Demand estimation Early in 1993, the Southeastern Transportation Authority (STA)
ID: 1205859 • Letter: D
Question
Demand estimation
Early in 1993, the Southeastern Transportation Authority (STA), a public agency responsible for serving the commuter rail transportation needs of a large Eastern city, was faced with rising operating deficits on its system. Also, because of a fiscal austerity program at both the federal and state levels, the hope of receiving additional subsidy support was slim.
The board of directors of STA asked the system manager to explore alternatives to alleviate the financial plight of the system. The first suggestion made by the manager was to institute a major cutback in service. This cutback would result in no service after 7:00 pm, no service on weekends, and a reduced schedule of service during the midday period Monday through Friday. The board of STA indicated that this alternative was not likely to be politically acceptable and could only be considered as a last resort
The board suggested that because it had been over five years since the last basic fare increase, a fare increase from the current level of $1 to a new level of $1.50 should be considered. Accordingly, the board ordered the manager to conduct a study of the likely impact of this proposed fare hike.
The system manager has collected data on important variables thought to have a significant impact on the demand for rides on STA. These data have been collected over the past 24 years and include the following variables:
Price per ride (in cents) - This variable is designated P in Table 1. Price is expected to have a negative impact on the demand for rides on the system.
Population in the metropolitan area serviced by STA - It is expected that this variable has a positive impact on the demand for rides on the System. This variable is designated T in Table 1
Disposable per capita income - This variable was initially thought to have a positive impact on the demand for rides on STA This variable is designated I in Table 1
Parking rate per hour in the downtown area (in cents) this variable is expected to have a positive impact on demand for rides on the STA. It is designated H in Table 1.
Table 1
Year
Weekly Riders (Y) (X1,000)
Price (P) per Ride
Population (T) (X1,000)
Income (I)
Parking Rate (H) (Cents)
1966
1,200
15
1,200
2,900
50
1967
1,190
15
1,790
3,100
50
1968
1,195
15
1,780
3,200
60
1969
1,110
25
1,778
3,250
60
1970
1,105
25
1,750
3,275
60
1971
1,115
25
1,740
3,290
70
1972
1,130
25
1,725
4,100
75
1973
1,095
30
1,725
4,300
75
1974
1,090
30
1,720
4,400
75
1975
1,087
30
1,705
4,600
80
1976
1,080
30
1,710
4,815
80
1977
1,020
40
1,700
5,285
80
1978
1,010
40
1,695
5,645
85
1979
1,010
40
1,695
5,800
100
1980
1,005
40
1,690
5,900
105
1981
995
40
1,630
5,915
105
1982
930
75
1,640
6,325
105
1983
915
75
1,635
6,500
110
1984
920
75
1,630
6,612
125
1985
940
75
1,620
6,883
130
1986
950
75
1,615
7,005
150
1987
910
100
1,605
7,234
155
1988
930
100
1,590
7,500
165
1989
933
100
1,595
7,600
175
1990
940
100
1,590
7,800
175
1991
942
100
1,600
8,000
190
1992
955
100
1,610
8,100
200
The transit manager has decided perform a multiple regression on the data to deter mine the impact of the rate increase.
QUESTIONS I
1. What is the dependent variable in this demand study?
2. What are the independent variables?
3. What are the expected signs of the variables thought to affect transit ridership on STA?
4. Using a multiple regression program available estimate the coefficients of the demand model for the data given in Table 1
5. Provide an economic interpretation for each of the coefficients in the regression equation you have computed.
6. What is the value of the coefficient of determination? How would you interpret this result?
7. Calculate the price elasticity using 1992 data.
8. Calculate the income elasticity using 1992 data.
9. If the fare is increased to $1.50, what is the expected impact on weekly revenues to the transit system if all other variables remain at their 1992 levels?
Question II
Repeat the problem using Logarithmic transformation
Year
Weekly Riders (Y) (X1,000)
Price (P) per Ride
Population (T) (X1,000)
Income (I)
Parking Rate (H) (Cents)
1966
1,200
15
1,200
2,900
50
1967
1,190
15
1,790
3,100
50
1968
1,195
15
1,780
3,200
60
1969
1,110
25
1,778
3,250
60
1970
1,105
25
1,750
3,275
60
1971
1,115
25
1,740
3,290
70
1972
1,130
25
1,725
4,100
75
1973
1,095
30
1,725
4,300
75
1974
1,090
30
1,720
4,400
75
1975
1,087
30
1,705
4,600
80
1976
1,080
30
1,710
4,815
80
1977
1,020
40
1,700
5,285
80
1978
1,010
40
1,695
5,645
85
1979
1,010
40
1,695
5,800
100
1980
1,005
40
1,690
5,900
105
1981
995
40
1,630
5,915
105
1982
930
75
1,640
6,325
105
1983
915
75
1,635
6,500
110
1984
920
75
1,630
6,612
125
1985
940
75
1,620
6,883
130
1986
950
75
1,615
7,005
150
1987
910
100
1,605
7,234
155
1988
930
100
1,590
7,500
165
1989
933
100
1,595
7,600
175
1990
940
100
1,590
7,800
175
1991
942
100
1,600
8,000
190
1992
955
100
1,610
8,100
200
Explanation / Answer
(1) Dependent variable: demand for rides
(2) Independent variables: Price per ride (in cents) , Population in the metropolitan area, Disposable per capita income , Parking rate per hour
(3) Price per ride (in cents) - negative impact
Population in the metropolitan area serviced by STA - positive impact
Disposable per capita income - positive impact
Parking rate per hour in the downtown area - positive impact
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