ECON 7810 Assignment 2
Q1 [W4 Problem 10]
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 known at the beginning of the period help to predict stock returns, then we could use this information in choosing stocks.
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:
= −14.37 + .321 + .043 − .0051 + .0035
(6.89) (.201) (.078) (.0047) (.0022) n=142 =.0395
Test whether the explanatory variables are jointly significant at the 5% level. Is any explanatory variable individually significant?
(ii) Now, reestimate the model using the log form for netinc and salary:
= −36.30 + .327 + .069 − 4.74log() + 7.24log()
(39.37) (.203) (.080) (3.39) (6.31) n=142 =.0330
Do any of your conclusions from part (i) change?
(iii) How come we do not also use logs of dkr and eps in part (ii)?
(iv) Overall, is the evidence for predictability of stock returns strong or weak?
Q2 [W4 Computer Exercise C3]
Use the data in HPRICE1.RAW (same as Assignment 1) to estimate the model
log() = + + + .
(i) You are interested in estimating and obtaining a confidence interval for the percentage change in price when a 150-square-foot bedroom is added to a house. In decimal form, this is = 150 + . Use the data in HPRICE1.RAW to estimate .
(ii) Write in terms of and and plug this into the log() equation.
(iii) Use part (ii) to obtain a standard error for and use this standard error to construct
95% confidence interval.
Q3 [W6 Problem 4]
The following model allows the return to education to depend upon the total amount of parent’s education, called pareduc:
log() = + + × + + .
(i) Show that the proportionate effect on wage of another year of education is +
.
(ii) Using the data in HTV.RAW, the estimated equation is
log() = .515 + .093 + .00099 × + .034
(.179) (.013) (.00026) (.007) n = 1,230, = .186.
If someone’s parents have 32 years of total education, by what percentage is that person’s return to education estimated to exceed that of someone whose parents have 24 years of education? Is the difference statistically significant?
(iii) When pareduc is added as a separate regressor, we get
log() = .772 + .186 + .054 − .0028 × + .034
(.401) (.029) (.015) (.0011) (.007) n = 1,230, = .195.
Now how does the return to education depend on parent education? Find the two-sided p-value for testing the null hypothesis that the return to education does not depend on parent education. What do you conclude?
Q4 [W6 Computer Exercise C5]
Using the same data set HPRICE1.RAW as Q2 (i) Estimate the model
log() = + log() + + + ,
And report the results in the usual OLS format.
(ii) Find the predicted value of log(price), when lotsize=20,000, sqrft=2,500, and
bdrms=4. Using the methods in Section 6.4, find the predicted value of price at the
same values of the explanatory variables.
(iii) For explaining variation in price, decide whether you prefer the model from part (i) or
the model
price = + + + + ,