The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

Observation
GDP
M2
CPI
LTRATE
TBRATE
1980
2795.6
1600.4
82.4
11.27
11.506
1981
3131.3
1756.1
90.9
13.45
14.029
1982
3259.2
1911.2
96.5
12.76
10.686
1983
3534.9
2127.8
99.6
11.18
8.630
1984
3932.7
2311.7
103.9
12.41
9.580
1985
4213.0
2497.4
107.6
10.79
7.480
1986
4452.9
2734.0
109.6
7.78
5.980
1987
4742.5
2832.8
113.6
8.59
5.820
1988
5108.3
2995.8
118.3
8.96
6.690
1989
5489.1
3159.9
124.0
8.45
8.120
1990
5803.2
3279.1
130.7
8.61
7.510
1991
5986.2
3379.8
136.2
8.14
5.420
1992
6318.9
3434.1
140.3
7.67
3.450
1993
6642.3
3487.5
144.5
6.59
3.020
1994
7054.3
3502.2
148.2
7.37
4.290
1995
7400.5
3649.3
152.4
6.88
5.510
1996
7813.2
3824.2
156.9
6.71
5.020
1997
8300.8
4046.7
160.5
6.61
5.070
1998
8759.9
4401.4
163.0
5.58
4.810
Notes:
GDP: gross domestic product ($ billions).
M
2
: M
2
money supply.
CPI: Consumer Price Index (1982–1984
=
100).
LTRATE: long-term interest rate (30-year Treasury bond).
TBRATE: three-month Treasury bill rate (% per annum).
TABLE 7.10
Demand for Money
in the United States,
1980–1998
Source: 
Economic Report of the
President,
2000, Tables 
B-1, B-58, B-67, B-71.
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224
Part One
Single-Equation Regression Models
a.
Given the data, estimate the above demand function. What are the income and
interest rate elasticities of demand for money?
b.
Instead of estimating the above demand function, suppose you were to fit the
function (
M
/
Y
)
t
=
α
1
r
α
2
t
e
u
t
.
How would you interpret the results? Show the
necessary calculations.
c.
How will you decide which is a better specification? (
Note: 
A formal statistical
test will be given in Chapter 8.)
7.22. Table 7.11 gives data for the manufacturing sector of the Greek economy for the
period 1961–1987.
a.
See if the Cobb–Douglas production function fits the data given in the table and
interpret the results. What general conclusion do you draw?
b.
Now consider the following model:
Output/labor
=
A
(
K
/
L
)
β
e
u
where the regressand represents labor productivity and the regressor represents the
capital labor ratio. What is the economic significance of such a relationship, if any?
Estimate the parameters of this model and interpret your results.
Capital-to-Labor
Observation
Output*
Capital
Labor
†
Ratio
1961
35.858
59.600
637.0
0.0936
1962
37.504
64.200
643.2
0.0998
1963
40.378
68.800
651.0
0.1057
1964
46.147
75.500
685.7
0.1101
1965
51.047
84.400
710.7
0.1188
1966
53.871
91.800
724.3
0.1267
1967
56.834
99.900
735.2
0.1359
1968
65.439
109.100
760.3
0.1435
1969
74.939
120.700
777.6
0.1552
1970
80.976
132.000
780.8
0.1691
1971
90.802
146.600
825.8
0.1775
1972
101.955
162.700
864.1
0.1883
1973
114.367
180.600
894.2
0.2020
1974
101.823
197.100
891.2
0.2212
1975
107.572
209.600
887.5
0.2362
1976
117.600
221.900
892.3
0.2487
1977
123.224
232.500
930.1
0.2500
1978
130.971
243.500
969.9
0.2511
1979
138.842
257.700
1006.9
0.2559
1980
135.486
274.400
1020.9
0.2688
1981
133.441
289.500
1017.1
0.2846
1982
130.388
301.900
1016.1
0.2971
1983
130.615
314.900
1008.1
0.3124
1984
132.244
327.700
985.1
0.3327
1985
137.318
339.400
977.1
0.3474
1986
137.468
349.492
1007.2
0.3470
1987
135.750
358.231
1000.0
0.3582
*Billions of Drachmas at constant 1970 prices.
†
Thousands of workers per year.
TABLE 7.11
Greek Industrial
Sector
Source: I am indebted to
George K. Zestos of
Christopher Newport
University, Virginia, for these
data.
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Chapter 7
Multiple Regression Analysis: The Problem of Estimation
225
7.23.
Monte Carlo experiment: 
Consider the following model:
Y
i
=
β
1
+
β
2
X
2
i
+
β
3
X
3
i
+
u
i
You are told that
β
1
=
262,
β
2
= −
0
.
006,
β
3
= −
2
.
4,
σ
2
=
42, and
u
i
∼
N
(0, 42).
Generate 10 sets of 64 observations on
u
i
from the given normal distribution and use
the 64 observations given in Table 6.4, where
Y
=
CM,
X
2
=
PGNP, and
X
3
=
FLR
to generate 10 sets of the estimated
β
coefficients (each set will have the three estimated
parameters). Take the averages of each of the estimated
β
coefficients and relate them to
the true values of these coefficients given above. What overall conclusion do you draw?
7.24. Table 7.12 gives data for real consumption expenditure, real income, real wealth, and
real interest rates for the U.S. for the years 1947–2000. These data will be used again
for Exercise 8.35.
a.
Given the data in the table, estimate the linear consumption function using income,
wealth, and interest rate. What is the fitted equation?
b.
What do the estimated coefficients indicate about the variables’ relationships to
consumption expenditure?
Year
C
Yd
Wealth
Interest Rate
1947
976.4
1035.2
5166.8
−
10.351
1948
998.1
1090.0
5280.8
−
4.720
1949
1025.3
1095.6
5607.4
1.044
1950
1090.9
1192.7
5759.5
0.407
1951
1107.1
1227.0
6086.1
−
5.283
1952
1142.4
1266.8
6243.9
−
0.277
1953
1197.2
1327.5
6355.6
0.561
1954
1221.9
1344.0
6797.0
−
0.138
1955
1310.4
1433.8
7172.2
0.262
1956
1348.8
1502.3
7375.2
−
0.736
1957
1381.8
1539.5
7315.3
−
0.261
1958
1393.0
1553.7
7870.0
−
0.575
1959
1470.7
1623.8
8188.1
2.296
1960
1510.8
1664.8
8351.8
1.511
1961
1541.2
1720.0
8971.9
1.296
1962
1617.3
1803.5
9091.5
1.396
1963
1684.0
1871.5
9436.1
2.058
1964
1784.8
2006.9
10003.4
2.027
1965
1897.6
2131.0
10562.8
2.112
1966
2006.1
2244.6
10522.0
2.020
1967
2066.2
2340.5
11312.1
1.213
1968
2184.2
2448.2
12145.4
1.055
1969
2264.8
2524.3
11672.3
1.732
1970
2314.5
2630.0
11650.0
1.166
1971
2405.2
2745.3
12312.9
−
0.712
1972
2550.5
2874.3
13499.9
−
0.156
1973
2675.9
3072.3
13081.0
1.414
1974
2653.7
3051.9
11868.8
−
1.043
1975
2710.9
3108.5
12634.4
−
3.534
1976
2868.9
3243.5
13456.8
−
0.657
TABLE 7.12
Real Consumption
Expenditure, Real
Income, Real Wealth,
and Real Interest
Rates for the U.S.,
1947–2000
Sources: 
C
, Yd, and quarterly
and annual chain-type price
indexes (1996 = 100): Bureau
of Economic Analysis, U.S.
Department of Commerce
(http://www.bea.doc.gov/bea/
dn1.htm).
Nominal annual yield on
3-month Treasury securities:
Economic Report of the
President, 2002.
Nominal wealth 
=
end-of-
year nominal net worth of
households and nonprofits
(from Federal Reserve flow
of funds data: http://www.
federalreserve.gov).
Continued
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226
Part One
Single-Equation Regression Models
7.25.
Estimating Qualcomm stock prices
. As an example of the polynomial regression,
consider data on the weekly stock prices of Qualcomm, Inc., a digital wireless
telecommunications designer and manufacturer over the time period of 1995 to
2000. The full data can be found on the textbook’s website in Table 7.13. During
the late 1990, technological stocks were particularly profitable, but what type of
regression model will best fit these data? Figure 7.4 shows a basic plot of the data for
those years.
This plot does seem to resemble an elongated S curve; there seems to be a slight
increase in the average stock price, but then the rate increases dramatically toward the
far right side of the graph. As the demand for more specialized phones dramatically
increased and the technology boom got under way, the stock price followed suit and
increased at a much faster rate.
a.
Estimate a linear model to predict the 
closing stock price
based on 
time
. Does this
model seem to fit the data well?
b.
Now estimate a squared model by using both 
time
and 
time-squared
. Is this a bet-
ter fit than in (
a
)?
Year
C
Yd
Wealth
Interest Rate
1977
2992.1
3360.7
13786.3
−
1.190
1978
3124.7
3527.5
14450.5
0.113
1979
3203.2
3628.6
15340.0
1.704
1980
3193.0
3658.0
15965.0
2.298
1981
3236.0
3741.1
15965.0
4.704
1982
3275.5
3791.7
16312.5
4.449
1983
3454.3
3906.9
16944.8
4.691
1984
3640.6
4207.6
17526.7
5.848
1985
3820.9
4347.8
19068.3
4.331
1986
3981.2
4486.6
20530.0
3.768
1987
4113.4
4582.5
21235.7
2.819
1988
4279.5
4784.1
22332.0
3.287
1989
4393.7
4906.5
23659.8
4.318
1990
4474.5
5014.2
23105.1
3.595
1991
4466.6
5033.0
24050.2
1.803
1992
4594.5
5189.3
24418.2
1.007
1993
4748.9
5261.3
25092.3
0.625
1994
4928.1
5397.2
25218.6
2.206
1995
5075.6
5539.1
27439.7
3.333
1996
5237.5
5677.7
29448.2
3.083
1997
5423.9
5854.5
32664.1
3.120
1998
5683.7
6168.6
35587.0
3.584
1999
5968.4
6320.0
39591.3
3.245
2000
6257.8
6539.2
38167.7
3.576
Notes:
Year 
=
calendar year.
C
=
real consumption expenditures in billions of chained 1996 dollars.
Yd 
=
real personal disposable income in billions of chained 1996 dollars.
Wealth 
=
real wealth in billions of chained 1996 dollars.
Interest 
=
nominal annual yield on 3-month Treasury securities–inflation rate (measured by the annual % change in annual chained
price index).
The nominal real wealth variable was created using data from the Federal Reserve Board’s measure of end-of-year net worth for
households and nonprofits in the flow of funds accounts. The price index used to convert this nominal wealth variable to a real wealth
variable was the average of the chained price index from the 4th quarter of the current year and the 1st quarter of the subsequent year.