1
Research Methods in Economics
ECO 4451
2
Introduction
y
There might be consequences to adding variables
to a model
“Multicollinearity” is high correlation involving two or
more IVs
y
1. One IV influences another IV
y
2. Two or more IVs influence (or influenced by) a third
IV
Slide # 3
Multicollinearity
y
Consequences
y
1. Can drastically alter results from one model to another
y
2. Can cause problems in interpreting results
Slide # 4
Do Market Size and Wins Affect NBA Teams’ Profits?
Profit
Market Size
Wins
33.4
3
57
22.0
3
63
16.0
3
46
8.7
2
42
5.4
2
44
4.7
2
55
1 5
1
35
Slide # 5
See regression output for multicollinearity.
-1.5
-2.1
1
13
-4.0
1
28
NOTE: NBA market size = 3 for large, 2 for medium, 1 for small
NOTE: Don't use this approach for measuring market size.
Use a better measure like population.
Profit is in millions of $.
Example
Where
PROFIT i
l
fi (
M)
PROFIT =
β
0
+
β
1
MKTSIZE +
β
2
WINS+
μ
y
PROFIT is annual team profit ($1M)
y
MKTSIZE = 3 for large, 2 for medium,
1 for small
y
WINS is no. of wins in one season
Slide # 6

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2
Variables
A
B
C
Constant
‐
17.16
‐
16.74
‐
17.06
(0.009)
(0.10)
(0.03)
MKTSIZE
13.17
13.28
(
6)
(
)
Example (cont.)
(0.0006)
(0.02)
WINS
0.61
‐
.008
(0.02)
(0.98
)
Slide # 7
(p-values in parentheses)
Variables
A
B
C
Constant
‐
17.16
‐
16.74
‐
17.06
(0.009)
(0.10)
(0.03)
MKTSIZE
13.17
13.28
(
6)
(
)
Examine t-stat p-values
Models A & B vs. model C
(0.0006)
(0.02)
WINS
0.61
‐
.008
(0.02)
(0.98
)
Slide # 8
(p-values in parentheses)
Variables
A
B
C
Constant
‐
17.16
‐
16.74
‐
17.06
(0.009)
(0.10)
(0.03)
MKTSIZE
13.17
13.28
Examine coefficient values
Models A & B vs. model C
(0.0006)
(0.02)
WINS
0.61
‐
.008
(0.02)
(0.98
)
Slide # 9
(p-values in parentheses)
Example (cont.)
y
Point
y
1.
Observed changes across models due to
high correlation/multicollinearity
between WINS & MKTSIZE
y
correlation = 0.835
Slide # 10
Note
y
1. High correlation among IVs BAD
y
2. High correlation between IV, DV
GOOD
Slide # 11
Exact Multicollinearity
y
A.
Definition
y
1. Two or more IVs perfectly
(or nearly perfectly)
correlated
y
2 What would be values of correlation coefficients?
2. What would be values of correlation coefficients?
Slide # 12