SD USAY
T07017815/1973
4349ONOMETRIC ANALYSIS OF THE AN EC EDMONTON FINANCE-DE
AN ECONOMETRIC ANALYSIS OF THE DETERMINANTS OF DEMAND FOR LOCAL TRANSIT IN EDMONTON,
1961 - 1970
TIE CITY OF EDMONTON
4400.8a .E3 1973
ECONOMIC STUDIES REPORT NO. 1
AN ECONOMETRIC ANALYSIS OF THE DETERMINANTS OF DEMAND FOR LOCAL TRANSIT IN EDMONTON, 1961 - 1970
Tien-Jong Huang, Ph.D. March, 1973.
Economic Studies and Fiscal Planning Branch, Finance Department, The City of Edmonton.
TABLE OF CONTENTS PAGE
I.
INTRODUCTION
1
METHODOLOGY
3
II. THE THEORETICAL MODEL
5
III.STATISTICAL RESULTS
9
IV. PROJECTIONS OF THE PAST AND THE FUTURE TO 1%0 V.
CONCLUSIONS FOOTNOTES
14 23
25
BIBLIOGRAPHY
27
APPENDIX
28
AN ECONOMETRIC ANALYSIS OF THE DETERMINANTS OF DEMAND FOR LOCAL TRANSIT IN EDMONTON, 1961 - 1970
by
Tien-Jong Huang
Introduction
The operation of the Edmonton Transit System brought about a large deficit every year in the past decade. These deficits added a tremendous financial burden to the City and densified its financial crisis. A lot of proposals have been made by various departments and people concerned in order, on one hand, to reduce the deficit, and, on the other, to improve the quality of service for the residents of each area. It was suggested by some people, for instance, that an increase in the transit fare rate is necessary in order to enlarge the total revenue of the System and to bring down its deficit. To the contrary, other people argued against this proposal, based upon the reason that an increase in the transit fare rate would result in a redistribution of the real community income against the low-income residents, an unjust
1
consequence.
It is a fundamental economic principle that a change in the total revenue of the System as a result of a change in the transit fare rate depends completely on the magnitude of the price elasticity in the demand for the local transit. The total revenue will increase with a rise in the fare rate if the price elasticity is smaller than one (i.e., the demand is inelastic); conversely, the total revenue will fall with a rise in the fare rate if the price elasticity is greater than one (i.e., the demand is elastic). The price elasticity should
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therefore be determined before the effect of a change in the transit fare rate on the total revenue can be known. Fortunately, the price elasticity can be estimated from the historical data, employing a quantitative study on the demand for the local transit. In addition to the transit fare rate, the demand for the local transit relies on other factors, namely, the size of city population, the cost of other transportation facilities, the size of total employment in the city, etc. However, nobody in the past ever studied and tested how these factors influenced the demand for the local transit in Edmonton. It can be justified that determination of the variables to be included in the demand function for the local transit is important both in the financial planning and in the transportation planning. Different from the private sector, public sector is principally people-oriented rather than profit-oriented.
Supply of public
services is basically determined by the demand of the community population for the services. A people-supported government must provide in one way or another with those services which are needed by their population. The distribution of the limited financial resources among different types of services should also be based upon the criterion that a priority is always given to the kind of service which is needed most and urgently by the population. The demand of the population in the future must be first taken into consideration before a planning for the future is to be implemented. The demand cannot, however, be accurately forecasted without a priori knowledge of the factors which affect the demand. It is therefore critical that the determinants of the people's demand must be decided and made known in any planning of a project.
- 3 -
Local transportation is one of public services, the above statements are, of course, also feasible. Therefore, the variables influencing the demand for the local transit in Edmonton should be studied if we expect to have a satisfied transportation planning for Edmonton and want to see the deficit of the Transit System reduced. This paper is composed of five sections. The first section deals with the methodology employed, and the second section with the assumptions used in our demand functions. In the third section the statistical results are presented, and in the fourth section the goodness of the model used for forecasting future demand is discussed, and a projection of the number of total passengers through the decade of 1970 is made. Finally, a conclusion is reached.
I. Methodology Our analysis will be discussed in two fashions. The first one is the investigation of the aggregate demand for the local transit, and the second is the examination of the component demand for the transit. Based on the account kept by the Edmonton Transit System, the total passengers were segregated into four components: cash passengers, ticket passengers, pass passengers and student passengers. Since each component has its own different feature and may be influenced by different exogenous variables, it becomes necessary to analyse each component separately. In doing so, a demand function was constructed for each component in order to track the different factors embodied in different components. The record of the Transit System which ยงegregat,e the total passengers has made this component analysis possible.
- 4 -
The number of passengers for each component was recorded monthly. A summation of the monthly data for each year gives us the annual data which was employed in this study. On the other hand, an aggregate demand function was also built to reflect the overall demand for the local transit and to catch the important exogenous factors determining the overall demand. For the total passengers, the cash and the ticket components, the period under study was from 1961 to 1970; for the pass component, it was from 1962 to 1970; and for the student component, it was from 1965 to 1972. The decision to use a different time span for each item is purely determined by the availability of data required. Note that the public pass was first introduced in June 1962, and the student pass was not used until October 1962 for university students and until October 1964 for the Public and Separate School students. Both the years 1971 and 1972 were not considered except in the student component because the data for per capita income which was thought to be important was not available for the two years. The demand functions were formulated in such a way that the best fit can be obtained, and the percentage change of the demand resulting from a one per cent change in one and only one of the explanatory variables included in the function can be simultaneously determined. In other words, the demand functions were expressed linearly in logarithm. Econometrically, we employed the multiple regression analysis to relate our demand for the local transit with the selected explanatory variables, and adopted the method of ordinary least squares to estimate all the parameters in the regressions. The coefficients of the explanatory variables in each regression were tested for their statistical
-5 -
significance using the Student's "t" test.
The coefficient of determination, showing the percentage of the total variance of the demand for the local transit explained by all the explanatory variables included in the regression, was computed and tested for its statistical significance at least at the five per cent level using the Fisher's "F" test.
II. The Theoretical Model A. The Aggregate Demand Function It seems to be reasonable to assume that as the size of city population increases, the demand for the local transit will also increase. This reflects that the city population size has a positive effect on the total number of passengers. Similarly, a rise in the total number of employees in the city is expected to increase the aggregate demand for the local transit. It is known that a rise in the per capita income of the city population will raise the purchasing power of the population which, in turn, will increase their demand for consumer goods including the local transit. As a result, the total number of transit passengers will be up with an increase in the per capita income. The habit persistence postulate in the consumer theory tells us that people used a special type of good or service to satisfy their need last year are very likely to use the same type of good or service 2 to satisfy the same kind of need this year.
This postulate, as applied
to our study, shows that people used the transit for their transportation are likely to keep using it. As a consequence, the total number of
transit passengers in this year would increase with an increase in the total number of passengers in the frevious year. Furthermore, a rise in the transit fare rate would produce a negative effect on the use of the local transit. The demand for the transit would therefore decrease as a result of a rise in the transit fare. Not only a rise in the current year's fare but also a rise in the previous year's fare will, ceteris paribus, bring about a fall in the total number of transit passengers. Conversely, an increase in the cost of other transportation would encourage people to use the public transit and therefore raise up the total number of transit passengers. However, the total number of automobiles registered in the city may have a negative effect on the use of transit as a means of transportation. By taking into consideration all the factors presented above, the demand function for the transit in Edmonton can be mathematically expressed as follows: P = F(N, Y, R, R_/, C, P_1, E, A) with FN > 0, Fy > 0, FR < 0, FR_i < 0, Fc > 0, FE _1 > 0, FE > 0, and F < 0â&#x20AC;˘ A which shoWJs that demand for the local transit in Edmonton (P) is a function of the city population size (N), the per capita income of the city (Y), the transit fare rates of the current year (R) and of the previous year (R_1), the total cost of other transportation (C), the total number of transit passengers in the previous year (P_1), the total number of employees in the city (E) and the total number of automobiles registered in the city (A). The following Cobb-Douglas form is employed to fit the demand function,
al a2 a3 45 a6 a7 a8 P = a N Y R R C P E A o -1 -1
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where a.s (i = 0, 1,
8) are the parameters to be estimated and
tested. a2 is the so-called income elasticity, a3 the short-run price elasticity and a the long-run price elasticity. After converted into 4 a logarithmic form, the demand function becomes
log P = log a + a Log N + a2 log Y + a3 log R + a4 log R-1 l o + a5 log C + a6 log P 1 + a7 log E + a8 log A.
This is a form of linearity such that the ordinary least squares is eligible to be adopted for the estimation of the coefficients.
B. The Component Demand Functions As described in the previous section, the total transit passengers is composed of
four components. Since each component
is embodied with different nature, a demand function is needed for each component. Nevertheless, the demand functions for the cash, ticket and pass components have the same form as the aggregate demand function, and most of the explanatory variables appearing in the aggregate demand function are also important in explaining the variations of the three components. For instance, an increase in the city population size, or in the total number of employees in the city, or in the per capita income, or in the other transportation costs may also pull up the total number of passengers in each of the three components. In addition, there would exist a strong substitution among the three components. A change of the transit fare rate in any of the three components would cause a shift of riders among the three components. In other words, an increase in the cash fare rate would encourage riders to buy tickets or passes rather than pay cash. Consequently, the number of
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cash passengers would fall and the numbers of ticket and pass passengers would rise. Hence, both the cash rate and the ticket rate should be 3 included in their demand functions . As discussed before, the habit persistence may also play a significant role in the fluctuation of the demand of each components. A change in the total number of automobiles registered may cause an opposite change in the demand as well. The demand function can therefore be expressed as: Pi = C. (N, Y, RC, RC /, RT, RT_,, P1_1, E, C)
where Pi (i = C, T, P) is the number of passengers of the i-th component, RC the cash fare rate of the current year, RT the ticket fare rate of the current year, RC_i the cash fare rate of the previous year, RT..4 the ticket fare rate of the previous year and Pi_i is the number of passengers of the i-th component in the previous year. If the Cobb-Douglas form is employed, we have b b b b b b b b b b 10 9 8 4 5 6 7 l 2 3 RT RT Pi E C C Pi = bN Y RC RC -1 -1 o -1
where b.'s
= 0, 1,
,10) are the parameters to be estimated and
tested. Converting the above form into the logarithmic, we obtain
log Pi = log b
o
+ 1)1 log N + b2 log Y + b3 log RC + b4 log RC -1
+ b5 log RT + b6 log RT_
J_
+ b7 log Pi_, + b8 log E
+ b9 log C + 1310 log A
Again, this is a linear form, the ordinary least squares can be applied. Different from the above three components, the student passengers depend mainly on the total number of student enrolments in Edmonton which includes the numbers of student enrolments in the University of Alberta, in the Northern
-9-
Alberta Institute of Technology, in the Public and in the Separate School Districts. Therefore, the demand function can be simply expressed as Sc PS = c o or
1
log PS = log c + cl log S o
where PS is the number of student passengers and S the total number of student enrolments.
III. Statistical Results A computer program called "MREG" written by the General Electric Company was used to estimate and to test the demand functions presented in the previous section. While not all the explanatory variables included in each function turned out to be statistically significant, all the possible combinations of the variables were run and the best result was chosen for 4 each function. These chosen results are shown as follows : 5 1. The Total Passengers :
log P = -0.2632 + 0.3667 log N + 0.8730 log Y - 0.2354 log R (3.5337)
(4.7263)
(3.1046)
-0.1765 log R_ /. (2.4531) 2 R = 0.9909
F = 136.5906 (100%), 4,5
d = 2.3308
2. The Cash Passengers:
log PC = 5.4192 - 2.3654 log RC - 3.8924 log RC...1 + 1.3634 log RT (2.2776) (2.8303) (2.0096) + 3.0363 log RT_ (3.3240) 2 R = 0.9827
I.
+ 0.3151 log PC_
I.
(2.2063) F5,4 = 45.3812 (99.87%),
d = 2.7391
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3. The Ticket Passengers:
log PT =-O.2243Âą 1.7279 Log RC - 1.5860 lbg RT - 0.3140 log A (3.2707)
(4.6982)
(1.2319)
+ 0.9898 log E + 0.7540 log PT_ I. (2.2767) (5.8743)
2 R = 0.9715,
F
5.4
= 27.3375 (99.66%),
d = 2.4766
4. The Pass Passengers6: log PP = -3.8487 + 5.0258 log RC + 0.3214 log PP_i (10.0676) 2 R = 0.9906
(4.0755) F = 262.9061 (100%), 2.5
d = 2.7065
F = 6.1609 (95.23%), 1.6
d = 1.6908
5. The Student Passengers: log PS = -1.1042 + 0.9183 log S (2.4821) 2 R = 0.5066
(1). In the demand function of the total passengers, only the size of city population, the per capita income, the transit fare rates of the current year and of the previous year were statistically significant at the five per cent level in explaining the variation of the total passengers. 99.09 per cent of the total variance was caused by these four variables during the period 1961 - 1970. The growths of the city population and of the per capita income in the city brought about very significantly an increase in the aggregate demand for the local transit. However, a rise in the transit
fare rate in the current year usually resulted in a fall in the overall demand for the local transit in the same year and in the following year. As reflected in their separate coefficients, while both the short-run and the long-run price elasticities were smaller than one, the former was larger than the latter. This indicates that the short-run effect of a change in the transit fare rate was more significant that the long-run 7 effect. Among the four variables, the per capita income appeared to be the most important factor influencing the overall demand for the local transit. A one per cent increase in the per capita income would give rise to a 0.87 per cent increase in the total passengers; a one per cent growth of the city population would produce a 0.37 per cent increase in the total passengers; and a one per cent increase in the transit fare rate in the current year would cause a 0.24 per cent fall in the same year and a 0.18 per cent fall in the following year in the total passengers. The above statements can be put in a different way. We know that the present pDpulation is approximately 450-thousand persons, the present per capita income $ 7,000 and the present transit average fare 20 cents. If the present city population increases by a thousand persons, the total passengers will increase by 34,400 persons. On the other hand, if the present per capita income is up by $ 100, the total passengers will rise by 524,600 persons. Finally, if the present transit fare is raised by 5 cents, the total passengers will fall by 2,530,550 persons this year and by another 1,897,375 persons next year. (2).
In the case of cash passengers, the cash fare rates and
the ticket fare rates of the current year and of the previous year showed a significant influence. In addition, the number of cash passengers in the preceding year made a contribution to the current year. These five
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variables together explained 98.27 per cent of the total variance in the number of cash passengers. The substitution effect caused by a change in any of the fare rates played a major role in the cash passenger function. rise in the cash fare rate shifted the cash riders to using tickets or passes. Conversely, an increase in the ticket fare rate drove the ticket riders to paying cash. The changes in the fare rates not only had a short-run effect, but they also exerted a long-run effect on the riding pattern. It is worth noting that all the price elasticities were larger than one, indicating the substitution effect among the different riding patterns was very significant. Moreover, the long-run effect of the fare rate change appeared to be more significant than the short-run effect. A one per cent increase in the cash fare rate in the current year would bring down the number of cash passengers by a 2.37 per cent in the same year and by a 3.89 per cent in the following year. To the contrary, a one per cent increase in the ticket fare rate this year would push up the number of cash passengers by a 1.36 per cent in this year and a 3.04 per cent in next year. Obviously, some of the cash passengers formed a habit of continuing paying cash to have a ride. Therefore, if the number of passengers paying cash in the current year was high, the number in the following year tended to be high as well. A one per cent increase in this year would cause a 0.32 per cent increase in next year. (3). As to the ticket passengers, the substitution effect and the habit persistence also played a very significant role. A one per cent rise in the cash fare rate would bring about a 1.73 per cent
- 13 rise in the ticket passengers, and a one per cent increase in the ticket fare rate would result in a 1.59 per cent fall in the ticket passengers. If more riders used tickets in the preceding year, then more riders would also use tickets in this year. A 0.75 per cent increase would be resulted from a one per cent increase in the previous year. As expected, the size of employment in the city made a significant contribution to the number of ticket passengers. A one per cent increase in the former would cause a 0.99 per cent increase in the latter. The total number of automobiles registered in the city also showed somewhat important in the variation of transit passengers using tickets. A one per cent increase in the total number of automobiles would push down a 0.31 per cent fall in the 8 number of ticket passengers . The five explanatory variables together determined 97.15 per cent of the total variance of the ticket passengers. (4). In the case of pass passengers, only the cash fare rate and the habit persistence appeared to be statistically significant at the five per cent level. The cash fare rate, especially, exerted a very significant influence. A one per cent increase in the cash fare rate would give rise to a 5.03 per cent increase in the number of pass passengers. The contribution of the habit persistence was also not negligible. A one per cent higher in the number of pass passengers in the previous year would bring about a 0.32 per cent more in the current year. Both variables together contributed 99.06 per cent of the total variance of the pass passengers in the past decade. (5). As expected, the number of student passengers was mainly determined by the number of student enrolments in the city. As shown in the function, a one per cent increase in the number of student enrolments would result in a 0.92 per cent increase in the number of student passengers. However, the number of student enrolments alone only explained
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50.66 per cent of the total variance of the student passengers, indicating that there still existed other significant factors which also played an important role. These factors might be the size of parking space provided by the universities and the schools, etc. Unfortunately, lack of data made it impossible to have these factors included in our function.
IV. Projections of the Past and the Future to 1980 In order to judge how good is our model for forecasting the number of passengers in the future, we used the model to predict the past period 1961 - 1970, based on the given explanatory variables included in each function. We then compared the predicted values with the actual values and computed the percentage errors. As shown in table 1, the prediction of the number of total passengers was exceptionally good. Thehighest percentage error was only 1.73 per cent in 1963 and the lowest error was as low as 0.05 per cent in 1968. The average absolute percentage error for the period 1961-1970 was merely 0.94 per cent. This shows that the model is well built to reflect the reality, and use of the model to forecast the future will provide us with a relatively high accuracy of the forecasted values. In the case of cash passengers, the average percentage error in predicting the number of cash passengers for the same period, as shown in table 2, was only 1.42 per cent. The highest error was 3.31 per cent in 1965 and the lowest one was 0.09 per cent in 1968. Although the error is slightly higher than the previous function, the demand function for the cash passengers is still very good for forecasting the future. Table 3 presents the actual and the predicted numbers of ticket
- 15 passengers. It shows that the highest error was 3.33 per cent in 1962 and the lowest one was only 0.01 per cent in 1967, with an average error of 0.90 per cent. Again, this function can track with a high accuracy the fluctuation of the number of ticket passengers. In table 4, we find that the prediction error was relatively higher in the case of pass passengers, as compared with the previous three cases. The highest error in this case was 20.65 per cent in 1969 and the lowest one was 0.24 per cent in 1967, with an average error of 6.04 per cent. As expected, the prediction error in the case of student passengers was the highest among all the cases. Table 5 shows that the average prediction error was 7.74 per cent, with the largest error of 23.76 per cent in 1969 and the smallest of 1.64 per cent in 1966. As shown above, the best fitted model which can predict the number of passengers with the smallest error is the demand function of the total passengers. In addition, the tickets were not available any more after June 1972. This would change the structure of the component demand function. We therefore do not have intention here to forecast the number of component passengers for the future. However, we do project the numbers of total passengers through the year 1980. Several assumptions are required in order to forecast the future using our estimated demand function of the total passengers. These assumptions are: (1) from 1973 on, the city population will grow at a constant annual rate of 3 per cent each year; (2) from 1971 on, the average income per tax return in the city will increase at a constant annual rate of 7 per cent each year; and (3) the cash fare rates for both adults and children will increase by 5 cents respectively in 1974, and again by another 5 cents in 1978. Based on these assumptions, the
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resulted values for the three explanatory variables through the year 1980 are shown in columns (1) - (3) of table 6, and the forecasted numbers of total passengers are shown in the last column of the same table. In 1975 the projected number of total passengers is 46,209 thousands persons, a 20 per cent increase from its 1970 level; and in 1980, it is 60,801 thousands persons, a 58 per cent higher than its 1970 level.
TABLE 1 The Total Passengers (thousand persons)
Predicted Value
Absolute % Error
Year
Observed Value
1961
27,161
27,077
0.31
1962
27,849
27,466
1.38
1963
27,049
27,517
1.73
1964
28,049
28,080
0.11
1965
31,567
31,203
1.15
1966
33,119
33,052
0.20
1967
34,434
35,026
1.72
1968
34,889
34,906
0.05
1969
35,196
35,563
1.04
1970
38,466
37,818
1.68
Average
0.94
TABLE 2 The Cash Passengers (thousand persons)
Year
Observed Value
1961
6,507
6,530
0.35
1962
5,882
5,821
1.04
1963
4,987
5,103
2.33
1964
4,678
4,734
1.20
1965
4,799
4,640
3.31
1966
4,621
4,677
1.21
1967
4,649
4,619
0.65
1968
4,544
4,548
0.09
1969
5,612
5,724
2.00
1970
6,242
6,118
2.00
Average
Predicted Value
Absolute % Error
1.42
TABLE 3 The Ticket Passengers (thousand persons)
Year
Observed Value
1961
20,654
20,867
1.03
1962
21,454
20,739
3.33
1963
20,850
21,066
1.03
1964
21,247
21,594
1.63
1965
22,636
22,737
0.44
1966
23,975
23,901
0.30
1967
24,794
24,798
0.01
1968
21,372
21,331
0.19
1969
20,140
20,045
0.47
1970
18,803
18,924
0.64
-
-
0.90
Average
Predicted Value
Absolute % Error
TABLE 4 The Pass Passengers (thousand persons)
Year
Observed Value
Predicted Value
Absolute % Error
1963
806
795
1.36
1964
943
992
5.20
1965
1,059
1,043
1.51
1966
1,103
1,082
1.90
1967
1,263
1,260
0.24
1968
4,988
4,861
2.55
1969
6,263
7,556
20.65
1970
9,560
8,134
14.92
--
--
6.04
Average
TABLE 5 The Student Passengers (thousand persons)
Year
Observed Value
Predicted Value
Absolute % Error
1965
3,073
3,157
2.73
1966
3,420
3,364
1.64
1967
3,728
3,546
4.88
1968
3,985
3,734
6.30
1969
3,182
3,938
23.76
1970
3,861
4,105
6.32
1971
4,451
4,155
6.65
1972
4,541
4,105
9.60
Average
7.74
TABLE 6 Assumptions and Forecasts of the Total Passengers for the Period 1971-1980
City Population (1)
Average Income Per Tax Return (2)
Average Fare Rate (3)
Forecasted Total Passengers
(persons)
(dollars)
(cents)
(thousand persons)
1971
438,155
6,303
18.13
40,190
1972
441,530
6,745
20.00
41,796
1973
454,776
7,217
20.00
44,051
1974
468,419
7,722
25.00
44,823
1975
482,472
8,262
25.00
46,209
1976
496,946
8,841
25.00
49,559
1977
511,854
9,460
25.00
53,147
1978
527,210
10,122
30.00
54,600
1979
543,026
10,830
30.00
56,697
1980
559,317
11,588
30.00
60,801
Year
NOTE: (1) From 1973 on, the population is assumed to grow at a constant annual rate of 3 per cent. (2) From 1971 on, the average income per tax return is supposed to increase at a constant annual rate of 7 per cent. (3) The cash fare rates for both adults and children are assumed to increase by 5 cents in 1974 and by another 5 cents in 1978.
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V. Conclusions The aggregate demand for the local transit in Edmonton was found to be significantly determined by the size of city population, the per capita income in the city, and the transit fare rates of the current year and of the preceding year. If the present city population increases by a thousand persons, the total passengers will increase by 34,400 persons. On the other hand, if the present per capita income is up by $ 100, the total passengers will rise by 524,600 persons. Finally, if the present transit fare is raised by 5 cents, the total passengers will fall by 2,530,550 persons this year and by another 1,897,375 persons next year. In the case of component passengers, the substitution effect among the components of cash, ticket and pass passengers played a crucial role in their demand functions. In addition, the habit persistence was also an important factor in determining their variations. Therefore, in the demand function of cash passengers, the cash fare rates and the ticket fare rates of the current year and the previous year, together with the number of passengers in the previous year, contributed a 98.27 per cent of the total variance. A one per cent increase in the cash rate would cause a reduction in the number of cash passengers by a 2.37 per cent in the current 3ear and by a 3.89 per cent in the following year. To the contrary, a one per cent rise in the ticket fare would result in a rise in the cash passengers by 1.36 per cent in the same year and by 3.04 per cent in the following year.
-24-
So far as the ticket passengers are concerned, a one per cent increase in the cash fare rate would give rise to a 1.93 per cent increase; and, conversely, a one per cent rise in the ticket rate would bring about a 1.69 per cent fall. Furthermore, the size of employment in the city contributed also to the number of ticket passengers. A one per cent increase in the former would pull up a 0.33 per cent increase in the latter. In the case of pass passengers, the principal factor which determined the demand for passes was the cash fare rate. A one per cent increase in the cash fare rate would produce a 5.03 per cent increase in the number of pass passengers. Besides, the formation of a habit also explained significantly the variation of the pass passengers. As to the student passengers, the total student enrolments in the city alone explained a 50.66 per cent of the total variation. The aggregate demand function formulated in this study can track the variation path of the total passengers with a considerable high degree of accuracy. If we use this model to predict the number of total passengers for the past decade, it only produces a prediction error of 0.94 per cent. If we assume a 3 per cent annual growth in the city population, a 7 per cent annual increase in the per capita income in the city, and five cent increases in the transit fare rates both in the year of 1974 and in the year of 1978, the forecasted number of total transit passengers by this model is 46,209 thousands persons in 1975 and 60,801 thousands persons in 1980.
- 25 -
Footnotes
1. See, for example, M.C. Hodgson, The Fiscal Development of the City of Edmonton Since 1946, Unpublished M.A. thesis, University of Alberta, 1965. p.p. 78 - 80. 2. The habit persistencepostulate has been employed as one of the explanatory variables determining the variation of the demand for consumer goods in many studies, e.g., among others, H.S. Houthakker and L.D. Taylor, Consumer Demand in the United States : Analyses and Projections, 2nd edition, Cambridge, Mass: Harvard University Press, 1970. 3. The pass rate is not included because the rate has been kept unchanged since it was introduced the first time. 4. Figures presented in the parentheses under the coefficients are the t values and those following the F values are the confidence levels. Passengers are expressed in thousand persons; the students, the employment and the population are in persons, the per capita income is in dollars, the transit fare rates are in cents, and the cost of transportation is an index in terms of 1961 dollars. 5. Alternatively, if we included the cost of other transportation in the regression and simultaneously used the real per capita income (Yr) rather than the nominal income, the estimated demand function in the total passengers becomes log P = -2.3955 + 0.3624 log N + 1.1151 log Yr - 0.2179 log R (1.6476)
(1.3089)
(3.1502)
-0.1677 log R_1 + 0.6337 log C (1.9220) 2 R = 0.9935
(1.9816) = 122.9449 (99.98%) F 5.4
All the coefficients in the regression show significant at least at the 13 per cent level. It is shown that the cost of the other transportation determined partially the overall demand for the local transit, a one per cent increase in this variable would bring about a 0.63 per cent increase in the demand. 6. Alternatively, if we substituted for the habit persistence variable by the size of employment (total number of income tax returns) in the demand function for passes, we obtained the following regression: log PP = -12.4723 + 5.2084 Log RC + 1.78558 log E (5.0662) (2.1273) 2 R = 0.9703
F = 98.1699 (100%) 2.6
-26-
which reflects that the size of employment is significant at the 5 per cent level in determining the demand for passes. A 1.79 per cent increase would result from a one per cent rise in the size of employment in the city. Because there existed a high correlation between the habit persistence variable and the size of employment, if we included both variables in the regression, as shown in the following, the size of employment became insignificant. log PP = -4.6337 + 4.9476 log RC + 0.1787 log E + 0.3026 log PP...1 (7.8604) 2 R = 0.9907
(0.2608)
(2.6659)
f = 142.6227 (99.98%) 3,5
7. A different finding was obtained by H.S. Houthakker for the local transportation (including street and electric railway and local bus) in the United States. What he found was that while the shortrun price elasticity was smaller than one, the long-run elasticity was greater than one. See H.S. Houthakker and L.D. Taylor, op. cit. 8. The total number of automobiles registered, if incorporated in the rest of equations, either showed insignificant or did not turn out to be a correct sign.
- 27 -
Bibliography Bakker, J.J., Public Transportation in Edmonton, January 1968. Borcherding, T.E. and R.T. Deacon, "The Demand for the Services of Non-Federal Governments", The American Economic Review, December 1972, p.p. 891 - 901. Department of Extension, University of Alberta, The Future of Transportation in Edmonton, 1971. Edmonton Transit System, Annual Report, The City of Edmonton, 1971. Finance Department, The City of Edmonton, Financial Statements and Reports, 1960 - 1972. Hodgson, M.C., The Fiscal Development of The City of Edmonton Since 1946, unpublished M.A. thesis, University of Alberta, 1965. Houthakker, H.S. and L.D. Taylor, Consumer Demand in the United States : Analyses and Projections, 2nd edition, Cambridge, Mass.: Harvard University Press, 1970. Stone, R. and D.A. Rowe, The Measurement of Consumers' Expenditure and Behaviour in the United Kingdom 1920 - 1938, Cambridge: The Cambridge University Press, 1966. Transportation and Engineering Department, The City of Edmonton, General Transportation Plan, 1972.
- 28 APPENDIX A NUMBER OF, PASSENGERS USING EDMONTON TRANSIT SYSTEM BY COMPONENTS 1951 - 1972
Year 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969(1) 1970 1971 1972
Cash
Tickets
Passes
Students
^
7,343,470 6,768,190 6,507,347 5,881,519* 4,987,188 4,678,271 4,799,016 4,621,010 4,648,901 4,544,144* 5,612,010 6,241,639 6,760,521 15,648,308
21,799,427 21,388,656 20,654,023 21,454,097* 20,850,420 21,247,199 22,636,327 23,975,072 24,794,008 21,371,870* 20,139,857 18,802,656 17,971,505,,, 7,563,026â&#x20AC;&#x153;-)
405,100(3) 805,900 942,600 1,058,900 1,103,060 1,262,800 4,987,600 6,262,5001, \ 9,560,477"i 10,727,452 13,356,167
Source: The City of Edmonton, Edmonton Transit System. Note: (1) Strike in August 1969. (2)Tickets were not available after June 1972. (3)Pass was introduced in June 1962. (4)Includes courtesy passes. (5)Student pass was introduced in October 1962. (6)School pupils started to use in October 1964. * Fare changes in the year.
108,360(5) 405,682 1,180,445(6) 3,072,970 3,420,136 3,728,286 3,985,270 3,182,100 3,860,938 4,450,505 4,541,272
Total 36,260,014* 36,221,499 35,869,927* 35,869,477 34,666,598 34,534,500 34,137,948 31,551,502* 29,142,897 28,156,846 27,161,370 27,849,076* 27,049,190 28,048,515 31,567,213 33,119,278 34,433,995 34,888,884* 35,196,467 38,465,710 39,909,983 41,108,773
- 29 APPENDIX B WEIGHTED AVERAGE TRANSIT RATE PER RIDE IN EDMONTON, 1950 - 1972
Unit : Cents Year
Adult
Ticket Rate Children
Average
Adult
Cash Rate Children
Average
Grand Average
1950
5.88
2.50
4.19
10.00
5.00
7.50
5.85
1951
6.49
2.66
4.58
10.00
5.00
7.50
6.04
1952
8.33
3.13
5.73
10.00
5.00
7.50
6.62
1953
9.03
3.13
6.08
10.00
5.00
7.50
6.79
1954
9.09
3.13
6.11
10.00
5.00
7.50
6.81
1955
9.09
3.13
6.11
10.00
5.00
7.50
6.81
1956
9.09
3.13
6.11
10.00
5.00
7.50
6.81
1957
9.09
3.13
6.11
10.00
5.00
7.50
6.81
1958
11.37
3.83
7.60
13.35
8.35
10.85
9.23
1959
12.50
4.17
8.34
15.00
10.00
12.50
10.42
1960
12.50
4.17
8.34
15.00
10.00
12.50
10.42
1961
12.50
4.17
8.34
15.00
10.00
12.50
10.42
1962
13.70
5.56
9.63
18.35
10.00
14.18
11.91
1963
14.29
6.25
10.27
20.00
10.00
15.00
12.64
1964
14.29
6.25
10.27
20.00
10.00
15.00
12.64
1965
14.29
6.25
10.27
20.00
10.00
15.00
12.64
1966
14.29
6.25
10.27
20.00
10.00
15.00
12.64
1967
14.77
6.77
10.77
20.42
10.42
15.42
13.10
1968
20.00
12.50
16.25
25.00
15.00
20.00
18.13
1969
20.00
12.50
16.25
25.00
15.00
20.00
18.13
1970
20.00
12.50
16.25
25.00
15.00
20.00
18.13
1971
20.00
12.50
16.25
25.00
15.00
20.00
18.13
1972
N.A.
N.A.
N.A.
25.00
15.00
20.00
20.00
Sources:
Computed from the data supplied in J.J. Bakker, Public Transportation in Edmonton, January 1968, Appendix 3 and from Edmonton Transit System, The City of Edmonton, Annual Report.
- 30 APPENDIX C EDMONTON STATISTICS USED IN THE ESTIMATION OF THE REGRESSIONS
Year
1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972
veLage money Income Per Tax Return
Average Real Income in 1961 Dollars
City Population
No. of Income Tax Returns
(1)
(2)
(3)
(4)
158,912 169,196 183,411 197,835 209,353 223,549 238,353 252,131 260,733 269,314 276,018 294,967 303,756 311,804 371,265 381,330 393,563 410,105 422,418 435,503 438,155 441,530
79,724 88,258 95,474 102,339 105,969 109,966 117,025 119,676 116,419 120,218 132,560 140,471 144,611 151,130 160,786 180,864 194,078 204,242 219,750 224,934 -
2,693 2,868 2,930 2,808 3,018 3,269 3,357 3,473 3,656 3,620 3,747 3,839 3,968 4,065 4,262 4,501 4,803 5,160 5,560 5,891 -
2,966 3,124 3,213 3,055 3,291 3,530 3,534 3,577 3,715 3,646 3,747 3,801 3,886 3,962 4,094 4,187 4,296 4,422 4,576 4,709 -
Transportation Cost Index 1961 = 100 (5) 82.8 83.0 87.1 88.4 86.4 87.2 92.2 95.9 98.5 100.0 100.0 99.2 98.9 98.6 101.5 103.4 107.8 113.2 117.4 121.3 126.3 -
Employment Index 1961 = 100 (6) 63.5 68.7 77.2 76.4 81.6 91.9 98.6 96.8 100.4 98.6 100.0 104.4 104.7 109.9 117.4 125.6 130.8 136.0 145.1 145.7 -
City Census, except for the year 1971 which is a national census figure. Sources: (1) (2) - (4) Computed from Department of National Revenue, Taxation Statistics. Statistics Canada, Prices & Price Indexes, January 1969, Catalogue No. 8201-508. (5) D.B.S., Review of Employment and Average Weekly Wages and Salaries, Catalogue No. 72-201. (6) D.B.S., The Motor Vehicle Registration, Catalogue No. 53-219 (7)
No. ot Automobiles Registered (7) 43,228 50,973 59,142 63,764 71,869 78,891 83,495 96,154 98,249 9,787 110,285 114,815 118,744 119,435 132,459 160,453 170,489 176,518 184,817 195,080 203,547 -
- 31 APPENDIX D STUDENT ENROLMENTS IN EDMONTON 1950 - 1972
1950 - 1951
University of Alberta (1) 5,114
Public School (2) 19,404
1951 - 1952
4,846
20,737
4,949
1952 - 1953
4,926
22,924
5,449
1953 - 1954
5,116
25,572
1954 - 1955
5,312
1955 - 1956
Academic Year
Catholic School (3) 4,689
NAIT (4) --
Total
2-Year Average
29,207 30,532
29,869
--
33,299
31,915
6,112
--
36,800
35,049
28,225
6,883
--
40,420
38,610
5,773
30,741
7,713
--
44,227
42,323
1956 - 1957
6,360
33,300
8,681
--
48,341
46,284
1957 - 1958
6,921
36,152
9,842
--
52,915
50,628
1958 - 1959
7,964
38,750
10,774
--
57,488
55,201
1959 - 1960
8,983
41,065
11,711
--
61,759
59,623
1960 - 1961
10,015
43,488
13,097
--
66,600
64,179
1961 - 1962
10,741
46,120
14,276
--
71,137
68,868
1962 - 1963
11,627
49,426
16,156
--
77,209
74,173
1963 - 1964
13,192
51,353
17,577
1,500
83,622
80,415
1964 - 1965
13,387
62,019
21,929
2,000
99,335
91,478
1965 - 1966
15,988
64,541
23,532
2,600
106,661
102,998
1966 - 1967
17,865
67,036
25,851
3,300
114,052
110,356
1967 - 1968
19,110
68,973
27,795
3,800
119,678
116,865
1968 - 1969
22,118
71,827
29,394
4,300
127,639
123,658
1969 - 1970
25,544
73,787
30,672
4,400
134,403
131,021
1970 - 1971
26,720
76,606
31,592
4,800
139,718
137,060
1971 - 1972
26,616
75,140
31,501
4,800
138,057
138,887
1972 - 1973
27,010
72,997
31,166
4,900
136,073
137,065
Sources: (1) The University of Alberta, Registrar Office. (2) The Edmonton Public School Board, Assistant Superintendent -- Research & Information. (3) The Edmonton Catholic School Board, Deputy Superintendent Office. (4) The Northern Alberta Institute of Technology, Registrar Office.