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ECMT6007/6702: Econometric Applications Problem Set 3
发布时间：2022-11-10
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ECMT6007/6702: Econometric Applications
Problem Set 3
Semester 2 2022
Question 1. Regression analysis can be used to test whether the market efficiently uses information in valuing stocks. For concreteness, let return be the total return from holding a firm’s stock over the four-year period from the end of 1990 to the end of 1994. The“efficient markets hypothesis” says that these returns should not be systematically related to information known in 1990. If firm characteristics are known at the beginning of the period to predict stock returns, then we could use that information in choosing which stocks to buy (and hence become very wealthy; according to the hypothesis competition among profit-seeking traders who have access to the information will remove all such opportunities).
For 1990, let dkr be a firm’s debt to capital ratio, let eps denote the earnings per share, let netinc denote net income, and let salary denote total compensation for the CEO.
(i) Using the data in RETURN .RAW, the following equation was estimated:
r—eturn = −14.37 + 0.321 dkr + 0.043 eps − 0.0051 netinc + 0.0035 salary (6.89) (0.201) (0.078) (0.0047) (0.0022)
n = 142, R2 = 0.0395
Test whether the explanatory variables are jointly significant at the 5% level. Note: the re-
stricted model – with no explanatory variables – has R2 = 0
(ii) The model was re-estimated using the log form for netinc and salary :
r—eturn = −36.30 + 0.327 dkr + 0.069 eps − 4.77 log (netinc) + 7.24 log (salary)
(39.37) (0.203) (0.080) (3.39) (6.31)
n = 142, R2 = 0.0330
With this model, test the joint significance of the explanatory variables using a 5% significance level.
(iii) Are any of the explanatory variables in model (ii) individually significant at the 5% level? (iv) Overall, is the evidence for the predictability of stock returns strong or weak ? Explain.
Question 2. Computer Exercise: Explaining the Salary of MBA Graduates The following model can be used to study the salary of graduates from MBA programs:
log (salary) = β0 + β1 testsc + β2 WAM + β3 log (libsize) + β4 rank + u
where salary is median annual salary for the graduating class, testsc is the median test score on a professional exam by members of the graduating class, WAM is the median weighted average (course) mark for members of the graduating class, libsize is the number of volumes in the univer- sity library, and rank is world-wide rank of the MBA program (where rank = 1 is the best).
(i) Download the data set mba3.dta from the Canvas webpage. What are the average, minimum and maximum values for each variable?
(ii) What is the interpretation of β4 , and explain why we expect β4 ≤ 0. What is the interpretation of the coefficient on libsize?
(iii) Estimate the above model, and present the results in the usual form.
(iv) State and test the null hypothesis that the rank ofthe MBA program has no ceteris paribus effect on median salary (against the one-sided alternative that it is negative). Use a 5% significance level.
(v) Are the two features of the graduating class – testsc and WAM – jointly significant in ex- plaining log (salary)? Carry out the appropriate F-test using a 5% significance level. (Perform the test by estimating the unrestricted and restricted models, and forming the test statistic us- ing either the SSR or R2 form).
(vi) Test the null hypothesis that testsc and WAM have the same effect on salary (i.e. test the null H0 : β 1 = β2 against the alternative H1 : β 1 
β2 ) using a 5% significance level. Carry out this test as a t-test on a single coefficient in the model estimated where one explanatory variable has been transformed.
Note: The mba3 .dta dataset can be downloaded from the Canvas webpage. This file has 250 observations and 5 variables: salary, testsc, WAM, libsize and rank.
