UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
Homework 18 Solutions
Multiple Choice
1
2
3
4
5
6
7
8
C
D
D
A
D
B
B
B
9
10
11
12
13
14
15
16
A
E
B
A
B
omitted
omitted
A
17
18
19
20
21
22
23
24
A
I
C
D
C
F
E
G
25
26
27
28
29
30
31
32
B
B
B
C
D
D
A
C
33
34
35
36
37
38
39
40
D
B
3,2,4,1
B
C
E
C
C
41
42
43
44
45
46
47
48
49
50
51
52
F
B
E
C
B
E
3,4,2,1
B
D
D
G
D
Short Answer / Calculation Problems
1) Suppose you are estimating a Probit model and you would like to do a Likelihood Ratio (LR) test to determine the
statistical significance of the model as a whole. You have the following information n = 70, k = 6, P = 0.62 and
ln(LU) = -12.43.
(a) What are the null and alternative hypotheses for this test?
(b) Calculate the value of ln(LR) for this test. SHOW YOUR WORK.
(c) Calculate the value of LRtest for this test. SHOW YOUR WORK.
(d) Calculate the value of LRcritical for this test for a significance level of α = 0.05. SHOW YOUR WORK.
(e) What is the result of the LR test for a significance level of α = 0.05? SHOW YOUR WORK.
(a) H0: all β's are zero
H1: one or more of the β's is not zero
(b) ln(LR) = n[P*ln(P) + (1-P)*ln(1-P)] = 70[0.62*ln(0.62) + (1-0.62)*ln(1-0.62)] = - 46.4845
(c) LRtest = 2·ln(LU/LR) = 2·[ln(LU) – ln(LR)] = 2·[(-12.43) – (- 46.4845)] = 68.11
(d) LRcritical = 11.0705 (from chi-square table using k-1=5 and α = 0.05)
(e) Since LRtest > LRcritical, reject H0 and accept H1.
2) For the problem above, calculate the value of McFadden’s R2? SHOW YOUR WORK
R2McFadden = 1 – (ln(LU)/ln(LR)) = 1 – [(-12.43)/(-46.4845)] = 0.7326