Summary CH 2 Essays: Transportation Economics: Analysis of Demand II
Summary CH 2 Essays: Transportation Economics: Analysis of Demand II
Summary CH 2 Essays: Transportation Economics: Analysis of Demand II
Transportation Economics:
Analysis of Demand II
II Discrete Choice
2
Vjn = β1 (c j / w n ) + β 2 t j + β 3 t j
ε
ε 2-ε 1>V1- 2
ε 2-ε 1<V1-
V2
(choose mode 2) V2
(choose mode 1)
ε
1
ε 2-ε 1=V1-V2
Probit distribution:
• For example, suppose there are only two items i=1,2,
and that the utility difference is normally distributed
• Denote the density function for the standard normal
ε −ε
distribution as 2 1
2
1 −x / 2
φ(x) = Prob[ε 2 − ε1 = x ] = e
2π
Buy
good 1
Buy
good 2
V1-V2 0 ε 2-ε 1
Estimation of Probit (cont’d):
• Example, from a sample of 280 urban commuters
choosing between two modes of transportation in
Chicago:
• (1) auto and
• (2) transit
• We use data on mode characteristics (time to travel,
cost, distance), and also the income of consumers.
• The estimated systematic utility function is:
Estimation of Probit (cont’d):
∂Vjn
=−0.0186
∂c j
• So the integral under the normal curve
is re-computed, and we obtain a
downward sloping demand!
Value of Time:
• We can also compute the value of time as:
∂Vjn / ∂t j − 0.00759w n
VOTjn = = = 0.41w n
∂Vjn / ∂c j − 0.0186
• So, ∂X i N
= − ∑ 0.0412 Pin (1 − Pin )
∂ci n =1
wn