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About 833 results. 1294 free access solutions
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| m79512 | Use the data in TWOYEAR.RAW for this exercise.
(i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and standard deviation of stotal.
(ii) Run simple regressions of jc and univ on stotal. Are both college education variables statistically related to stotal? Explain.
(iii) Add stotal to equation (4.17) and test the hypothesis that the returns to two- and four-year colleges are the same against the alternative that the return to four-year colleges is greater. How do your findings compare with those from Section 4.4?
(iv) Add stotal2 to the equation estimated in part (iii). Does a quadratic in the test score variable seem necessary?
(v) Add the interaction terms stotal-jc and stotal-univ to the equation from part (iii). Are these terms jointly significant?
(vi) What would be your final model that controls for ability through the use of stotal? Justify your answer. |
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| m79513 | Use the data in VOLAT.RAW for this exercise.
(i) Confirm that Isp500 = log(sp500) and lip = log(ip) appear to contain unit roots. Use Dickey-Fuller tests with four lagged changes and do the tests with and without a linear time trend.
(ii) Run a simple regression of lsp500 on lip. Comment on the sizes of the I statistic and R-squared.
(iii) Use the residuals from part (ii) to test whether Isp500 and lip are co integrated. Use the standard Dickey-Fuller test and the ADF test with two lags. What do you conclude?
(iv) Add a linear time trend to the regression from part (ii) and now test for co integration using the same tests from part (iii).
(v) Does it appear that stock prices and real economic activity have a long-run equilibrium relationship? |
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| m79514 | Use the data in VOLAT.RAW for this exercise.
(i) Estimate an AR(3) model for pcip. Now, add a fourth lag and verify that it is very insignificant.
(ii) To the AR(3) model from part (i), add three lags of pcsp to test whether pcsp Granger causes pcip. Carefully, state your conclusion.
(iii) To the model in part (ii), add three lags of the change in i3, the three-month T-bill rate. Does pcsp Granger cause pcip conditional on past Δi3? |
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| m79515 | Use the data in VOLAT.RAW for this exercise. The variable rsp500 is the monthly return on the Standard & Poor s 500 stock market index, at an annual rate. (This includes price changes as well as dividends.) The variable i3 is the return on
rsp500t = (0 + (1 pcipt + (2i3t + u,
(i) What signs do you think (1, and (2 should have?
(ii) Estimate the previous equation by OLS, reporting the results in standard form. Interpret the signs and magnitudes of the coefficients.
(iii) Which of the variables is statistically significant?
(iv) Does your finding from part (iii) imply that the return on the S&P 500 is predictable? Explain. |
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| m79516 | 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 expendA on voteA? Is the expected sign for (4 obvious?
(ii) Estimate the equation in part (i) and report the results in the usual form. Is the interaction term statistically significant?
(iii) Find the average of expendA in the sample. Fix expendA at 300 (for $300,000). What is the estimated effect of another $100,000 spent by Candidate B on voteA? Is this a large effect?
(iv) Now fix expendB at 100. What is the estimated effect of hexpendA = 100 on voteA? Does this make sense?
(v) Now, estimate a model that replaces the interaction with shareA, Candidate A s percentage share of total campaign expenditures. Does it make sense to hold both expendA and expendB fixed, while changing shareA?
(vi) (Requires calculus) In the model from part (v), find the partial effect of expendB on voteA, holding prtystrA and expendA fixed. Evaluate this at expendA - 300 and expendB = 0 and comment on the results. |
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| m79517 | Use the data in WAGE 1 .RAW for this exercise,
(i) Use OLS to estimate the equation
log(wage) = (0 + (1 educ + (2 exper + (3 exper2 + u
and report the results using the usual format.
(ii) is exper2 statistically significant at the 1% level?
(iii) Using the approximation
Find the approximation return to the fifth year of experience. What is the approximate return to the twentieth year of experience?
(iv) At what value of exper does additional experience actually lower predicated log(wage)? How many people have more experience in this sample? |
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| m79518 | 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 of the President (2004 or later), obtain and report the Consumer Price Index (CPI) for the years 1976 and 2003.
(iv) Use the CPI values from part (iii) to find the average hourly wage in 2003 dollars. Now does the average hourly wage seem reasonable?
(v) How many women are in the sample? How many men? |
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| m79519 | Use the data in WAGE 1 .RAW for this exercise.
(i) Estimate the equation
wage = (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 the level-level model or the log-level model? |
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| m79520 | Use the data in WAGE 1 .RAW for this exercise.
(i) Use equation (7.18) to estimate the gender differential when educ = 12.5. Compare this with the estimated differential when educ = 0.
(ii) Run the regression used to obtain (7.18), but with female ( (educ - 12.5) replacing female-educ. How do you interpret the coefficient on female now?
(iii) Is the coefficient on female in part (ii) statistically significant? Compare this with (7.18) and comment. |
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| m79521 | Use the data in WAGE2.RAW for this exercise.
(i) Consider the standard wage equation
log(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) Test the null hypothesis in part (i) against a two-sided alternative, at the 5% significance level, by constructing a 95% confidence interval. What do you conclude? |
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| m79522 | Use the data in WAGE2.RAW for this exercise.
(i) Estimate the model
and report the results in the usual form. Holding other factors fixed, what is the approximate difference in monthly salary between blacks and non blacks? Is this difference statistically significant?
(ii) Add the variables exper2 and tenure2 to the equation and show that they are jointly insignificant at even the 20% level.
(iii) Extend the original model to allow the return to education to depend on race and test whether the return to education does depend on race.
(iv) Again, start with the original model, but now allow wages to differ across four groups of people: married and black, married and nonblack, single and black, and single and nonblack. What is the estimated wage differential between married blacks and married nonblacks? |
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| m79523 | Use the data in WAGE2.RAW for this exercise.
(i) In Example 15.2, using sibs as an instrument for educ, the IV estimate of the return to education is . 122. To convince yourself that using sibs as an IV for educ is not the same as just plugging sibs in for educ and running an OLS regression, run the regression of og(wage) on sibs and explain your findings.
(ii) The variable brthord is birth order (brthord is one for a first-born child, two for a second-born child, and so on). Explain why educ and brthord might be negatively correlated. Regress educ on brthord to determine whether there is a statistically significant negative correlation.
(iii) Use brthord as an IV for educ in equation (15.1). Report and interpret the results.
(iv) Now, suppose that we include number of siblings as an explanatory variable in the wage equation; this controls for family background, to some extent:
Log(wage) = β0 + β1 educ + β2sibs + u.
Suppose that we want to use brthord as an IV for educ, assuming that sibs is exogenous. The reduced form for educ is
educ = π0 + π1 sibs + π2 brthord + v.
State and test the identification assumption.
(v) Estimate the equation from part (iv) using brthord as an IV for educ (and sibs as its own IV). Comment on the standard errors for educ and sibs, |
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| m79524 | 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 standard deviation equal to 15.)
(ii) Estimate a simple regression model where a one point increase in IQ changes wage by a constant dollar amount. Use this model to find the predicated increase in wage for an increase in IQ of 15 points. Does IQ explain most of the variation in wage?
(iii) Now, estimate a model where each one point increase in IQ has the same percent age effect on wage. If IQ increases by 15 points, what is the approximate percent age increase in predicted wage? |
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| m79525 | Use the data in WAGEPAN.RAW for this exercise.
(i) Consider the unobserved effects model
Iwage it = (0 + (1d81t+ ... + (7d87t + (1educi
+ (1d81t, educi + ... + (7dx87t educi + (2 unionit + ai + uit,
Where ai is allowed to be correlated with educi and unionit, Which parameters can you estimate using first differencing?
(ii) Estimate the equation from part (i) by FD, and test the null hypothesis that the return to education has not changed over time.
(iii) Test the hypothesis from part (ii) using a fully robust test, that is, one that allows arbitrary heteroskedasticity and serial correlation in the FD errors, (uit. Does your conclusion change?
(iv) Now allow the union differential to change over time (along with education) and estimate the equation by FD. What is the estimated union differential in 1980? What about 1987? Is the difference statistically significant?
(v) Test the null hypothesis that the union differential has not changed over time, and discuss your results in light of your answer to part (iv)? |
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| m79526 | Use the data in WAGEPRC.RAW for this exercise. Problem 11.5 gave estimates of a finite distributed lag model of gprice on gwage, where 12 lags of gwage are used.
(i) Estimate a simple geometric DL model of gprice on gwage. In particular, estimate equation (18.11) by OLS. What are the estimated impact propensity and LRP? Sketch the estimated lag distribution.
(ii) Compare the estimated IP and LRP to those obtained in Problem 11.5. How do the estimated lag distributions compare?
(iii) Now, estimate the rational distributed lag model from (18.16). Sketch the lag distribution and compare the estimated IP and LRP to those obtained in part (ii). |
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| m79527 | Use the data set 401KSUBS.RAW for this exercise.
(i) Using OLS, estimate a linear probability model for e401k, using as explanatory variables inc, inc2, age, age2, and male. Obtain both the usual OLS standard errors and the heteroskedasticity-robust versions. Are there any important differences?
p(x), where p(x) = (0 + (1x1 + ... + (kxk.}
(iii) For the model estimated from part (i), obtain the White test and see if the coefficient estimates roughly correspond to the theoretical values described in part (ii).
(iv) After verifying that the fitted values from part (i) are all between zero and one, obtain the weighted least squares estimates of the linear probability model. Do they differ in important ways from the OLS estimates? |
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| m79528 | Use the data set CONSUMP.RAW for this exercise.
(i) Estimate a simple regression model relating the growth in real per capita consumption (of nondurables and services) to the growth in real per capita disposable income. Use the change in the logarithms in both cases. Report the results in the usual form. Interpret the equation and discuss statistical significance.
(ii) Add a lag of the growth in real per capita disposable income to the equation from part (i). What do you conclude about adjustment lags in consumption growth?
(iii) Add the real interest rate to the equation in part (i). Does it affect consumption growth? |
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| m79529 | Use the data set GPA 1.RAW for this exercise.
(i) Use OLS to estimate a model relating colGPA to hsGPA, ACT, skipped, and PC. Obtain the OLS residuals.
(ii) Compute the special case of the White test for heteroskedasticity. In the regression of
obtain the fitted values, say i.
(iii) Verify that the fitted values from part (ii) are all strictly positive. Then, obtain the weighted least squares estimates using weights l/i. Compare the weighted least squares estimates for the effect of skipping lectures and the effect of PC ownership with the corresponding OLS estimates. What about their statistical significance?
(iv) In the WLS estimation from part (iii), obtain heteroskedasticity-robust standard errors. In other words, allow for the fact that the variance function estimated in part (ii) might be misspecified. Do the standard errors change much from part (iii)? |
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| m79530 | Use the data set in BEAUTY.RAW, which contains a subset of the variables (but more usable observations than in the regressions) reported by Hamermesh and Biddle (1994).
(i) Find the separate fractions of men and women that are classified as having above average looks. Are more people rated as having above average or below average looks?
(ii) Test the null hypothesis that the population fractions of above-average-looking women and men are the same. Report the one-sided p-value that the fraction is higher for women. (Hint: Estimating a simple linear probability model is easiest.)
(iii) Now estimate the model
log(wage) = (0 + (1 belavg + (2 abvavg + u
separately for men and women, and report the results in the usual form. In both cases, interpret the coefficient on belavg. Explain in words what the hypothesis H0:(1, = 0 against H1: (1 < 0 means, and find the p-values for men and women.
(iv) Is there convincing evidence that women with above average looks earn more than women with average looks? Explain.
(v) For both men and women, add the explanatory variables educ, exper, exper2, union, goodhlth, black, married, south, bigcity, smllcity, and service. Do the effects of the "looks" variables change in important ways? |
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| m79531 | Use the data set in FISH.RAW, which comes from Graddy (1995), to do this exercise. The data set is also used in Computer Exercise C12.9. Now, we will use it to estimate a demand function for fish.
(i) Assume that the demand equation can be written, in equilibrium for each time period, as
log(totqtyt) = α1log(avgprct) + β10 + β11mont + β12tuest + β13wedt + β14thurst + ut1,
so that demand is allowed to differ across days of the week. Treating the price variable as endogenous, what additional information do we need to consistently estimate the demand-equation parameters?
(ii) The variables wave2t and wave3t are measures of ocean wave heights over the past several days. What two assumptions do we need to make in order to use wavet and wave3t as IVs for log{avgprct) in estimating the demand equation?
(iii) Regress log(avgprct) on the day-of-the-week dummies and the two wave measures. Are wave2t and wave3t jointly significant? What is the p-value of the test?
(iv) Now, estimate the demand equation by 2SLS. What is the 95% confidence interval for the price elasticity of demand? Is the estimated elasticity reasonable?
(v) Obtain the 2SLS residuals, t1. Add a single lag, t-1,1, in estimating the demand equation by 2SLS. Remember, use t-1,1, as its own instrument. Is there evidence of AR( 1) serial correlation in the demand equation errors?
(vi) Given that the supply equation evidently depends on the wave variables, what two assumptions would we need to make in order |
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