Introductory Econometrics
Lecture 4: Hypothesis Testing
by Hieu Nguyen
Fall 2024
1.
Consider an equation to explain salaries of CEOs in terms of annual firm sales
return on equity (roe in percentage form) and return on the firm’s stock (ros
in percentage form):
log(salary) = β0 + β1 log(sales) + β2roe + β3ros + u
• In terms of the model parameters, state the null hypothesis that after
controlling for sales and roe ros has no effect on CEO salary. State the
alternative that better stock market performance increases a CEO’s salary.
• Using the data in CEOSAL1.RAW the following equation was obtained by
OLS:
log(salary) = 4.32 + 0.280 log(sales) + 0.0174roe + 0.00024ros
(0.32) (0.035) (0.0041) (0.00054)
n = 209 R2
= 0.283
By what percentage is salary predicted to increase if ros increases by 50
points? Does ros have a practically large effect on salary?
• Test the null hypothesis that ros has no effect on salary against the alternative
that ros has a positive effect. Carry out the test at the 10%
significance level.
• Would you include ros in a final model explaining CEO compensation in
terms of firm performance? Explain.
2.
The variable rdintens is expenditures on research and development (RD) as
a percentage of sales. Sales are measured in millions of dollars. The variable
profmarg is profits as a percentage of sales.
1
Using the data in RDCHEM.RAW for 32 firms in the chemical industry the
following equation is estimated:
rdintens = 0.472 + 0.321 log(sales) + 0.050profmarg
(1.369) (0.216) (0.046)
n = 32 R2
= 0.099
• Interpret the coefficient on log(sales). In particular, if sales increases by
10% what is the estimated percentage point change in rdintens? Is this
an economically large effect?
• Test the hypothesis that R&D intensity does not change with sales against
the alternative that it does increase with sales. Do the test at the 5% and
10% levels.
• Does profmarg have a statistically significant effect on rdintens?
3.
Are rent rates influenced by the student population in a college town? Let
rent be the average monthly rent paid on rental units in a college town in the
United States. Let pop denote the total city population, avginc the average
city income, and pctstu the student population as a percentage of the total
population. One model to test for a relationship is
log(rent) = β0 + β1 log(pop) + β2 log(avginc) + β3pctstu + u
• State the null hypothesis that size of the student body relative to the population
has no ceteris paribus effect on monthly rents. State the alternative
that there is an effect.
• What signs do you expect for β1 and β2?
• The equation estimated using 1990 data from RENTAL.RAW for 64 college
towns is:
log(rent) = 0.043 + 0.066 log(pop) + 0.507 log(avginc) + 0.0056pctstu
(0.844) (0.039) (0.081) (0.0017)
n = 64 R2
= 0.458
What is wrong with the statement: “A 10% increase in population is
associated with about a 6.6% increase in rent”?
• Test the hypothesis stated in part (a.) at the 1% level.
2