University of Hong KongIntroductory Econometrics (ECON0701), Spring 2014

Assignment #3: Due March 7, 2014

1. (4.1) Which of the following can cause the usual OLS t statistics to be invalid (that is, notto have t distributions under 0)?(a) Heteroskedasticity.

(b) A sample correlation coecient of 0.95 between two independent variables that are inthe model.

(c) Omitting an important explanatory variable.

2. (4.3) The variable is expenditures on research and development (R&D) as a per-centage of sales. Sales are measured in millions of dollars. The variable is profitsas a percentage of sales. Using the data in rdchem.dta for 32 firms in the chemical industry,the following equation is estimated:

\ = 0472 + 0321 ln () + 0050 (1.369) (0.216) (0.046)

= 32 2 = 0099(a) Interpret the coecient on ln (). In particular, if increases by 10%, what is

the estimated percentage point change in ? Is this an economically large eect?(b) Test the hypothesis that R&D intensity does not change with sales against the alternative

that it does change with sales. Do the test at the 5% and 10% levels.

(c) Does have a statistically significant eect on ?3. (4.5) Consider the following estimated regression, which can be used to study the eectsof skipping class on college GPA. The variable is GPA in college; is highschool GPA, is the score on the ACT test and is the number of lectures missedper week.

\ = 139 + 0412 + 0015 0083 + (0.33) (0.094) (0.011) (0.026)

= 141 2 = 0234(a) Using the standard normal approximation, find the 95% confidence interval for .(b) Can you reject the hypothesis 0 : = 04 against the two-sided alternative at

the 5% level?

(c) Can you reject the hypothesis 0 : = 1 against the two-sided alternative at the5% level?

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4. (4.9) Consider the regression model

= 0 + 1 + 2 + 3 where is a persons total amount of sleep (in minutes per week), is his or hertotal amount of work (also in minutes per week), is years of education, and is yearsof age. The estimated equation is

[ = 363825 0148 1113 + 220 (112.28) (0.017) (5.88) (1.45)

= 706, 2 = 0113where the figures in parentheses are standard errors.

(a) Is either or individually significant at the 5% level? Show your work.(b) Dropping and from the equation gives

[ = 358698 0151 (38.91) (0.017)

= 706, 2 = 0103Are and jointly significant in the original equation at the 5% level? Justifyyour answer.

(c) Does including and in the model greatly aect the estimated tradeo betweensleeping and working?

(d) Suppose that the sleep equation contains heteroskedasticity. What does this mean aboutthe tests computed in parts (a) and (b)?

5. (4.16; computer exercise) Use the data in mlb1.dta for this exercise.

(a) Estimate the model

ln () = 0 + 1 + 2 + 3 + 4 + 5 + and then estimate it again, dropping the variable . What happens to the statis-tical significance of ? What about the size of the coecient on ?

(b) Add the variables , , and to the model from part (a). Which ofthese factors are individually significant?

(c) In the model from part (b), test the joint significance of , , and .

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