Homework
1. Decide whether you would expect relationships between the following pairs of dependent and independent variables (respectively) to be positive, negative or ambiguous. Explain your reasoning.
a. The amount of hair on the head of a male professor and the age of that professor.
b. Aggregate bet investment in China in a given year and the GDP in that year.
c. The growth rate of GDP in a year and the average hair length in that year.
d. The quantity of canned tuna demanded and the price of a can of tuna.
2. Return the height/weight example that we have discussed in Chapter 2.
a. Go back to the data set and identify the three customers who seem to be quite a distance from the estimated regression line. Would we have a better regression equation if we dropped these customers from the sample?
b. Why does the estimated equation predict the same weight for all males of the same weight for all males of the same height when it is obvious that all males of the same height do not necessarily weigh the same?
3. Consider the following equation relating the price of a house to its size:
SIZEi = -290 + 3.62 PRICEi
where SIZEi indicates the size (in sq ft) and PRICEi indicates the price (on 1000 dollars) of the ith house.
a. Carefully explain the meaning of the each of the estimated regression coefficients.
b. How would you evaluate the model if you were told that R2 for the model is 0.4?
c. What do you think would happen to the estimated coefficients of this equation if we had measured the price variable in dollars instead of in thousands of dollars? Be specific.
4. Calculate the coefficients of the model relating the percent of the labor force in agriculture (AGRi) and per capita income in thousands of dollars (PCGDPi) in 10 developed countries. Assume that there is no computer available, so you have to do the calculations yourself using the formulas we have learned in Chapter 2.
Model: PCGDPi = β0 + β1 AGRi + εi
Data:
|
Country
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
|
PCGDP
|
6
|
8
|
8
|
7
|
7
|
12
|
9
|
8
|
9
|
10
|
|
AGR
|
9
|
10
|
8
|
7
|
10
|
4
|
5
|
5
|
6
|
7
|
a. Calculate betas
b. Calculate R2 and adjusted-R2.
c. Plot the data and the regression line ton XY plane to visualize the fit.
5. Use the information given on Table 1 to answer the following questions:
Table 1:
|
U.S. 2011-2012 Expenditures ($ billions)
|
|
|
2011
|
2012
|
|
Personal consumption expenditures
|
10,729
|
11,120
|
|
Goods
|
3,625
|
3,783
|
|
Services
|
7,104
|
7,337
|
|
Gross private domestic investment
|
1,855
|
2,062
|
|
Fixed investment
|
1,818
|
2,004
|
|
Change in private inventories
|
37
|
58
|
|
Net exports of goods and services
|
-568
|
-560
|
|
Exports
|
2,094
|
2,184
|
|
Imports
|
2,662
|
2,744
|
|
Government expenditures
|
3,060
|
3,063
|
|
Federal
|
1,222
|
1,214
|
|
State and local
|
1,838
|
1,849
|
a. Calculate GDP in 2011 and 2012.
b. Is there trade deficit or surplus? What does it imply about the future?
6. Which of the following counts toward changes in the current GDP? Explain each of them briefly.
a. Increase in crime level.
b. Building new jails.
c. You find $10 on the sidewalk.
d. You fix your own sink.
7. Use the information given on Table 2 to answer the following questions:
Table 2:
|
National Income Accounting
|
|
|
2017
|
2018
|
|
Quantity of pistachios
|
1,000
|
1,100
|
|
Quantity of video games
|
500
|
500
|
|
Price of pistachios
|
$1.00
|
$1.50
|
|
Price of video games
|
$15.00
|
$14.75
|
a. Calculate the growth of the economy from 2017 to 2018.
b. Calculate inflation from 2017 to 2018.
8. What would happen to real GDP, if the nominal GDP rises by 6 percent and the price level rises by 3 percent?
9. Use the information given on Table 3 to answer the following questions:
Table 3:
|
U.S. and Eurozone Nominal GDP in 2011
|
|
|
2011
|
|
Eurozone nominal GDP (€ billions)
|
€13,144
|
|
U.S. nominal GDP ($ billions)
|
$15,100
|
|
Dollar/euro exchange rate
|
$1.28/€1
|
|
PEURO /PUS
|
0.96
|
a. What is the value of the Eurozone nominal GDP in U.S. dollars adjusted for price differences?
b. How big is the US economy compared to the Eurozone economy once adjusted for price differences?
10. Using the expenditure approach to national income accounting, when discussing government expenditures, do we include transfer payments? Why or why not?