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About 833 results. 1294 free access solutions
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| m79472 | Use the data in KIELMC.RAW for this exercise.
(i) The variable dist is the distance from each home to the incinerator site, in feet. Consider the model
log(price) = (0 + (0y81 + (1 log(dist) + (0y81 ( log(dist) + u.
If building the incinerator reduces the value of homes closer to the site, what is the sign of (1 > 0? What does it mean if (1 > 0?
(ii) Estimate the model from part (i) and report the results in the usual form. Interpret the coefficient on y81- log(dist). What do you conclude?
(iii) Add age, age2, rooms, baths, log(intst), log(land), and log(area) to the equation. Now, what do you conclude about the effect of the incinerator on housing values?
(iv) How come the coefficient on log (dist) is positive and statistically significant in part (ii) but not in part (iii)? What does this say about the controls used in part (iii)? |
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| m79473 | 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 price, consider the simple regression model
log(price) = (0 + (1 log(dist) + u,
where price is housing price in dollars and dist is distance from the house to the incinerator measured in feet. Interpreting this equation causally, what sign do you expect for (1 if the presence of the incinerator depresses housing prices? Estimate this equation and interpret the results.
(ii) To the simple regression model in part (i), add the variables log(intst), log(area), log(land), rooms, baths, and age, where intst is distance from the home to the interstate, area is square footage of the house, land is the lot size in square feet, rooms is total number of rooms, baths is number of bathrooms, and age is age of the house in years. Now, what do you conclude about the effects of the incinerator? Explain why (i) and (ii) give conflicting results.
(iii) Add [log(intst)]2 to the model from part (ii). Now what happens? What do you conclude about the importance of functional form?
(iv) Is the square of log(dist) significant when you add it to the model from part (iii)? |
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| m79474 | 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 jointly significant for explaining salary! (Be sure to account for missing data on LSAT and GPA.)
(iii) Test whether the size of the entering class (clsize) or the size of the faculty (faculty) needs to be added to this equation; carry out a single test. (Be careful to account for missing data on clsize and faculty.)
(iv) What factors might influence the rank of the law school that are not included in the salary regression? |
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| m79475 | Use the data in LOANAPP.RAW for this exercise.
(i) Estimate the equation in part (iii) of Computer Exercise C7.8, computing the heteroskedasticity-robust standard errors. Compare the 95% confidence interval on Bwhite, with the non-robust confidence interval.
(ii) Obtain the fitted values from the regression in part (i). Are any of them less than zero? Are any of them greater than one? What does this mean about applying weighted least squares? |
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| m79476 | 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, excluding observations with obrat > 40. What happens to the estimate and t statistic on white?
(iii) Does it appear that the estimate of (white is overly sensitive to the sample used? |
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| m79477 | Use the data in LOANAPP.RAW for this exercise; see also Computer Exercise C7.8.
(i) Estimate a probit model of approve on white. Find the estimated probability of loan approval for both whites and nonwhites. How do these compare with the linear probability estimates?
(ii) Now, add the variables hrat, obrat, loanprc, unem, male, married, dep, sch, cosign, chist, pubrec, mortlatl, mortlat2, and vr to the probit model. Is there statistically significant evidence of discrimination against nonwhites?
(iii) Estimate the model from part (ii) by logit. Compare the coefficient on white to the probit estimate.
(iv) Use equation (17.17) to estimate the sizes of the discrimination effects for probit and logit. |
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| m79478 | 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 data set are black and Hispanic.
To test for discrimination in the mortgage loan market, a linear probability model can be used:
approve = (0 + (1 white + other factors.
(i) If there is discrimination against minorities, and the appropriate factors have been controlled for, what is the sign of (1?
(ii) Regress approve on white and report the results in the usual form. Interpret the coefficient on white. Is it statistically significant? Is it practically large?
(iii) As controls, add the variables hrat, obrat, loanprc, unem, male, married, dep, sen, cosign, chist, pubrec, mortlatl, mortlat2, and vr. What happens to the coefficient on white? Is there still evidence of discrimination against nonwhites?
(iv) Now, allow the effect of race to interact with the variable measuring other obligations as a percentage of income (obrat). Is the interaction term significant?
(v) Using the model from part (iv), what is the effect of being white on the probability of approval when obrat = 32, which is roughly the mean value in the sample? Obtain a 95% confidence interval for this effect. |
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| m79479 | Use the data in MATHPNL.RAW for this exercise. You will do a fixed effects version of the first differencing done in Computer Exercise C13.11. The model of interest is
where the first available year (the base year) is 1993 because of the lagged spending variable.
(i) Estimate the model by pooled OLS and report the usual standard errors. You should include an intercept along with the year dummies to allow a. to have a nonzero expected value. What are the estimated effects of the spending variables? Obtain the OLS residuals, it.
(ii) Is the sign of the lunchit, coefficient what you expected? Interpret the magnitude of the coefficient. Would you say that the district poverty rate has a big effect on test pass rates?
(iii) Compute a test for AR(1) serial correlation using the regression it on i.t-1. You should use the years 1994 through 1998 in the regression. Verify that there is strong positive serial correlation and discuss why.
(iv) Now, estimate the equation by fixed effects. Is the lagged spending variable still significant?
(v) Why do you think, in the fixed effects estimation, the enrollment and lunch program variables are jointly insignificant?
(vi) Define the total, or long-run, effect of spending as θ1 = y1 + y2. Use the substitution y1 = θ1 - y2 to obtain a standard error for θ1. |
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| m79480 | Use the data in MEAP00_01 to answer this question.
(i) Estimate the model
mathA = (0 + (2 lexppp + (2 lenroIl + (3 lunch + u
by 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 part (i). What is the range of fitted values? How does it compare with the range of the actual data on mathA?
(iii) Obtain the residuals from the regression in part (i). What is the building code of the school that has the largest (positive) residual? Provide an interpretation of this residual.
(iv) Add quadratics of all explanatory variables to the equation, and test them for joint significance. Would you leave them in the model?
(v) Returning to the model in part (i), divide the dependent variable and each explanatory variable by its sample standard deviation, and rerun the regression. (Include an intercept unless you also first subtract the mean from each variable.) In terms of standard deviation units, which explanatory variable has the largest effect on the math pass rate? |
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| m79481 | Use the data in MEAP00_01.RAW to answer this question.
(i) Estimate the model
mathA = (0 + (1 lunch + (2 log(enroll) + (3log(exppp) + u
by OLS and obtain the usual standard errors and the fully robust standard errors. How do they generally compare?
(ii) Apply the special case of the White test for heteroskedasticity. What is the value of the F test? What do you conclude?
(iv) Obtain the standard errors for WLS that allow misspecification of the variance function. Do these differ much from the usual WLS standard errors?
(v) For estimating the effect of spending on math4, does OLS or WLS appear to be more precise? |
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| m79482 | Use the data in MEAP93.RAW to answer this question.
(i) Estimate the model
math10 = (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 intercept you estimated in part (i)? In particular, does it make sense to set the two explanatory variables to zero? [Recall that log(l) = 0.]
(iii) Now run the simple regression of mathl0 on log(expend), and compare the slope coefficient with the estimate obtained in part (i). Is the estimated spending effect now larger or smaller than in part (i)?
(iv) Find the correlation between lexpend = log(expend) and Inchprg. Does its sign make sense to you?
(v) Use part (iv) to explain your findings in part (iii). |
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| m79483 | Use the data in MINWAGE.DTA for sector 232 to answer the following questions.
(i) Confirm that lwage232t and lemp232t are best characterized as 1(1) processes. Use the augmented DF test with one lag of gwage232 and gemp232, respectively, and a linear time trend. Is there any doubt that these series should be assumed to have unit roots?
(ii) Regress lemp232t on lwage232t and test for co integration, both with and without a time trend, allowing for two lags in the augmented Engle-Granger test. What do you conclude?
(iii) Now regress lemp232t on log of the real wage rate, lrwage232t = lwage232t -lepit, and a time trend. Do you find co integration? Are they "closer" to being co integrated when you use real wages than nominal wages?
(iv) What are some factors that might be missing from the co integrating regression in part (iii)? |
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| m79484 | Use the data in MINWAGE.RAW for this exercise, focusing on the wage and employment series for sector 232 (Men s and Boys Furnishings). The variable gwagelil is the monthly growth (change in logs) in the average wage in sector 232; gempTil is the growth in employment in sector 232; gmwage is the growth in the federal minimum wage; and gcpi is the growth in the (urban) Consumer Price Index,
(i) Find the first order autocorrelation in gwage232. Does this series appear to be weakly dependent?
(ii) Estimate the dynamic model
gwage232, = (0 + (1 gwage232t-1 + (2 gmwage, + (3 gcpi, + u,
by OLS. Holding fixed last month s growth in wage and the growth in the CPI, does an increase in the federal minimum result in a contemporaneous increase in gwage232t? Explain.
(iii) Now add the lagged growth in employment, gemp232t-1 to the equation in part (ii). Is it statistically significant?
(iv) Compared with the model without gwage232t-1 and gemp232t-1, does adding the two lagged variables have much of an effect on the gmwage coefficient?
(v) Run the regression of gmwaget, on gwage232t-1 and gemp232t-l, and report the R-squared. Comment on how the value of R-squared helps explain your answer to part (iv). |
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| m79485 | Use the data in MINWAGE.RAW for this exercise, focusing on sector 232.
(i) Estimate the equation
gwage232t = (0 + (1 ygmwaget + (2 gcpi i+ ut,
and test the errors for AR( 1) serial correlation. Does it matter whether you assume gmwage and gcpi are strictly exogenous? What do you conclude overall?
(ii) Obtain the Newey-West standard error for the OLS estimates in part (i), using a lag of 12. How do the Newey-West standard errors compare to the usual OLS standard errors?
(iii) Now obtain the heteroskedasticity-robust standard errors for OLS, and compare them with the usual standard errors and the Newey-West standard errors. Does it appear that serial correlation or heteroskedasticity is more of a problem in this application?
(iv) Use the Breusch-Pagan test in the original equation to verify that the errors exhibit strong heteroskedasticity.
(v) Add lags 1 through 12 of gmwage to the equation in part (i). Obtain the p-value for the joint F test for lags 1 through 12, and compare it with the p-value for the heteroskedasticity-robust test. How does adjusting for heteroskedasticity affect the significance of the lags?
(vi) Obtain the p-value for the joint significance test in part (v) using the Newey-West approach. What do you conclude now?
(vii) If you leave out the lags of gmwage, is the estimate of the long-run propsensity much different? |
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| m79486 | Use the data in MINWAGE.RAW for this exercise. In particular, use the employment and wage series for sector 232 (Men s and Boy s Furnishings). The variable gwage232 is the monthly growth (change in logs) in the average wage in sector 232, gemp232 is the growth in employment in sector 232, gmwage is the growth in the federal minimum wage, and gcpi is the growth in the (urban) Consumer Price Index.
(ii) Add lags 1 through 12 of gmwage to the equation in part (i). Do you think it is necessary to include these lags to estimate the long-run effect of minimum wage growth on wage growth in sector 232? Explain.
(iii) Run the regression gemp232 on gmwage,gcpi. Does minimum wage growth appear to have a contemporaneous effect on gemp232?
(iv) Add lags 1 through 12 to the employment growth equation. Does growth in the minimum wage have a statistically significant effect on employment growth, either in the short run or long run? Explain. |
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| m79487 | 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 percentage), and sbasesyr (stolen bases per year) to the model from part (i). Which of these factors are individually significant?
(iii) In the model from part (ii), test the joint significance of bavg, fldperc, and sbasesyr? |
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| m79488 | Use the data in MURDER.RAW for this exercise.
(i) Using the years 1990 and 1993, estimate the equation
mrdrteit = (0 + (1d93t + (1execit + (2unemit + ai + uit,t = 1, 2
By pooled OLS and report the results in the usual form. Do not worry that the usual OLS standard errors are inappropriate because of the presence of ai. Do you estimate a deterrent effect of capital punishment?
(ii) Compute the FD estimates (use only the differences from 1990 to 1993; you should have 51 observations in the FD regression). Now what do you conclude about a deterrent effect?
(iii) In the FD regression from part (ii), obtain the residuals, say, i. Run the Breusch-Pagan regression 2i on (execi, (unemi and compute the F test for heteroskedasticity. Do the same for the special case of the White test [that is, regress 2i on i, 2i, where the fitted values are from part (ii)]. What do you conclude about heteroskedasticity in the FD equation?
(iv) Run the same regression from part (ii), but obtain the heteroskedasticity-robust t statistics. What happens?
(v) Which t statistic on (exec. do you feel more comfortable relying on, the usual one or the heteroskedasticity-robust one? Why? |
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| m79489 | Use the data in MURDER.RAW for this exercise. The variable mrdrte is the murder rate, that is, the number of murders per 100,000 people. The variable exec is the total number of prisoners executed for the current and prior two years; unem is the state unemployment rate.
(i) How many states executed at least one prisoner in 1991, 1992, or 1993? Which state had the most executions?
(ii) Using the two years 1990 and 1993, do a pooled regression of mrdrte on d93, exec, and unem. What do you make of the coefficient on exec?
(iii) Using the changes from 1990 to 1993 only (for a total of 51 observations), estimate the equation
Δmrdrte = δ0 + β1 Δexec + β2 Δunem + Au
by OLS and report the results in the usual form. Now, does capital punishment appear to have a deterrent effect?
(iv) The change in executions may be at least partly related to changes in the expected murder rate, so that Δexec is correlated with Au in part (iii). It might be reasonable to assume that Aexec-1. is uncorrelated with Au. (After all, Δexec-1 depends on executions that occurred three or more years ago.) Regress Δexec on Δexec-1 to see if they are sufficiently correlated; interpret the coefficient on Δexec-1,
(v) Reestimate the equation from part (iii), using Δexec-1, as an IV for Δexec. Assume that Δunem is exogenous. How do your conclusions change from part (iii)? |
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| m79490 | Use the data in MURDER.RAW for this exercise. The variable mrdrte is the murder rate, that is, the number of murders per 100,000 people. The variable exec is the total number of prisoners executed for the current and prior two years; unem is the state unemployment rate.
(i) How many states executed at least one prisoner in 1991, 1992, or 1993? Which state had the most executions?
(ii) Using the two years 1990 and 1993, do a pooled regression of mrdrte on d93, exec, and unem. What do you make of the coefficient on exec?
(iii) Using the changes from 1990 to 1993 only (for a total of 51 observations), estimate the equation
Δmrdrte = δ0 + β1 Δexec + β2 Δunem + Au
by OLS and report the results in the usual form. Now, does capital punishment appear to have a deterrent effect?
(iv) The change in executions may be at least partly related to changes in the expected murder rate, so that Δexec is correlated with Au in part (iii). It might be reasonable to assume that Aexec-1. is uncorrelated with Au. (After all, Δexec-1 depends on executions that occurred three or more years ago.) Regress Δexec on Δexec-1 to see if they are sufficiently correlated; interpret the coefficient on Δexec-1,
(v) Reestimate the equation from part (iii), using Δexec-1, as an IV for Δexec. Assume that Δunem is exogenous. How do your conclusions change from part (iii)? |
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| m79491 | Use the data in NBASAL.RAW for this exercise.
(i) Estimate a linear regression model relating points per game to experience 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.
(ii) Why do you not include all three position dummy variables in part (i)?
(iii) Holding experience fixed, does a guard score more than a center? How much more? Is the difference statistically significant?
(iv) Now, add marital status to the equation. Holding position and experience fixed, are married players more productive (based on points per game)?
(v) Add interactions of marital status with both experience variables. In this expanded model, is there strong evidence that marital status affects points per game?
(vi) Estimate the model from part (iv) but use assists per game as the dependent variable. Are there any notable differences from part (iv)? Discuss. |
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