5. 5
$ 50,000
$ 55,000
$ 60,000
$ 65,000
$ 70,000
$ 75,000
$ 80,000
$ 85,000
$ 90,000
$ 95,000
2002 2004 2006 2008 2010 2012 2014 2016
Millionsofdollars
Source: US. Bureau of the Census
US Total Construction Spending:
Highway and street
7. Literature
• Downs-Thomson paradox
▫ Downs (1962). Thomson (1977). Mogridge (1997)
• Hypothesis: in equilibrium car and bus generalized
cost will be equal (perfect substitutes)
• Consequence: increasing road capacity makes
congestion worse
• Graphically..
7
11. Literature
• Duranton & Turner (2011. AER): empirical
▫ Increasing lane kilometers leads to a proportional
increase of veh-km travelled.
▫ Elasticity is 1
▫ Holds for interstate travel
• Hsu & Zhang (2014. JUrbanE)
▫ The elasticity for Japan is 1.2 – 1.3
11
12. Literature
• Issues with this approach
▫ Aggregate (space and time of day).
▫ No distinction between increasing capacity of current
roads or extending the length of the roads
▫ It does not allow for comparing policies and assessing
the social benefit
12
18. The theory model
𝑃" − 𝑃' = 𝑌"
𝜕𝑡"
𝜕𝑌"
+ 𝑌'
𝜕𝑡'
𝜕𝑌"
LMNOP
− 𝑌'
𝜕𝑡'
𝜕𝑌'
+
𝜕𝑡1
𝜕𝑌'
MNOQR"NOSQ
+ 𝑌"
𝜕𝑡"
𝜕𝑌'
+ 𝜀
𝜕𝑡1
𝜕𝑌'
LMNOQ
• Only the price difference can be identified here, but separately in
the simulation model
• Interpretation as in separate models
18
19. The theory model
𝑃" − 𝑃' = 𝑌"
𝜕𝑡"
𝜕𝑌"
+ 𝑌'
𝜕𝑡'
𝜕𝑌"
LMNOP
− 𝑌'
𝜕𝑡'
𝜕𝑌'
+
𝜕𝑡1
𝜕𝑌'
MNOQR"NOSQ
+ 𝑌"
𝜕𝑡"
𝜕𝑌'
+ 𝜀
𝜕𝑡1
𝜕𝑌'
LMNOQ
• Only the price difference can be identified here, but separately in
the simulation model
• Interpretation as in separate models
19
20. The theory model
𝑃" − 𝑃' = 𝑌"
𝜕𝑡"
𝜕𝑌"
+ 𝑌'
𝜕𝑡'
𝜕𝑌"
LMNOP
− 𝑌'
𝜕𝑡'
𝜕𝑌'
+
𝜕𝑡1
𝜕𝑌'
MNOQR"NOSQ
+ 𝑌"
𝜕𝑡"
𝜕𝑌'
+ 𝜀
𝜕𝑡1
𝜕𝑌'
LMNOQ
• Only the price difference can be identified here, but separately in
the simulation model
• Cross-congestion effects.
20
21. The theory model
𝑃" − 𝑃' = 𝑌"
𝜕𝑡"
𝜕𝑌"
+ 𝑌'
𝜕𝑡'
𝜕𝑌"
LMNOP
− 𝑌'
𝜕𝑡'
𝜕𝑌'
+
𝜕𝑡1
𝜕𝑌'
MNOQR"NOSQ
+ 𝑌"
𝜕𝑡"
𝜕𝑌'
+ 𝜀
𝜕𝑡1
𝜕𝑌'
LMNOQ
• Only the price difference can be identified here, but separately in
the simulation model
• Bus stop and payment technology effects
21
22. The theory model
• Bus corridors
• 𝑃" − 𝑃' = 𝑌"
TUP
TVP
+ 𝑌'
TUQ
TVP
LMNOP
− 𝑌'
TUQ
TVQ
+
TUW
TVQ
MNOQR"NOSQ
+ 𝑌"
TUP
TVQ
+ 𝜖
TUW
TVQ
LMNOQ
• Time functions 𝑡" and 𝑡' are different with bus lanes
22
23. The theory model
• Increasing road capacity makes some terms less important. If road
capacity is very large:
• 𝑃" − 𝑃' = 𝑌"
TUP
TVP
+ 𝑌'
TUQ
TVP
LMNOP
− 𝑌'
TUQ
TVQ
+
TUW
TVQ
MNOQR"NOSQ
+ 𝑌"
TUP
TVQ
+ 𝜖
TUW
TVQ
LMNOQ
• 𝑃" ≈ 𝑃' −
TUW
TVQ
𝑌' + 𝜖𝑌"
• Hence, for any given PB, the optimal congestion toll may be very small.
Even hit zero. It depends heavily on 𝑡1
• => importance BS&P technology
23
24. The simulation model
• Based on Basso and Silva (2014, AEJ – Economic Policy)
• Total elastic demand. Two periods (peak and off-peak) with
intertemporal elasticity. Marginal cost of public funds
• We use the best possible engineering functions available for
𝑡", 𝑡', 𝑡1, ε and bus costs. Two bus stop technologies
(Tirachini, 2014 TR-A).
▫ Partial eq. (no housing. no labor) => fixed travel distance.
shorter run (than e.g. Duranton and Turner).
▫ Possibly more favorable for road expansion as induced
demand could be higher
24
26. • Real data
• Congested baseline scenario: 13-18 km/hr
• Two BS&P Tech: front door boarding only. Similar initial
speeds.
▫ Inefficient: (A) payment in cash. 1 berth
▫ Efficient: (B) contactless card. 2 berths.
• Bus corridor: at most one lane.
26
Data european city
27. 27
Efficiency Results
Scenario REF SUBref100 CONref DLref CAP SUB100 CON DL
Social Benefit 0 3550 6725 5179 5033 5998 6746 7376
CS change 0 37130 28672 33954 42207 44624 29808 42899
Bus fare peak 0.19 0.00 0.16 0.16 0.17 0.00 0.16 0.16
Bus fare off-peak 0.19 0.00 0.16 0.16 0.17 0.00 0.16 0.16
Car toll peak 0.00 0.00 0.62 0.00 0.00 0.00 0.58 0.00
Car toll off-peak 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Frequency peak 25 51 50 63 37 47 50 62
Frequency off-peak 25 30 24 44 24 28 24 39
Bus size 39 35 51 47 37 40 50 39
Car peak speed 13 15 22 13 21 21 22 18
Bus peak speed 11 12 15 19 16 15 15 21
Car off-peak speed 41 41 41 36 47 45 42 50
Bus off-peak speed 26 25 24 26 28 26 25 28
Peak share 41 43 41 43 45 45 42 45
Off-peak share 49 48 49 48 46 46 49 46
No Travel share 9 9 9 9 8 8 9 8
Car share | peak 85 74 61 57 81 74 63 66
Bus share | peak 15 26 39 43 19 26 37 34
Car share | offpeak 84 76 83 79 83 77 83 81
Bus share | offpeak 16 24 17 21 17 23 17 19
Bus stops per km 2 2 2 3 2 2 2 3
Number of bus lanes 0 0 0 1 0 0 0 1
Road Capacity 3600 3600 3600 3600 4662 4355 3706 4446
3 Lanes – BS&P Tech A