Economics 430–Applied Econometrics
Homework #4 (100 Points)
Instructions: Please answer all of the following questions as best as possible in
groups up to 3 students. If you have any questions please contact me. The point value for
each question is in parentheses. This assignment is due April 2nd via email before we
start our virtual class.
1. (45) The following equation was obtained using OLS:
̂rdintens = 2.613 (0.429)
+ 0.00030 (0.00014)
sales− 0.0000000070 (0.0000000037)
n = 32, R2 = 0.1484
Where rdintens is the R&D spending as percent of sales and sales represents firm
sales in millions dollars.
(a) (5) What shape does the quadratic of sales has? parabolic shape? U shape?
(b) (10) At what point does the marginal effect of sales on rdintens become nega-
(c) (10) Is the quadratic term statistically significant? Would you keep the quadratic
term in the model?
(d) (10) Define salesbil as sales measured in billions of dollars: salesbil =
sales/1, 000. Rewrite the estimated equation with salesbil and salesbil2 as the
independent variables. Be sure to report standard errors and the R2. (Hint:
Note that salesbil2 = sales2/(1, 000)2.
(e) (5) What would happen to the statistical inference (the statistical significance
level of the variables)?
(f) (5) For the purpose of reporting the results, which equation do you prefer?
2. (55) Consider a model in which the return to education depends upon the amount of
work experience (and vice versa):
log(wage) = β0 + β1educ+ β2exper + β3educ ∗ exper + u, (1)
(a) (10) Show that the return to another year of education, holding exper fixed, is
β1 + β3exper.
(b) (10) State the null hypothesis that the return to education does not depend on
the level of exper. What do you think is the appropriate alternative?
(c) (15) Use the data in WAGE2 to run model (1) and report you results.
(d) (10) Test the Null Hypothesis in (b) against your stated alternative. What do
(e) (10) What is the R2 (the value)? What is the R̄2 (the value). Conceptually,
what is the difference between these two?