CHAPTER 16
Exercise Solutions
The authors produced these solutions. They will be independently checked and reformatted in the future. We urge
instructors to download them again next term.
1
, Chapter 16, Exercise Solutions, Principles of Econometrics, 5e 2
EXERCISE 16.1
(a)
Using the logit estimates, the probability of a person choosing automobile transportation given
that DTIME = 1 is
Λ( γ 1 + γ 2 DTIME ) = Λ(−0.2376 + 0.5311× 1) = 0.5729
(b)
Using the probit estimates, the probability of a person choosing automobile transportation
given that DTIME = 1 is
Φ(β 1 + β 2 DTIME ) = Φ ( −0.0644 + 0.3000 × 1) = Φ ( 0.2356 ) = 0.5931
There is very little difference between the logit and probit predicted probabilities. We have
used computer software for normal cdf.
(c)
The logit marginal effect is
dp d Λ(l ) dl
= ⋅ = λ( γ1 + γ 2 x) γ 2 , where l = γ1 + γ 2 x
dx dl dx
The logistic pdf from (16.16) is
λ ( l ) = ( e − l ) (1 + e − l )
2
Given that DTIME = 3, the marginal effect of an increase in DTIME using the logit estimates
is
dp
= λ( γ 1 + γ 2 30) γ 2 = λ(1.3557)0.5311 = ( 0.1629396 ) 0.5311 = 0.086537
dx
The estimated linear probability model is in Example 16.2. The marginal effect is the estimated
slope of 0.0703, which is a bit smaller than the logit estimate. But the important point is that
for the linear probability model the marginal effect is constant and doesn’t depend on the
existing commute time.
Copyright © 2018 Wiley
, Chapter 16, Exercise Solutions, Principles of Econometrics, 5e 3
(d)
For this exercise DTIME = ( BUSTIME − AUTOTIME ) 10 = −50 10 = −5 .
The logit estimate is
dp
= λ( γ 1 + γ 2 × −5) γ 2 = λ(−2.8931)0.5311 = ( 0.04974 ) 0.5311 = 0.02642
dx
The probit estimate is
dp
= λ (β 1 + β 2 × −5)β 2 = φ(−1.5644) ( 0.3) = 0.035204
dx
Copyright © 2018 Wiley
Exercise Solutions
The authors produced these solutions. They will be independently checked and reformatted in the future. We urge
instructors to download them again next term.
1
, Chapter 16, Exercise Solutions, Principles of Econometrics, 5e 2
EXERCISE 16.1
(a)
Using the logit estimates, the probability of a person choosing automobile transportation given
that DTIME = 1 is
Λ( γ 1 + γ 2 DTIME ) = Λ(−0.2376 + 0.5311× 1) = 0.5729
(b)
Using the probit estimates, the probability of a person choosing automobile transportation
given that DTIME = 1 is
Φ(β 1 + β 2 DTIME ) = Φ ( −0.0644 + 0.3000 × 1) = Φ ( 0.2356 ) = 0.5931
There is very little difference between the logit and probit predicted probabilities. We have
used computer software for normal cdf.
(c)
The logit marginal effect is
dp d Λ(l ) dl
= ⋅ = λ( γ1 + γ 2 x) γ 2 , where l = γ1 + γ 2 x
dx dl dx
The logistic pdf from (16.16) is
λ ( l ) = ( e − l ) (1 + e − l )
2
Given that DTIME = 3, the marginal effect of an increase in DTIME using the logit estimates
is
dp
= λ( γ 1 + γ 2 30) γ 2 = λ(1.3557)0.5311 = ( 0.1629396 ) 0.5311 = 0.086537
dx
The estimated linear probability model is in Example 16.2. The marginal effect is the estimated
slope of 0.0703, which is a bit smaller than the logit estimate. But the important point is that
for the linear probability model the marginal effect is constant and doesn’t depend on the
existing commute time.
Copyright © 2018 Wiley
, Chapter 16, Exercise Solutions, Principles of Econometrics, 5e 3
(d)
For this exercise DTIME = ( BUSTIME − AUTOTIME ) 10 = −50 10 = −5 .
The logit estimate is
dp
= λ( γ 1 + γ 2 × −5) γ 2 = λ(−2.8931)0.5311 = ( 0.04974 ) 0.5311 = 0.02642
dx
The probit estimate is
dp
= λ (β 1 + β 2 × −5)β 2 = φ(−1.5644) ( 0.3) = 0.035204
dx
Copyright © 2018 Wiley
