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free/or 0.5$ |
| m67735 | Continue with Question 6.6 but now consider the following model:
Yi = B0 + B1Xi + B2D2i + B3D3i + B4 (D2iXi) + B5 (D3iXi) + ui
a. What is the difference between this model and the one given in Question 6.6?
b. What is the interpretation of B4 and B5?
c. If B4 and B5 are individually statistically significant, would you choose this model over the previous one? If not, what kind of bias or error are you committing?
d. How would you test the hypothesis that B4 = B5 = 0? |
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| m67736 | Continue with Question C.2
Consider a random variable (r.v.) X ~ N (8, 16). State whether the following statements are true or false:
a. What is the probability distribution of the sample mean obtained from a random sample from this population?
b. Does your answer to (a) depend on the sample size? Why or why not?
c. Assuming a sample size of 25, what is the probability of obtaining an of 6? |
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| m67737 | Continue with the preceding problem but now assume that
Di = 2 for female
= 1 for male
With this dummy scheme re-estimate regression (6.1) using the data of Table 6-2 and compare your results. What general conclusions can you draw from the various dummy schemes? |
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| m67738 | Continue with the wage data given in Table 9-2 (found on the textbook s Web site) and now consider the following regressions:
wagei = A1 + A2 experiencei + ui
In wagei =B1 + B2 In experiencei + ui
a. Estimate both regressions.
b. Obtain the absolute and squared values of the residuals for each regression and plot them against the explanatory variable. Do you detect any evidence of heteroscedasticity?
c. Verify your qualitative conclusion in part (b) with the Glejser and Park tests.
d. If there is evidence of heteroscedasticity, how would you transform the data to reduce its severity? Show the necessary calculations. |
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| m67739 | Continuing with problem D.9, based on a random sample of 1000 members, suppose that you find the sample mean income, to be $900.
a. Given that µ = $1000, what is the probability of obtaining such a sample mean value?
b. Based on the sample mean, establish a 95% confidence interval for µ and find out if this confidence interval includes µ = $1000. If it does not, what conclusions would you draw?
c. Using the test of significance approach, decide whether you want to accept or reject the hypothesis that µ = $1000. Which test did you use and why? |
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| m67741 | Continuing with the preceding problem, if there is severe collinearity, which variable would you drop and why? If you drop one or more X variables, what type of error are you likely to commit? |
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| m67760 | Count R2. Since the conventional R2 value may not be appropriate for linear probability models, one suggested alternative is the count R2, which is defined as:
Since in LPM the dependent variable takes a value of 1 or 0, if the predicted probability is greater than 0.5, we classify that as 1, but if the predicted probability is less than 0.5, we classify that as 0. We then count the number of correct predictions and compute the count R2 from the formula given above.
Find the count R2 for the model (6.32). How does it compare with the conventional R2 given in that equation? |
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| m67855 | Describe the Breusch-Pagan (BP) test. Verify that, on the basis of this test, Eq. (9.33) shows no evidence of heteroscedasticity. |
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| m67997 | Do economic events affect presidential elections? To test this so-called political business cycle theory, Gary Smith20 obtained the following regression results based on the U.S. presidential elections for the four yearly periods from 1928 to 1980 (i.e., the data are for years 1928, 1932, etc.):
Ŷt = 53.10 - 1.70Xt
t = (34.10) (- 2.67) r2 = 0.37
where Y is the percentage of the vote received by the incumbent and X is the unemployment rate change-unemployment rate in an election year minus the unemployment rate in the preceding year.
a. A priori, what is the expected sign of X?
b. Do the results support the political business cycle theory? Support your contention with appropriate calculations.
c. Do the results of the 1984 and 1988 presidential elections support the preceding theory?
d. How would you compute the standard errors of b1 and b2? |
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| m68025 | Does more money help schools? To answer this question, Ruben Hernandez-Murillo and Deborah Roisman present the data given in Table 7-9 on the textbook s Web site.
These data relate to several input and outcome variables for school districts in the St. Louis area and are for the academic year 1999 to 2000.
a. Treating the Missouri Assessment Program (MAP) test score as the dependent variable, develop a suitable model to explain the behavior of MAP.
b. Which variable(s) is crucial in determining MAP-economic or social?
c. What is the rationale for the dummy variable?
d. Would it be prudent to conclude from your analysis that spending per pupil and or smaller student/teacher ratio are unimportant determinants of test scores? |
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| m68039 | Download the data set Benign, which is Table 12-11 on the textbook s Web site. The variable cancer is a dummy variable, where 1 = had breast cancer and 0 = did not have breast cancer.27 Using the variables age (age of subject), HIGH (highest grade completed in school), CHK (= 0 if the subject did not undergo regular medical checkups and = 1 if the subject did undergo regular checkups), AGPI (age at first pregnancy), miscarriages (number of miscarriages), and weight (weight of subject), perform a logistic regression to conclude if these variables are statistically useful for predicting whether a woman will contract breast cancer or not. |
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| m68054 | Durbin h statistic. In autoregressive models like Eq. (10.7):
Yt = B1 + B2Xt + B3Yt-1 + vt
the usual d statistic is not applicable to detect autocorrelation. For such models, Durbin has suggested replacing the d statistic by the h statistic defined as
where
n = the sample size
= the estimator of the autocorrelation coefficient ρ
var (b3) = the variance of the estimator of B3, the coefficient of lagged Y variable
Durbin has shown that for large samples, and given the null hypothesis that true ρ = 0, the h statistic is distributed as
h ~ N (0, 1)
It follows the standard normal distribution, that is, normal distribution with zero mean and unit variance. Therefore, we would reject the null hypothesis that ρ = 0 if the computed h statistic exceeds the critical h value. If, e.g., the level of significance is 5%, the critical // value is -1.96 or 1.96. Therefore, if a computed h exceeds |l.96|, we can reject the null hypothesis; if it does not ex-ceed this critical value, we do not reject the null hypothesis of no (first-order) autocorrelation. Incidentally, p entering the h formula can be obtained from any one of the methods discussed in the text.
Now consider the following demand for money function for India for the periods 1948 to 1949 and 1964 to 1965:
lnMt = 1.6027 - 0.1024 In Rt + 0.6869 In Yt + 0.5284 In Mt-1
se = (1.2404) (0.3678) (0.3427) (0.2007) R2 = 0.9227
d = 1.8624
where M = real cash balances
R = the long-term interest rate
Y = the agg |
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| m68055 | Durbin s two-step method of estimating ρ Write the generalized difference equation (10.14) in a slightly different but equivalent form as follows:
Yt = B1(l - ρ) + B2Xt - ρB2Xt-1 + ρYt-1 + vt
In step 1 Durbin suggests estimating this regression with Y as the dependent variable and Xt, Xt-1, and Yt-1 as explanatory variables. The coefficient of Yt-1 will provide an estimate of ρ. The ρ thus estimated is a consistent estimator; that is, in large samples it provides a good estimate of true ρ.
In step 2 use the p estimated from step 1 to transform the data to estimate the generalized difference equation (10.14).
Apply Durbin s two-step method to the U.S. import expenditure data discussed in Chapter 7 and compare your results with those shown for the original regression. |
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| m68110 | Establish Eq. (10.8). |
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| m68111 | Establish Eq. (B.15). |
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| m68112 | Establish Eq. (B.17). |
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| m68113 | Establish Eqs. (8.12) and (8.13). |
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| m68123 | Estimate the counterparts of Equations (9.10) to (9.12) using Exper and Wagef as the deflators. |
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| m68183 | Example 2.2 discusses Okun s law, as shown in Eq. (2.22). This equation can also be written as Xt = B1 + B2Yt, where X = percent growth in real output, as measured by GDP and Y = change in the unemployment rate, measured in percentage points. Using the data given in Table 2-13 on the textbook s Web site,
a. Estimate the preceding regression, obtaining the usual results as per Eq. (3.46).
b. Is the change in the unemployment rate a significant determinant of percent growth in real GDP? How do you know?
c. How would you interpret the intercept coefficient in this regression? Does it have any economic meaning? |
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| m68202 | Explain briefly the logic behind the following methods of detecting heteroscedasticity:
a. The graphical method
b. The Park test
c. The Glejser test |
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