A4 Industrial produces hydraulic pumps using a process that can be approximated
ID: 1113205 • Letter: A
Question
A4 Industrial produces hydraulic pumps using a process that can be approximated by a Cobb-Douglas production function. The production method uses tool shops that contain pieces of equipment that can be operated by a varying number of workers. The number of shops (units of variable capital) used during the month are given. The firm also hires skilled workers, and the number of full-time skilled workers hired for the month is given. The monthly output (number of pumps) produced is also given. The manager wants to estimate the Cobb-Douglas production function in order to determine the number of shops and number of workers required to achieve various levels of production.
The manager thus asks you to estimate a log-linear regression model based on the following monthly data over the last 2 years.
Q = quantity of boats produced per year
L = number of full-time workers per year
K = capital (number of shops) rented per year
P = average selling price per pump sold
Month
t
L
K
Q
P
Oct-15
1
120
25
1150
$438.93
Nov-15
2
122
25
1170
$437.88
Dec-15
3
118
26
1160
$438.46
Jan-16
4
110
26
1122
$440.14
Feb-16
5
116
24
1128
$439.96
Mar-16
6
120
24
1146
$439.01
Apr-16
7
124
27
1193
$436.90
May-16
8
125
27
1202
$436.38
Jun-16
9
130
28
1235
$434.92
Jul-16
10
127
28
1219
$435.58
Aug-16
11
128
27
1216
$435.85
Sep-16
12
136
27
1250
$434.09
Oct-16
13
140
27
1265
$433.54
Nov-16
14
135
28
1255
$433.85
Dec-16
15
130
28
1233
$435.05
Jan-17
16
135
29
1264
$433.43
Feb-17
17
128
29
1235
$434.95
Mar-17
18
138
30
1286
$432.39
Apr-17
19
145
30
1315
$431.19
May-17
20
141
28
1282
$432.58
Jun-17
21
134
29
1260
$433.78
Jul-17
22
140
29.0
1290
$432.20
Aug-17
23
142
30.0
1300
$431.89
Sep-17
24
146
30.0
1324
$430.72
1. Type the OLS log-linear regression production function,
with t-statistics in parentheses below each of the three coefficients.
Round coefficients to 4 decimal places, and round t-statistics to 2 decimal places.
ln Q = # + # ln L + # ln K
(#) (#) (#)
Month
t
L
K
Q
P
Oct-15
1
120
25
1150
$438.93
Nov-15
2
122
25
1170
$437.88
Dec-15
3
118
26
1160
$438.46
Jan-16
4
110
26
1122
$440.14
Feb-16
5
116
24
1128
$439.96
Mar-16
6
120
24
1146
$439.01
Apr-16
7
124
27
1193
$436.90
May-16
8
125
27
1202
$436.38
Jun-16
9
130
28
1235
$434.92
Jul-16
10
127
28
1219
$435.58
Aug-16
11
128
27
1216
$435.85
Sep-16
12
136
27
1250
$434.09
Oct-16
13
140
27
1265
$433.54
Nov-16
14
135
28
1255
$433.85
Dec-16
15
130
28
1233
$435.05
Jan-17
16
135
29
1264
$433.43
Feb-17
17
128
29
1235
$434.95
Mar-17
18
138
30
1286
$432.39
Apr-17
19
145
30
1315
$431.19
May-17
20
141
28
1282
$432.58
Jun-17
21
134
29
1260
$433.78
Jul-17
22
140
29.0
1290
$432.20
Aug-17
23
142
30.0
1300
$431.89
Sep-17
24
146
30.0
1324
$430.72
Explanation / Answer
Use command in STATA tsset t gen ln_Q = log(q) gen ln_L =log(l) gen ln_K =log(k) reg ln_Q ln_L ln_K Results lnQ = 4.08 + 0.4668*lnL + 0.2278*lnK (137.36) (45.40) (19.89)