data set?
(ii) Use OLS to estimate the model
nettfa = (0 + (1 inc + (2 age + u,
and report the results using the usual format. Be sure to use only the single-person households in the sample. Interpret the slope coefficients. Are there any surprises in the slope estimates?
(iii) Does the intercept from the regression in part (ii) have an interesting meaning? Explain.
(iv) Find the p-value for the test H0: (2 = 1 against H0: (2 < 1. Do you reject H0 at the 1% significance level?
(v) If you do a simple regression of nettfa on inc, is the estimated coefficient on inc much different from the estimate in part (ii)? Why or why not? |
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| m78454 | 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 simple regression was estimated using data on n = 1,388 births:
(i) What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.
(ii) Does this simple regression necessarily capture a casual relationship between the child s birth weight and the mother s smoking habits? Explain.
(iii) To predict a birth weight of 125 ounces, what would cigs have to be? Comment.
(iv) The proportion of women in the who do not smoke while pregnant is about .85. Does this help reconcile your finding from part (iii)? |
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| m78455 | 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 CEOs are in their first year as CEO (that is, ceoten = 0)? What is the longest tenure as a CEO?
(iii) Estimate the simple regression model
Log (salary) = (0 + (1 ceoten+ u,
And report your result in the usual form. What is the (approximate) predicated percentage increase in salary given one more year as a CEO? |
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| m78456 | 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 other variables should appear in level form. Report the results in the usual way.
(ii) Holding college years and age fixed, at what value of experience does the next year of experience actually reduce points-per-game? Does this make sense?
(iii) Why do you think coll has a negative and statistically significant coefficient? (NBA players can be drafted before finishing their college careers and even directly out of high school.)
(iv) Add a quadratic in age to the equation. Is it needed? What does this appear to imply about the effects of age, once experience and education are controlled for?
(v) Now regress log(wage) on points, exper, exper2, age, and coll. Report the results in the usual format.
(vi) Test whether age and coll are jointly significant in the regression from part (v). What does this imply about whether age and education have separate effects on wage, once productivity and seniority are accounted for? |
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| m78457 | 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. |
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| m78517 | 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. Write the results out in equation form.
(ii) Add profits to the model from part (i). Why can this variable not be included in logarithmic form? Would you say that these firm performance variables explain most of the variation in CEO salaries?
(iii) Add the variable ceoten to the model in part (ii). What is the estimated percentage return for another year of CEO tenure, holding other factors fixed?
(iv) Find the sample correlation coefficient between the variables log(mktval) and profits. Are these variables highly correlated? What does this say about the OLS estimators? |
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| m78518 | The file FISH.RAW contains 97 daily price and quantity observations on fish prices at the Fulton Fish Market in New York City. Use the variable log(avgprc) as the dependent variable.
(i) Regress log{avgprc) on four daily dummy variables, with Friday as the base. Include a linear time trend. Is there evidence that price varies systematically within a week?
(ii) Now, add the variables wave 2 and wave3, which are measures of wave heights over the past several days. Are these variables individually significant? Describe a mechanism by which stormy seas would increase the price of fish.
(iii) What happened to the time trend when wave2 and wave3 were added to the regression? What must be going on?
(iv) Explain why all explanatory variables in the regression are safely assumed to be strictly exogenous.
(v) Test the errors for AR( 1) serial correlation.
(vi) Obtain the Newey-West standard errors using four lags. What happens to the t statistics on wave! and wave3! Did you expect a bigger or smaller change compared with the usual OLS t statistics?
(vii) Now, obtain the Prais-Winsten estimates for the model estimated in part (ii). Are wave 2 and wave 3 jointly statistically significant? |
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| m78519 | The file JTRAIN2.RAW contains data on a job training experiment for a group of men. Men could enter the program starting in January 1976 through about mid-1977. The program ended in December 1977. The idea is to test whether participation in the job training program had an effect on unemployment probabilities and earnings in 1978.
(i) The variable train is the job training indicator. How many men in the sample participated in the job training program? What was the highest number of months a man actually participated in the program?
(ii) Run a linear regression of train on several demographic and pretraining variables: unem74, unem75, age, educ, black, hisp, and married. Are these variables jointly significant at the 5% level?
(iii) Estimate a probit version of the linear model in part (ii). Compute the likelihood ratio test for joint significance of all variables. What do you conclude?
(iv) Based on your answers to parts (ii) and (iii), does it appear that participation in job training can be treated as exogenous for explaining 1978 unemployment status? Explain.
(v) Run a simple regression of unem78 on train and report the results in equation form. What is the estimated effect of participating in the job training program on the probability of being unemployed in 1978? Is it statistically significant?
(vi) Run a probit of unem78 on train. Does it make sense to compare the probit coefficient on train with the coefficient obtained from the linear model in part (v)?
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| m78520 | The file MATHPNL.RAW contains panel data on school districts in Michigan for the years 1992 through 1998. It is the district-level analogue of the school-level data used by Papke (2005). The response variable of interest in this question is math4, the percentage of fourth graders in a district receiving a passing score on a standardized math test. The key explanatory variable is rexpp, which is real expenditures per pupil in the district. The amounts are in 1997 dollars. The spending variable will appear in logarithmic form.
(i) Consider the static unobserved effects model
math4it = (1y93t + ... + (6y98t + (1 log (rexppit)
+ (2 log (enrollit) + (3 lunchit + ai + uit
Where enrolit is total district enrollment and lunchit is the percentage of students in the district eligible for the school lunch program. (So lunchit is a pretty good measure of the district-wide poverty rate.) Argue that (1, /10 is the percentage point change in math4it, when real per-student spending increases by roughly 10%.
(ii) Use first differencing to estimate the model in part (i). The simplest approach is to allow an intercept in the first-differenced equation and to include dummy variables for the years 1994 through 1998. Interpret the coefficient on the spending variable.
(iii) Now, add one lag of the spending variable to the model and reestimate using first differencing. You lose another year of data, so you are only using changes starting in 1994. Discuss the coefficients and significan |
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| m78521 | The file PENSION.RAW contains information on participant-directed pension plans for U.S. workers. Some of the observations are for couples within the same family, so this data set constitutes a small cluster sample (with cluster sizes of two).
(i) Ignoring the clustering by family, use OLS to estimate the model
where the variables are defined in the data set. The variable of most interest is choice, which is a dummy variable equal to one if the worker has a choice in how to allocate pension funds among different investments. What is the estimated effect of choice? Is it statistically significant?
(ii) Are the income, wealth, stock holding, and IRA holding control variables important? Explain.
(iii) Determine how many different families there are in the data set.
(iv) Now, obtain the standard errors for OLS that are robust to cluster correlation within a family. Do they differ much from the usual OLS standard errors? Are you surprised?
(v) Estimate the equation by differencing across only the spouses within a family. Why do the explanatory variables asked about in part (ii) drop out in the first-differenced estimation?
(vi) Are any of the remaining explanatory variables in part (v) significant? Are you surprised? |
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| m78522 | The file TRAFFIC2.RAW contains 108 monthly observations on automobile accidents, traffic laws, and some other variables for California from January 1981 through December 1989. Use this data set to answer the following questions.
(i) During what month and year did California s seat belt law take effect? When did the highway speed limit increase to 65 miles per hour?
(ii) Regress the variable log(totacc) on a linear time trend and 11 monthly dummy variables, using January as the base month. Interpret the coefficient estimate on the time trend. Would you say there is seasonality in total accidents?
(iii) Add to the regression from part (ii) the variables wkends, unem, spdlaw, and beltlaw. Discuss the coefficient on the unemployment variable. Does its sign and magnitude make sense to you?
(iv) In the regression from part (iii), interpret the coefficients on spdlaw and beltlaw. Are the estimated effects what you expected? Explain.
(v) The variable prcfat is the percentage of accidents resulting in at least one fatality. Note that this variable is a percentage, not a proportion. What is the average of prcfat over this period? Does the magnitude seem about right?
(vi) Run the regression in part (iii) but use prcfat as the dependent variable in place of log(totacc). Discuss the estimated effects and significance of the speed and seat belt law variables. |
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| m78574 | 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 interpretation of (1? Explain.
(ii) Why might nox [or more precisely, log (nox)] and rooms be negatively correlated?
If this is the case, does the simple regression of log (price) on log(nox) produce and upward or a downward biased estimator of (1?
(iii) Using the data in HPRICE2.RAW, the following equations were estimated:
Is the relationship between the simple and multiple regression estimates of the elasticity of price with respect to nox what you would have predicted, given your answer in part (ii)? Does this mean that - .718 is definitely closer to the true elasticity than - 1.043? |
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| m78575 | 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:
Tv hours* = (0 + (1 age + (2age2 + (3 motheduc + (4 fatheduc + (5 sibs + u.
We are worried that tv hours* is measured with error in our survey. Let tv hours denote the reported hours of television viewing per week.
(i) What do the classical errors-in-variables (CEV) assumptions require in this application?
(ii) Do you think the CEV assumptions are likely to hold? Explain. |
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