|
About 833 results. 1294 free access solutions
| № |
Condition |
free/or 0.5$ |
| m75964 | (i) For a binary response y, let y be the proportion of ones in the sample (which is equal to the sample average of the y.). Let 0 be the percent correctly predicted for the outcome y = 0 and let 1 be the percent correctly predicted for the outcome y = 1. If p is the overall percent correctly predicted, show that p is a weighted average of 0 and 1:
(ii) In a sample of 300, suppose that = .70, so that there are 210 outcomes with yt = 1 and 90 with yt = 0. Suppose that the percent correctly predicted when yt = 0 is 80, and the percent correctly predicted when yt = 1 is 40. Find the overall percent correctly predicted. |
doc |
| m75965 | (i) For Example 12.4, using the data in BARIUM.RAW, obtain the iterative Cochrane-Orcutt estimates,
(ii) Are the Prais-Winsten and Cochrane-Orcutt estimates similar? Did you expect them to be? |
doc |
| m75966 | (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 satisfied in the CEO salary example. |
doc |
| m75967 | (i) In Example 11.4, it may be that the expected value of the return at time t, given past returns, is a quadratic function of returnt-1. To check this possibility, use the data in NYSE.RAW to estimate
return, = (0 + (1 returnt-1 + (2 return2t-1 + u,;
report the results in standard form.
(ii) State and test the null hypothesis that E(returnt|returnt-1) does not depend on return, v (There are two restrictions to test here.) What do you conclude?
(iii) Drop return2t-1 from the model, but add the interaction term returnt-1 ( returnt-2. Now test the efficient markets hypothesis.
(iv) What do you conclude about predicting weekly stock returns based on past stock returns? |
doc |
| m75968 | (i) In part (i) of Computer Exercise CI 1.6, you were asked to estimate the accelerator model for inventory investment. Test this equation for AR(1) serial correlation.
(ii) If you find evidence of serial correlation, reestimate the equation by Cochrane-Orcutt and compare the results. |
doc |
| m75969 | (i) In the enterprise zone event study in Computer Exercise CI0.5, a regression of the OLS residuals on the lagged residuals produces-= .841 and se() = .053. What implications does this have for OLS?
(ii) If you want to use OLS but also want to obtain a valid standard error for the EZ coefficient, what would you do? |
doc |
| m75970 | (i) In the model with one endogenous explanatory variable, one exogenous explanatory variable, and one extra exogenous variable, take the reduced form for y2, (15.26), and plug it into the structural equation (15.22). This gives the reduced form for y1:
y1 = α0 + α1z1 + α2z2 + v1,
Find the α in terms of the B and the TT..
(ii) Find the reduced form error, v1, in terms of u1, v2, and the parameters.
(iii) How would you consistently estimate the aj? |
doc |
| m75971 | (i) In the wage equation in Example 14.4, explain why dummy variables for occupation might be important omitted variables for estimating the union wage premium.
(ii) If every man in the sample stayed in the same occupation from 1981 through 1987, would you need to include the occupation dummies in a fixed effects estimation? Explain.
(iii) Using the data in WAGEPAN.RAW, include eight of the occupation dummy variables in the equation and estimate the equation using fixed effects. Does the coefficient on union change by much? What about its statistical significance? |
doc |
| m75972 | (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 c1.yi on c2.xi. Show that = (c1/c2) and = c1, thereby verifying the claims on units of measurement is Section 2.4. [To obtain , plug the scaled versions of x and y into (2.19). Then, use (2.17) for being sure to plug in the scaled x and y and the correct slope].
(ii) Now, let and be from the regression of (c1 + yi) on (c2 + xi) (with no restriction on c1 or c2). Show that / = and = / + c1 - c2.
(iii) Now, let / and / be the OLS estimates from the regression log (yi) on xi, where we must assume yi > 0 for all i. For c1 > 0, let and / be the intercept and slope from the regression of log (c1,yi) on xi. Show that and / be the intercept and slope from the regression of yi on log(c2xi). How do and / compare with the intercept and slope from the regression of yi on log (xi)? |
doc |
| m75973 | (i) Use NYSE.RAW to estimate equation (12.48). Let t be the fitted values from this equation (the estimates of the conditional variance). How many t are negative?
(ii) Add return2t-1 to (12.48) and again compute the fitted values, t. Are any t negative?
(iii) Use the t from part (ii) to estimate (12.47) by weighted least squares (as in Section 8.4). Compare your estimate of (1 with that in equation (11.16). Test H0: (1 = 0 and compare the outcome when OLS is used.
(iv) Now, estimate (12.47) by WLS, using the estimated ARCH model in (12.51) to obtain the t. Does this change your findings from part (iii)? |
buy |
| m75974 | (i) Use the data in HPRICE1.RAW to obtain the heteroskedasticity-robust standard errors for equation (8.17). Discuss any important differences with the usual standard errors.
(ii) Repeat part (i) for equation (8.18).
(iii) What does this example suggest about heteroskedasticity and the transformation used for the dependent variable? |
buy |
| m75975 | (i) Using the data in INJURY.RAW for Kentucky, the estimated equation when afchnge is dropped from (13.12) is
Is it surprising that the estimate on the interaction is fairly close to that in (13.12)? Explain.
(ii) When afchnge is included but highearn is dropped, the result is
Why is the coefficient on the interaction term now so much larger than in (13.12)? [In equation (13.10), what is the assumption being made about the treatment and control groups if (1 = 0?] |
buy |
| m75976 | (i) Using the data in WAGEPRC.RAW, estimate the distributed lag model from Problem 11.5. Use regression (12.14) to test for AR(1) serial correlation.
(ii) Reestimate the model using iterated Cochrane-Orcutt estimation. What is your new estimate of the long-run propensity?
(iii) Using iterated CO, find the standard error for the LRP. (This requires you to estimate a modified equation.) Determine whether the estimated LRP is statistically different from one at the 5% level. |
buy |
| m76082 | If we think that (1 is positive in (13.14) and that (ui. and (unemi are negatively correlated, what is the bias in the OLS estimator of (1, in the first-differenced equation? [Review equation (5.4).] |
buy |
| m76101 | In 1985, neither Florida nor Georgia had laws banning open alcohol containers in vehicle passenger compartments. By 1990, Florida had passed such a law, but Georgia had not.
(i) Suppose you can collect random samples of the driving-age population in both states, for 1985 and 1990. Let arrest be a binary variable equal to unity if a person was arrested for drunk driving during the year. Without controlling for any other factors, write down a linear probability model that allows you to test whether the open container law reduced the probability of being arrested for drunk driving. Which coefficient in your model measures the effect of the law?
(ii) Why might you want to control for other factors in the model? What might some of these factors be?
(iii) Now, suppose that you can only collect data for 1985 and 1990 at the county level for the two states. The dependent variable would be the fraction of licensed drivers arrested for drunk driving during the year. How does this data structure differ from the individual-level data described in part (i)? What econometric method would you use? |
buy |
| m76154 | In a random effects model, define the composite error vit = ai + uit, where ai is uncorrelated with uit and the uit have constant variance σ2it and are serially uncorrelated. Define eit = vit (λi, where λ is given in (14.10).
(i) Show that E(eit) = 0.
(ii) Show that Var(eit) = σ2it, t = 1,...., T.
(iii) Show that for t ≠ s, Cov(eit, eit) = 0. |
buy |
| m76157 | In a recent article, Evans and Schwab (1995) studied the effects of attending a Catholic high school on the probability of attending college. For concreteness, let college be a binary variable equal to unity if a student attends college, and zero otherwise. Let CathHS be a binary variable equal to one if the student attends a Catholic high school. A linear probability model is
college = β0 + B1 CathHS + other factors + u,
where the other factors include gender, race, family income, and parental education.
(i) Why might CathHS be correlated with M?
(ii) Evans and Schwab have data on a standardized test score taken when each student was a sophomore. What can be done with this variable to improve the ceteris paribus estimate of attending a Catholic high school?
(iii) Let CathRel be a binary variable equal to one if the student is Catholic. Discuss the two requirements needed for this to be a valid IV for CathHS in the preceding equation. Which of these can be tested?
(iv) Not surprisingly, being Catholic has a significant effect on attending a Catholic high school. Do you think CathRel is a convincing instrument for CathHS? |
buy |
| m76222 | 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 activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four actives must be 168.
(i) In the model
GPA = (0 + (1 study + (2 sleep + (3 work + (4 leisure + u,
Does it make sense to hold sleep, work, and leisure fixed, while changing study?
(ii) Explain why this model violates Assumption MLR.3.
(iii) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3? |
buy |
| m76269 | In Computer Exercise C10.7, you estimated a simple relationship between consumption growth and growth in disposable income. Test the equation for AR( 1) serial correlation (using CONSUMP.RAW).
(ii) In Computer Exercise CI 1.7, you tested the permanent income hypothesis by regressing the growth in consumption on one lag. After running this regression, test for heteroskedasticity by regressing the squared residuals on gct-1, and gc2t-r What do you conclude? |
buy |
| m76282 | 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 restricted model is estimated using only those observations for which all variables in the unrestricted model are available (see Example 4.9). |
buy |
|