Atul A. Dar
November 18, 2017
This assignment is due in my my office no later than 6pm on November 28. Please pay attention to the following:
1. Make sure you attach a copy of your computer printouts to the assignment. Camera shots are not acceptable.
2. Answers to questions should not be written/typed in the computer printout.
3. See me if are not sure about anything on this assignment.
Do not hand in Question 4. It is only for review.
Question 1 (12 points)
Consider the following model for studying the relationship between investment and saving among countries:
INV = β1 + β2SAV + e, where INV = investment as percentage of GDP and SAV = saving as a percentage of GDP.
According to one view, this equation can be used to estimate the extent to which capital is mobile across countries. The
argument is that, if capital is perfectly mobile internationally, an increase in saving in a country need not have any effect
on domestic investment, since savers would look for the highest return on capital. There is no reason to suppose that
higher returns are available in the domestic economy. So, if capital were perfectly mobile, investment and saving would
not be related. On the other hand, a one-to-one relationship would suggest that capital is completely immobile; every
additional dollar of saving stays home to finance domestic investment. The size of the coefficient β2 would, therefore,
measure the degree of capital mobility. This is the argument initially tested by Feldstein and Horioka in a now famous
1980 article, which has led to an enormous literature and which continues to attract the interest of researchers. You are
going to re-examine the issue using an international cross section of advanced economies, using data on saving and
investment, both expressed as a percent (%) of GDP. This data are in the file cap-mob.dta for the years: 1995, 2005, and
a. Estimate the above model separately for each of the three years. Present your results in compact form as shown in
class. (4 points)
Interpret the slope coefficient and the goodness of fit. (3 points)
b. Conduct tests at the 1 percent level of significance to determine if there is (i) perfect capital mobility,
against the hypothesis of less than perfect capita mobility, and (ii) zero capital mobility. (3 points)
c. What can you conclude from your results about capital mobility over the years? (2 points)
Question 2 (8 points)
A. A researcher estimated the following model from the 1992 family expenditure survey of Canada.
lnF^ = 1.82 +0.0204X
R-squared = 0.59, N=8054
F = family expenditure on food ($ 000), and X = family income ($ 000)
1. Interpret the slope coefficient. (3 points)
2. If family A spends 10 percent more on food than family B, by how much would the two families
differ in terms of income? Show your work. (2 points).
B. Using the same family expenditure survey, the following model was estimated:
lnR^= -4.42 +1.46lnX
R-squared = 0.49, N=8054
where R is family expenditure on recreation ($000). Test the hypothesis that recreation is a “luxury” good; that is, its
income elasticity is greater than one. Use the 5 percent significance level. (3 points)
Question 3 (10 points)
It has been argued by many that economies that are more open to trade would tend to grow faster than those that are
less open, other things being equal. Consider the following simple model for examining this issue.
GY= β1 + β2TRADE + β3GKAP+ β4GLAB + e
GY=growth rate of real GDP (%), TRADE= trade to GDP ratio (%), GKAP growth rate of capital (%), and GLAB=growth rate
of employment (%). An economy’s openness is being measured by TRADE, the ratio of total trade (exports plus imports)
to GDP in percent. The higher the ratio, the more open the economy. The estimated model is:
GY^ = -4.18 + 0.0074TRADE + 0.27729GKAP +0.3829GLAB,
N=31, R2= 0.66
cov(b3 ,b4) = 0.00475
1. Interpret the GLAB and GKAP coefficients. (2 points)
2. Test whether openness promotes growth (Use α=0.05). (3 points)
3. Test the hypothesis that the impact of the growth in employment (β4) is equal to the impact of the
growth in capital (β3), against the alternative that it is not. Use the 5 percent level of significance. (3 points)
4. Test the significance of the entire regression at the 5 percent level. (2 points)
Question 4 (not to be handed in)
Consider Andy’s Big Burger chain once again.
S= β1 +β2P + β3A + β4 A2, where P= price ($), A = advertising expenditure ($000), S= sales revenue ($ 000).
It can shown that the optimal (most profitable) level of advertising is determined by the condition: β3 + 2β4A =1. For
convenience you can also write this as λ=1 where λ = β3 + 2β4A. Based on 75 observations, the model was estimated and
gave the following results.
Ŝ =109.72 -7.640P +12.151A - 2.768A2
(1.046) (3.566) (0.941)
1. Estimate the optimal level of advertising expenditures (A) based on your estimates.
2. If the firm currently spends $1.9 thousand on advertising (A=1.9), test whether it is spending an optimal amount on
advertising, against the alternative that it is not. Use the 5 percent significance level.
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