a model to estimate the price elasticity of demand for

M.

D.

FIT Z PA T RIC K

B.Sc .(Mel b.), B.Co m.(NewcasUe). Officer-in-C harge, Transport Needs Section, Bureau of Transport Economics

J.

H.

E.

TAP LI N

B.A., M. Ag.Ec. (N.E.), Ph. D. (Cornell) , Director, Bureau of T ransport Economics

A MODEL TO ESTIMATE THE PRICE ELASTICITY OF DEMAND FOR TRANSPORT OF GOODS BY ROAD (Paper No. 922)

Theoretical considerations have been applied to the freight sector of transport in formu lating a demand equation for road transport. A constant elasticity model is employed and it is demonstrated that the direct price elasticity and the cross price elasticity in the two-mode case have approximately the same absolute value. Proxy variables have been employed to overcome the data difficulties which plague research in this sector. To allow for the influence of the intrinsic characteristics of originating cities, dummy variables have been used. Sufficient observations, to ensure reasonable accuracy of estimates, were obtained by using pooled cross-section and time-series data. Some estimation problems introduced by the pooling of data are outweighed by the high significance levels on the unbiased estimates. It is concluded from this analysis that the price elasticity of demand for road transport of goods between major Australian cities is approximately -2. INTRODUCTION 1. The study reported in this paper arose from a need that was felt very soon after the Bureau of Transport Economics began its work. The authors found that calculations of consumers' surplus, needed for a number of evaluations, were severely hampered by the lack of price elasticity estimates. * Whereas a number of such estimates have been made for passenger travel, there has been only a limited amount of work on price elasticities of demand for transport of goods.

2. Scarcity of data has evidently been a major impediment to work on price response in freight shipments. The authors have endeavoured to overcome th is problem by using a proxy variable - recorded truck movements - in place of actual tonnages carried between major centres. Owing to the nature of the data, this analysis treats the commodities carried by road as a single aggregate. FORMULAT ION OF THE MODEL

3. The demand for transport services is derived from the final demand for the goods carried. Consequently, the authors are concerned with the relation between the elasticity of final demand and the derived elasticity of demand for transport to take the goods to their destination. This is the first of two theoretical relationships ' Some w ays o f u sing the concept o f consumers' surplus in tran sport evaluation are discussed by Ne ubur ger

(Ref. 1).

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ELASTICITY OF DEMAND FOR ROAD TRANSPORT

th at have important implications for the formulation of the model. The second is the relation between direct and cross elasticities. ELASTICITY OF DEMAND FOR TRANSPORT AS A WHOLE

4. The cost of transporting an item to its destination is generally only a small proportion of the price it will bring at that destination. Consequently, the transport cost can vary considerably without having a strong effect On the number of items sold. In the simplest case, where elasticity of supply of the goods is infinite, the elasticity of demand for transport is the elasticity of final demand multiplied by the proportion of the final price contributed by the cost of transport (Ref. 3). For a single movement of freight between major Australian cities, this proportion would probably be of the order of 5 per cent and would rarely be as high as 10 per cent. * Thus, the transport elasticity would be about one-fifteenth of the elasticity at the final point of sale. In fact, it might even be less because supply elasticities are finite. The complete formul a for the price elasticity of demand for transport is:

E

lmos

= f

[E ~iE~ OEd] s

_

where f is the proportion of the final price contributed by the cost of transport, and E s , E d are the elasticities of supply and demand. (See Bennathan and Walters ( R ef. 3).)

5. It is the authors' conclusion that the final demand in aggregate for goods transported by road is little more elastic than -1.0. This conclusion is based On estimates of the price elasticity of demand for major categories of goods at retail. Aggregate food and apparel elasticities range from -0.6 to -1.0, and elasticities for consumer durables from -1.1 to -1.9 (see Refs 4, 5 and 6) . Demand for producers' goods carried by road would tend to be less elastic. On this basis, it is inferred th at elasticity of demand for transport of goods in aggregate is of the order of -0.07. ELASTICITIES OF DEMAND FOR PARTICULAR MODES

6. A basic theorem states that the sum of all the elasticities of demand for a particular good or service with respect to the prices of all goods, services and income is equ al to zero, provided that the demand function is homogeneous of degree zero (Ref. 7 ) . This proviso means that if all prices and income (in money terms) were increased by some uniform percentage, then demand would not be affected. 7. Another way of stating the homogeneity condition is that the price elasticity of demand for transport is the negative of the sum of all the cross elasticities of demand for transport and its income elasticity. However, it was shown in the last section that, because of the scaling effect due to the small proportion that transport cost is of final price, the elasticity of demand for transport is very small. Now, this can be interpreted as saying that the sum of the cross elasticities and the income elasticity of dem and for transport is very small. " Rimmer (Ref. 2) classifies over 70 per cent of the commodities shipped by road transport between Australian capital cities as fabricating. assembling or assembled. These commodities are high value items and include cars, car parts, tyres, medical supplies, books, chemicals, refrigerators, etc.

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253



8. When transport is split into two competing modes, an interesting thing happens to the formal demand relationship. Each demand function (road or rail) now has a relatively large cross elasticity with respect to the price of the competing mode, and this cross elasticity dwarfs the previous sum of elasticities. That sum is represented by the price elasticity of demand for transport as a whole (the sign being changed). 9. Consequently, the direct price elasticity of demand for road transport differs in absolute magnitude from the cross elasticity with respect to the rail price (freight rate) by only a relatively small amount. It is this observation that leads to the major simplification incorporated in the authors' estimating model. Road freight traffic is expressed as a function of the ratio of the road price to the rail price. Because the elasticity of demand for transport as a whole is low - less elastic than -0.1 - the direct and cross elasticities can be expected to be almost equal but of opposite sign. Thus, when the estimation has been carried out in logarithms using the price ratio, one has both the estimated (positive) cross elasticity with respect to rail price and the estimated elasticity with respect to road price, which is equal to the cross elasticity in magnitude but negative in sign. 10. Because there is some elasticity of demand for transport, this method can be expected to slightly underestimate the magnitude of the direct price elasticity. The alternative approach is to estimate the two elasticities separately, but this causes collinearity difficulties because the two separate price (freight rate) variables are correlated with each other and with other variables in the model. Nevertheless, the latter method of estimation has also been used for comparison. THE PROBLEM OF DISTANCE IN THE GRAVITY ITEM

11. A gravity term is included in the model as a means of representing the influence of city size on freight generation. One expects the effects of this influence to show in the total quantities carried between cities, and it is the other variables that determine the portion of the tonnage that is carried by road . l2.

The gravity term is of the following form: population i X population j ] [ (miles)n

b

13. The population product is possibly not as appropriate to the freight case as to the passenger travel case, but it is nevertheless a reasonable representation of the interaction between the magnitudes of the two centres. Readers will be aware of the controversy on this topic. A case against gravity models has been presented by Heggie (Ref. 8) . Other factors such as industrial composition enter into consideration but these influences are handled by a method to be discussed in the next section. 14. The variable for distance in the denominator of the gravity term raises special problems. In the traditional passenger trip model, distance is a clear deterrent not only because of the cost of travel but also because of the discomfort, boredom and waste of time that many people experience when making trips from place to place. In addition, the circle of acquaintances diminishes with distance. 254

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15 . All of these influences, apart from price, are negligible in the case of freight. The network of business contacts covers places both near and far, and the price of a long-distance telephone call merely adds to transport cost. There is no analogue to the disadvantages of travel, the greater risk of damage being slight and covered in any case by a small additional insurance cost. 16. Thus, one is left with distance as virtually nothing more than a proxy for total cost of shipment, and here the a priori conclusion about price elasticity of demand for transport is relevant. Because the price elasticity of demand for transport is very low for the generalised commodity dealt with in thi s analysis, one cou ld have proceeded on the basis of this prior reasoning to impute a very small exponen t to the distance variable and so generate the gravity term . 17 . Certainly, it was not feasible to estimate the exponent associated with distance as part of the multiple regression because route mileage was strongly correlated with a number of other variables in the model. Instead, the authors adopted the common econometric technique of computing the values of the variable over a range of values for the exponent of miles and performing successive regressions to maximise R 2. (For other examples of the use of this technique, see Refs 9 and 10.) The range tested was from two - reflecting the traditional Newtonian approach - to zero. INTR INSIC CHARACTER ISTICS OF CITIES OF ORIGIN

18 . If a model is specified in which quantity of freight is a function of price and of the size of origin and destination, then an estimation problem arises from the intrinsic characteristics of the origins. (Intrinsic characteristics of destinations might also be expected to cause problems but tests indicated th at their influence is not significant.) This problem was recognised by Quandt and Young (Ref. 11) who pointed out that if nothing is done to take account of th e intrinsic characteristics, then the error term is made up of two components: one consisting of nonstochastic elements and the other being the normal random error term. Their solution was to make use of this fact to obtain a more efficient generalised least squares (GLS) estimator. From the GLS residuals they obtained constants for each city pair. 19. The authors' approach is a more direct one in that a dumm y variable has been incorporated for each origin. Thus a constant rep resenting the intrinsic characteristics is obtained directly and is analogous to the constant computed from their residuals by Quandt and Young. By explicitly allowing for the intrinsic characteristics of different origins, the authors remove the non-stoch astic element from the residual term and so avoid the problem of a residual with a non-zero mean and the resulting inconsistent parameter estimates. Each se t of intrinsic characteristics has been accounted for by an appropriate coefficient in the estimated equation. THE GENERAL MODEL

20. The foregoing discussion has highlighted the major components of the demand model. A trend variable has also been included in order to take account of trends in technology and any lagged responses to earlier changes. A final conVolume 6, Part 2, 1972

255



sideration was the 'speed-of-delivery' of goods, but preliminary investigations indicated that the measurement of this variable was not sufficiently refined to provide any explanatory power and it was not included in the final analysis. Thus the model takes the general form: ba t

Cl

Ck

Sl .. . Sir

Cn

... Sn

where Qi i

is road freight carried from i to j; are the rail and road freight rates from i to j; are the populations of i and j; is the distance (in miles) from i to j; mii t takes values 1, 2 .. . T in time periods 1, 2, ... T; Sl, . . .Sk, . . . Sn are dummy variables, Sk taking a value of e (the base of natural logarithms) when the origin is city k and 1 otherwise. (When natural logarithms are taken, these become one or zero.) r1, r2 Pi> Pi

21. This model is similar in some respects to models used for estimating trip demand by Quandt, Baumol and Young, modifications of the so-called 'abstract mode model' (Refs 12 and 13). In a number of their estimating equations, price responses have been handled by two terms, one being the cheapest cost of travel between two centres and the other being the ratio of the cost by a particular mode divided by the cheapest cost. 22 . The price ratio term is similar to the one the authors have specified. The cheapest cost term is desirable in the passenger model because there is an appreciable money price elasticity of demand for trips - of the order of -1, judging by Young's estimates. As explained earlier, any analogous term to represent total money cost of transport between points has been dropped from our estimating equation because the price elasticity of demand for total transport of goods is extremely low. ESTIMATI ON TREATMENT OF DATA

23. Because there are no statistics on tons moved by road, freight movements had to be represented by a proxy variable. This was the deseasonalised number of trucks , recorded by routes, passing each month through the N.S.W. Department of Motor Transport checking stations at Marulan and Berowra. * These stations are located so that it is difficult to avoid them. Where there is a satisfactory alternative which avoids both checking stations, such as Sydney-Adelaide via the Blue Mountains, the route was not included. The routes included were SydneyMelbourne, Sydney-Brisbane, Melbourne-Newcastle, Adelaide-Newcastle, together with the four routes in the reverse directions. Observations were monthly totals for the 24 months ending October, 1971. "There wo uld be no point in multiplying by the average tonn age per truck to convert these figures to tons. Multiplying the dependent va riable by a constant wo uld no t affect the el as ticity est imates.

256

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FITZPATRICK , TAPLIN -


24. There was a distinct possibility of introducing serial correlation into the analysis by choosing to examine flows in each direction, e.g., tons from Sydney to Melbourne as well as from Melbourne to Sydney, since truck movements in the two directions cannot be independent. The number of return journeys in one period is influenced by the number of outward trips in the same or earlier periods. For the centres covered by the data - Sydney, Melbourne, Brisbane, Adelaide and Newcastle - the authors felt that the problem would be most likely to occur on the Sydney-Melbourne and Sydney-Brisbane routes. Serial correlation does not lead to bias in the parameter estimates but may lead to a biased estimate of the variance. 25. The highly aggregated form of the freight data meant that it was impossible to obtain completely appropriate freight rates. For both road and rail, the freight rates used were based upon a regular 5-ton shipment measuring 60 cu ft/ton. Rail freights were also adjusted for the practice of wagon hire by assuming a 10 per cent discount for 50 per cent of the total rail cargo. However, these specific assumptions are of little consequence provided that all freight rates tend to move together. Under these conditions, the estimated elasticities will be virtually the same regardless of which representative rate is used. 26. Prices are pictured in a theoretical context as flexible, with instantaneous adjustment in either direction as the situation may require. In practice, prices are rarely lowered. In the case of rail transport, freight rates are reviewed on a triennial basis. Road freight rates have greater flexibility because of the nature of the competition, the presence of small operators making it difficult for a cartel to operate successfully. The common rate charged by the major freight forwarders becomes a maximum for the industry and shippers can often obtain a lower rate from a smaller operator. Provided one knows the correct weights, a current average freight rate can be obtained by a sample survey. However, an historical price series developed from a current survey could be misleading. Instead it has been assumed that over the two year period, the freight rates charged by the different operators have retained a constant intra-industry relativity. An index based on the price increases recommended by the various State road transport associations was formed and applied to quotations provided by a major forwarder. The price series thus exhibits a short-term rigidity and cannot be said to result from the contemporaneous interaction of supply and demand. Instead, price is taken as predetermined and the simultaneity aspect is not present. Consequently, ordinary least squares (OLS) is the appropriate estimation method. ESTIMATION PROCED URE

27. The data consist of cross-sectional details for the selected routes with a series of consecutive observations for each route. The variables have for the most part demonstrated only a mild short-term variability, and any meaningful analysis must rely upon the combined cross-section and time-series approach rather than the investigation of each route in tum. 28. A systematic investigation of each route has some appeal in that it avoids any estimation problem that may arise due to dependence between routes. FurtherVolume 6, Part 2, 1972

257


ELASTICITY OF DEMAND FOR RO AD TR ANSPORT

more, it would permit the estimation of the price elasticity for each route. In this situation, however, a route-by-route approach would be relying upon rail price data which has had only one price change over the observation period. As the prime reason for the analysis is to measure the susceptibility of road transport to price changes in the various modes, the study should be based upon as many price levels as possible, and this is achieved by pooling data for different routes. A summary of the advantages and disadvantages of the pooled data approach and the individual analysis approach has been given by Ben-David and Tomek (Ref. 14 ). RESULTS

29 . The iterative search for the most appropriate exponent of miles Ca' ) in the gravity term indicated that the fit of the regression to the data improved as the value approached zero. TABLE I shows that as 'a' was varied from two to zero, the error variance was reduced by more than 40 per cent, indicated by the increase in R2. Thus, the best value of 'a' appears to be zero, and this equation has been selected for closer examination. If the model had used the cheapest freight rate instead of miles as the 30. denominator, the elasticity of demand for transport could have been inferred from the value of 'a'. In fact, freight rate and miles are highly correlated, so that this substitution would not have greatly influenced the estimate of the exponent in the denominator. The low value of 'a' indicated by this study confirms the authors' prior conclusion that the elasticity of demand fo r transport is very low.

TABLE II presents a summary of the regression results for the price ratio 31. model corresponding to a = O. Results for the alternative model (also for a = 0), which included the two prices as separate variables, are also shown for comparison.

TABLE I CHANGES IN

258

'R2 AND

IN THE PRICE ELASTICITY COEFFICIENT AS THE EXPONENT OF DISTANCE IN THE GRAVITY TERM IS VARIED

Expo nent of Distance 'a'

Coefficient of Multiple Determination (adjusted for degrees of freedom)

Price Elastic ity Coefficient (t-value in brackets)

2.0

0 .974

1.5

0 .977

1.0

0.980

0.75

0 .982

0.5

0.983

0 .25

0 .984

0.1

0.985

0 .0

0 .985

1.26 (2.76) 1.38 (3.23) 1.55 (3.97) 1.67 (4.46) 1.81 (5 .05) 1.97 (5 .74) 2.08 (6.21) 2.16 (6.54)

R2

A RRB

PROCEEDINGS



TABLE II DEMAND FOR ROAD TRANSPORT OF GOODS: REGRESSION ESTIMATES OF COEFFICIENTS (t-values In brackets beneath the coefficients) Price Ratio Model

Variabl e'

( r, ) Rail / road price ratio: In ( - ) ( r2 ) Population product : In (Pi Pj) Trend : In (t) Sydney: Melbourne: Adelaide Brisbane: Newcastle:

1 if Sydney origin ,

o otherwise

1 if Melbourne origin

o otherwise

1 of Adelaide origin,

o otherwise

1 if Brisbane origin ,

o otherwise

1 If Newcastle

o otherwise

ori~in,

2.16 (6.54) 1.29 (40.49) -0.22 (-5.94) 2.09 (28.65) 1.99 (29.14) 1.84 (20.16) 1.90 (28.57) 1.83 (28.66)

Rail price : In (r,) Road price: In (r2)

0 .985

Separate Prices Model

1.31 (39.57) ...-0.20 (-5.41) 0.12 (0.15) 0.02 (0.02) -0.24 (-0.29) -0.07 (-0.09) -0 .21 (-0.26) 3.25 (5.96) -2.54 (-7.06) 0.985

'There is no constant because in this specification there is a dummy (O-1) variable for each origin.

32. The elasticity with respect to the price ratio is 2.16, implying that the cross elasticity of demand for road transport with respect to rail price is 2.16 and that the direct elasticity with respect to road price is -2.16. This is similar to the estimate of -2 .54 obtained with the alternative model. The cross elasticity estimate in the alternative model is somewhat larger in absolute value than the direct elasticity, thus violating the homogeneity condition. 33. The high t-value associated with the price elasticity estimate in the price ratio model indicates a relatively narrow confidence band. 34. The estimates for the dummy variables reflect the characteristics of the freight from each origin. The mix of goods will differ between origins and one can expect a variation in the average load per truck, depending upon the source. Furthermore, cities of equal size may have different propensities to export. Had a regression equation been estimated with a single constant term , these origin effects would have been absorbed into the error term causing a larger error variance and decreasing the power of the significance tests. 35 . An analysis of variance revealed that the dummy variables group was significant at the 99.9 per cent level. These dummy variables accounted for 4.5 per cent of the total variation, the gravity variable 85 per cent and the price variable Volume 6, Part 2, 1972

259



9.3 per cent (the trend variable made a negligible contribution), leaving a relatively small residual with 184 degrees of freedom. 36. Further pair-wise tests on individual origins indicated that a difference existed at the 95 per cent significance level between the Sydney-Adelaide and Sydney-Newcastle origin pairs, while the Sydney-Brisbane origin pair was significant at the 90 per cent level. Tests between other origin pairs were not significant. 37. Despite its slight contribution to explaining the variation, the time coefficient is significant at the 99.9 per cent level. The negative coefficient of this variable could be due to delays, as a result of contracts, etc., which occur before advantage is taken of the improving relative freight rates of railways. Another factor may be technical progress COMMENT

38. The estimation is based upon pooled cross-section and time-series data using the OLS technique. It is anticipated that several assumptions of this technique regarding the error terms are violated, and reduced efficiency of the estimation procedure has resulted . The number of truck trips varies in order of magnitude from route to route so that heteroskedasticity is bound to be present. Furthermore, the circular nature of most truck operations and the possibility of the transshipment of goods would suggest that a complex relationship exists between the residuals. A more appropriate estimation procedure would require the use of the GLS technique in a manner consistent with the assumptions regarding the relationship between residuals. For comparison of techniques under specified assumptions, see Ref. 15. 39. Nevertheless, the OLS procedure leads to unbiased estimates of the regression coefficients. In view of the high t-values on our estimates, it seems unlikely that the correction of any bias in the estimates of the standard errors will lead to the rejection of any parameter estimates. CONCLUSION

40. As discussed earlier, price variation in the data comes from both shortterm freight rate movements and the differences between the rates on various routes . Because the latter is the major source of price variation in the data, the price elasticity estimate must be seen mainly in this context. Although influenced by short-term rate variations, the relatively stable pattern of modal demand on each route represents a more or less long-run equilibrium. A price elasticity estimated mainly on the basis of differences between routes is consequently a fairly long-run elasticity. 41. Thus, it is suggested that the price elasticity of demand for road transport of approximately -2 be regarded as a medium to long-run elasticity. For forecasts of short-term responses it would be advisable to assume an elasticity that is much smaller in absolute magnitude. For calculations of consumers' surplus, however, the elasticity of -2 is appropriate. 260

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ELASTICITY OF DEMAND FOR ROAD TRANSPORT DISCUSSIONS

R EFERENCES 1. Neuburger, H., User benefit in the evaluation of transport and land use plans, J. Transp. Econ. and Policy, S : 1, 52 (1971). 2. Rimmer, P. J., Freight forwarding in Australia, A.N.U. (1970). 3. Bennathan, E. and Walters, A. A., The Economics ot Ocean Freight Rates, Praeger, New York (1969). 4. Byron, R. P., A simple method of estimating demand systems under separable utility assumptions, Rev. of Economic Studies, 37 : 110,261 (1970). 5. Court, R. H., An application of demand theory to projecting New Zealand retail consumption, Economic Rec. , 44: 107,303 (1968). 6. U.K. Ministry of Agriculture, Fisheries and Food, Household Food Consumption and Expenditure: 1966, H.M. Stationery Office, London, 48 (1968) . 7. Wold, H. and Jureen, L., Demand Analysis, Wiley, New York (1953). 8. Heggie, I. G., Are gravity and interactance models a valid technique for planning regional transport facilities? , Operat. Res. Quart., 20: 1 (1969). 9. Westfield, F., Technical progress and returns to scale, Rev. of Economics and Stats, 48 : 4, 229 (1966). 10. Wallis, K. F., Some recent developments in applied econometrics, J . Economic Literature, 7 : 3, 771 (1 Y6Y ) . 11. Quandt, R. E. and Yoilng, K. H., Cross-sectional travel demand models: estimates and tests, J. Regional Science, 9: 2, 201 (1969). 12. Quandt, R. E . and Baumol, W. J., The demand for abstract transport modes: theory and measurement, J . Regional Science, 6: 2, 13 (1969). 13. Young, K. H., An abstract mode approach to the demand for tr(ffiJel, Transpn Res., 3: 4,443 (1969). 14. Ben-David, S. and Tomek, W. G. , Allowing for slope and intercept changes in regression analysis, A.E. Res. 179, Dept of Agric. Econ., Cornell University, Itchaca, New York (1965) . 15. Kmenta, J. and Gilbert, R. F. , Estimation of seemingly unrelated regressions with autoregressive disturbances, J. Amer. Statistical Assocn, Vol. 65, p. 196 (1970 ). DISCUSS I ONS L. E. S HEP HER D Senior Transport Planner, Commonwealth Bureau of Roads

42. To overcome the problem of heteroskedasticity and to follow the more usual econometric treatment of aggregate data, it would have been desirable to express the dependent variable in 'per capita' terms, i.e., removing the population variable as an explanatory variable and using it to adjust the dependent variable. This would also be more meaningful in terms of identifying the underlying factors relevant to freight movement and its modal split and would overcome the situation where 85 per cent of the variation in freight movements is explained by population differences , which is hardly surprising. Volume 6, Part 2, 1972

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ELASTICITY OF DEMAND FOR ROAD TRANSPORT DISCUSSIONS

43. The authors correctly point out the probable existence of serially correlated error terms. However, it would have been desirable to present some test (e.g. Durbin-Watson statistic) of this hypothesis in order to reveal the seriousness of this problem. If the serial correlation is serious, then use of the standard '1' test would be negated; it would be necessary to adopt alternative estimating procedures. 44 . Similarly, the authors state that 'heteroskedasticity is bound to be present' (para. 38) but no statistical testing of this hypothesis is present and the reader is unaware to what degree this assumption is violated. T.

M.

HOG G

Deputy Chief, Transport Planning Division, Commonwealth Bureau of Roads

45. No explanation is offered for assuming constant elasticity of demand. There is no a priori reason why this should be so. As well discussion should have been provided to indicate how the elasticity coefficient of demand so derived would be used in calculating consumers' surplus, for with a demand curve of form y = ap- x the usual consumers' surplus triangle calculation of t(6.p . 6.q) overstatf'S the increment in net benefit to new users. 46. Use of recorded truck movements as a proxy variable in place of actual tonnages between major centres probably under or overstates the responsiveness of freight shipments to a change in freight rates, as indications are that truck tonnages fluctuate more than do truck numbers over the course of the year and the business cycle. Thus the contention by the authors (footnote para. 23) regarding constancy of average tonnage per truck is not correct and as a result their assumption that 'multiplying the dependent variable by a constant would not affect the elasticity estimates' is not warranted. 47. With reference to para. 41, the conclusion reached should have been more carefully worded, perhaps with a rider to the effect 'that the price elasticity of demand for road transport of approximately -2.0 applies if there is another, readily substitutable mode - e.g. rail'. If there is no close substitute mode it is apparent that the price elasticity for road transport must perforce approximate towards the price elasticity of demand for transport - demonstrated in para. 5 as being only of the order of -0.07. 48. I would like to make a general comment about the author's approach. The approach is macroscopic and does not closely identify the various microeconomic factors at work determining modal split and hence through cross elasticity, the road price elasticity. 49 . One of the more important of these factors is the type of shipper: the larger the proportion of line haul costs incurred in supply and production the higher is the cross elasticity value likely to be and hence the price elasticity. Given the predominance of freight forwarders in interstate freight transport and given that they have a high line haul cost component of total costs, these organisations 262

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FITZPATRlCK, TAPLIN - ELASTICITY OF DEMAND FOR ROAD TRANSPORT DISCUSSIONS/ AUTHORS' CLOSURE

are both able and likely to substantially influence modal split, because their margin of profit is highly susceptible to changes in relative freight rates. Accordingly it is likely that the cross price elasticity is probably greater than + 2.0 and as a consequence, so too will the coefficient of price elasticity of demand for road transport be higher than -2.0. AUTHORS ' To L.

CLOSU R E

E. SHE P HER D

50. The authors agree that deseasonalised truck numbers are not the best form for the dependent variable and a per capita type variable would have been preferred. However, a suitable variable is difficult to find. The usual econometric practice of expressing data on a per capita basis is not readily applicable here as we are concerned with the freight movement between cities. A dependent variable expressed in a per capita form would obviously require the populations of both cities to be considered, and one is never sure of the best way of combining them. To simply divide the deseasonalised truck numbers by the product of the population is equivalent to constraining the value of the gravity term exponent (b 2 in om model) to 1. The gravity term is a proxy for the total freight flow between the different cities and there is no a priori reason why the exponent shuuld take this value. Indeed the exponents found for these models have taken a wide range of values and are obviously related to the characteristics of the cities. In our situation the value of 1.29 found for b 2 is significantly different from 1. 51 . Another version of the per capita type variable, the modal share, was considered but monthly data for the freight movements by rail were not available. Consequently the total freight movement and the modal share could not be calculated. 52. The authors realised when selecting their model that the variation would be explained by the size variable, i.e. the in part, explains the high values of R2 obtained and is the precision of three decimal places of R2 was used to select the

a large amount of gravity term. This, reason the unusual best value of 'a'.

On the second matter raised by Mr Shepherd, it must be remembered 53. that the data set used was a combination of cross section and time series observations. To apply the ordinary least squares regression procedure to this type of data requires a set of assumptions, regarding the independence of the residuals, which are extremely doubtful in our situation. The most serious violations would be the contemporaneous correlation of the residuals and the serial correlation of residuals on both the same route and across routes. These violations could occur because of the circular nature of truck operations and the possible transhipments of freight. Tests for serial correlation along individual routes using the DurbinWatson statistic indicated the existence of serially correlated residuals. However, this statistic was inappropriate for testing contemporaneous or serial cross-correlation and these hypotheses were not tested. Volume 6, P art 2, 1972

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ELASTICITY OF DEMAND FOR ROAD TRANSPORT AUTHORS' CLOSURE

54. Since the serial correlation along individual routes was only part of a larger issue for which the authors did not have complete hypothesis testing, they preferred to mention the existence of the problem and indicate the nature of the estimation procedure necessary to overcome the difficulties. It is restated, though , that the estimates are still unbiased, even if these independence assumptions are violated. In view of the high 't' values obtained, the bias introduced into the standard errors due to the violations would need to be several hundred per cent before the estimates would become non-significant. 55. The final point is another aspect of the problems discussed above, in that heteroskedasticity is covered in a generalised contemporaneous covariance matrix. The estimation procedures suggested as appropriate for this set of data would allow for such a matrix. To T. M.

HOG G

56. The authors agree with Mr Hogg when he says that there is no a priori reason why the price elasticity of demand should be constant. The multiplicative form is simply one of several alternatives possessing the desired theoretical properties. However, there is no a priori reason why it should take any other form. It is true that the constant elasticity curve does not lend itself to the usual 57. consumers' surplus formula. To calculate precisely the triangular region, in the particular case of a constant elasticity of -2, the correct formula is ql U.p) 2/ (PI - bop) where PI and ql are the base case price and volume values. The discrepancy between this formula and the usual one depends upon the size of bop; for small changes in the price the difference will be negligible but it becomes measurable for large price changes.

58 . On the matter of variations in the truck tonnages the authors feel that Mr Hogg has misunderstood the footnote. They were referring to the value of 14.5 tons per truck which the Department of Motor Transport uses each month to derive its tonnage estimate. There was no point in using these estimates when the actual truck numbers were available. 59. It is possible that the average load does vary, but there is no way of knowing at this stage. If the average varied during the sample period the authors' estimate mayor may not have been influenced, depending upon the pattern of this variation. A cyclical pattern due say to seasonal factors would be the most serious and is similar to the problems raised by Mr Shepherd. If there is a more complex change in the cOTQmodity mix resulting in an irregular pattern of variations , their impact will tend to increase the variance of the error term . In this case, the estimate would not be expected to change radically but the 't' values would be reduced. 60. Mr Hogg's comments on the applicability of the elasticity estimate are correct. It should be evident from the paper that the procedure is based upon the approximate equality of the direct price elasticity and the cross elasticity. Before one can talk of a cross elasticity there must of course be an alternative mode. 264

ARRB PROCEEDINGS


ELASTICITY OF DEMAND FOR ROAD TRANSPORT AUTHORS' CLOSURE

The authors' model in fact is applicable to the case where only two modes are available. Most cases in the Australian transport context can be approximated by this model, but in any situation where a third mode, e.g. sea, has a significant share of the traffic this estimate becomes less appropriate. Where there is only one mode, the value of -0.07 is the appropriate elasticity estimate. 61 . Mr Hogg, in his final comment, appears to have confused the authors' overall estimate with that for an individual firm. The authors agree with his comments on the relationship with the cross-elasticity but fail to see how he concludes that the price elasticity of demand must be more elastic than -2.0. They expect, as he does, that freight forwarders ' demand will be more elastic than -2.0, but demand by many other operators will be considerably less elastic than -2.0. The overall estimate is derived from considering the total traffic. It is precisely because our model is macroscopic that the influence of all 62. factors are incorporated in the value obtained. We have not identified the microeconomic factors but this was not our objective.

Volume 6, Part 2, 1972

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