厦门大学《计量经济学基础》
课程试卷
经济学院财政系
2012级本科——期末考试
主考教师：王艺明
B卷
1. The following equation was estimated using the data in CEOSAL1.RAW:
log(salary)?4.322?0.276log(sales)?0.0215roe?0.00008roe2
(0.324) (0.033) (0.0129) (0.00026) n=209, R2=0.282
This equation allows roe to have a diminishing effect on log(salary). Is this generality necessary? Explain why or why not.
2. Using the data in GPA2.RAW, the following equation was estimated:
sat?1,028.10?19.30hsize?2.19hsize2?45.09female?169.81black?62.31female*black
sa?t _1(6.29) _1(3.83)hsize _(0.53)hsiz5(4.29)fe e(12.71)bla c(18.15)femal n=4,137, R2=0.0858.
The variable sat is the combined SAT score, hsize is size of the student’s high school graduating class, in hundreds, female is a gender dummy variable, and black is a race dummy variable equal to one for blacks, and zero otherwise.
(i) Is there strong evidence that hsize2 should be included in the model? From this equation, what is the optimal high school size?
(ii) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? How statistically significant is this estimated difference?
(iii) What is the estimated difference in SAT score between nonblack males and black males? Test the null hypothesis that there is no difference between their scores, against the alternative that there is a difference.
(iv) What is the estimated difference in SAT score between black females and nonblack females? What would you need to do to test whether the difference is statistically significant?
3. An equation explaining chief executive officer salary is
log?salary? =4.59+0.257log?sales??0.11roe?0.158finance?0.181consprod?0.283utility(0.30) (.032) (.004) (.089) (.085) (.099)
N=209, R2=0.357.
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The data used are in CEOSAL1.RAW, where finance, consprod, and utility are binary variables indicating the financial, consumer products, and utilities industries. The omitted industry is transportation.
(i) Compute the approximate percentage difference in estimated salary between the utility and transportation industries, holding sales and roe fixed. Is the difference statistically significant at the 1% level?
(ii) Use equation (7.10) to obtain the exact percentage difference in estimated salary between the utility and transportation industries and compare this with the answer obtained in part (i).
(iii) What is the approximate percentage difference in estimated salary between the consumer products and finance industries? Write an equation that would allow you to test whether the difference is statistically significant.
4. The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. Using the data in SMOKE.RAW, we estimate a linear probability model for smokes:
smokes?0.656?0.069log?cigpric? ?0.012log?income??0.029educ?0.20age
(0.855) (0.204) (0.026) (0.006) (0.006)
[0.856] [0.207] [0.026] [0.006] [0.005]
?0.00026age2?0.101restaurn?0.026white (0.00006) (0.039) (0.052) [0.00006] [0.038] [0.050] n=807, R2=0.062.
The variable white equals one if the respondent is white, and zero otherwise; cigpric= the per pack of cigarettes (in cents) income=annual income educ= years of schooling age=measured in years
restaurn= a binary indictor equal to unity if the person resides in a state with restaurant smoking restrictions.
Both the usual and heteroskedasticityrobust standard errors are reported.
(i) Are there any important differences between the two sets of standard errors?
(ii) Holding other factors fixed, if education increases by four years, what happens to the estimated probability of smoking?
(iii) At what point does another year of age reduce the probability of smoking?
(iv) Interpret the coefficient on the binary variable restaurn (a dummy variable equal to one if the person lives in a state with restaurant smoking restrictions).
(v) Person number 206 in the data set has the following characteristics: Cigpric= 67.44, income =6,500, educ =16, age =77, restaurn =0, white =0, and smokes=0. Compute the predicted probability of smoking for this person and comment on the result.
5. Let gGDPt denote the annual percentage change in gross domestic product and let
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intt denote a short-term interest rate. Suppose thatgGDPt is related to interest rates by
gGDPt??0??0intt??1intt?1?ut
where ut is uncorrelated with intt, intt?1, and all other past values of interest rates. Suppose that the Federal Reserve follows the policy rule:
intt??0??1(gGDPt?1?3)??t
where ?1?0. (When last year’s GDP growth is above 3%, the Fed increases interest rates to prevent an “overheated” economy.) If ?t is uncorrelated with all past values of intt and ut, argue that intt must be correlated with intt?1. (Hint: Lag the first equation for one time period and substitute for gGDPt?1 in the second equation.) Which Gauss-Markov assumption does this violate? 6. Consider the following regression model:
11??1??2()?ui YixiNote: Neither Y nor X assumes zero value. (i) Is this a linear regression model?
(ii) How would you estimate this model?
(iii) What is the behavior of Y as X tends to infinity?
(iv) Can you give an example where such a model may be appropriate?
7. From the data for 46 states in the United States for 1992, Baltagi obtained the following regression results:
logC? 4.30?1.34 logP? 0.17 logY
se = (0.91) (0.32) (0.20) R2= 0.27
where C = cigarette consumption, packs per year
P = real price per pack
Y = real disposable income per capita
(i) What is the elasticity of demand for cigarettes with respect to price? Is it statistically significant? If so, is it statistically different from one?
(ii) What is the income elasticity of demand for cigarettes? Is it statistically significant? If not, what might be the reasons for it?
(iii) How would you retrieve R2 from the adjusted R2 given above?
8. Consider the following wage-determination equation for the British economy for the period 1950–1969:
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Wt?8.582?0.364?PF?t?0.004?PF?t?1?2.560Ut
(1.129) (0.080) (0.072) (0.658) R2= 0.873 df = 15
where W = wages and salaries per employee
PF = prices of final output at factor cost
U = unemployment in Great Britain as a percentage of the total number of
employees of Great Britain t = time
(The figures in the parentheses are the estimated standard errors.) (i) Interpret the preceding equation.
(ii) Are the estimated coefficients individually significant? (iii)What is the rationale for the introduction of?PF?t?1?
(iv) Should the variable ?PF?t?1 be dropped from the model? Why?
(v) How would you compute the elasticity of wages and salaries per employee with respect to the unemployment rate U ?
9.From data for 101 countries on per capita income in dollars (X) and life expectancy in years (Y) in the early 1970s, Sen and Srivastava obtained the following regression results:
Yi??2.40 ? 9.39 lnXi?3.36 [Di(lnXi?7)] se = (4.73) (0.859) (2.42) R2= 0.752
where Di = 1 if lnXi > 7, andDi= 0 otherwise. Note: WhenlnXi = 7, X = $1097 (approximately).
(i) What might be the reason(s) for introducing the income variable in the log form? (ii) How would you interpret the coefficient 9.39 of lnXi ?
(iii) What might be the reason for introducing the regressorDi(lnXi?7)? How do you explain this regressor verbally? And how do you interpret the coefficient ?3.36 of this regressor (Hint: linear piecewise regression)?
(iv) Assuming per capita income of $1097 as the dividing line between poorer and richer countries, how would you derive the regression for countries whose per capita is less than $1097 and the regression for countries whose per capita income is greater than $1097?
(v) What general conclusions do you draw from the regression result presented in this problem?
10. To assess the effect of state right-to-work laws (which do not require membership in the union as a precondition of employment) on union membership, the following regression results were obtained, from the data for 50 states in the United States for 1982:
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PVTi?19.8066?9.3917 RTWi
t = (17.0352) (?5.1086) r2= 0.3522
where PVT = percentage of private sector employees in unions, 1982, and RTW = 1 if right-to-work law exists, 0 otherwise.
Note: In 1982, twenty states had right-to-work laws.
(i) A priori, what is the expected relationship between PVT and RTW? (ii) Do the regression results support the prior expectations? (iii) Interpret the regression results.
(iv) What was the average percent of private sector employees in unions in the states that did not have the right-to-work laws?
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厦门大学 2013-2014计量期末试卷B
