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An econometric analysis of motorcycle ownership in the UK
International Journal of Transport Management 2 (2004) 111–121 www.elsevier.com/locate/traman
An econometric analysis of motorcycle ownership in the UK Martyn Duffy, Terry Robinson
*
Manchester Business School, The University of Manchester, Booth Street West, Manchester M15 6PB, UK Received 1 April 2004; received in revised form 1 March 2005; accepted 1 April 2005
Abstract This paper reports on an econometric investigation of motorcycle ownership in the UK. The favoured specification is a stock adjustment model augmented by a stochastic trend to allow for changing consumer preferences over modes of transport. Empirical estimates suggest that the future growth prospects for motorcycles may be quite good. This tentative conclusion follows primarily from what appears to be a significant, relatively high, long-run income elasticity of demand for motorcycles, combined with a high cross-elasticity of substitution effect with regard to a measure of the cost of motoring, which is dominated by the costs of buying and running a car. At the same time, our estimates indicate that these effects are subject to a countervailing tendency, represented by an on-going change in the publicÕs preferences away from motorcycles towards other modes of transport. Which of these tendencies will dominate in the motorcycle market over the next few years remains to be seen. 2005 Elsevier Ltd. All rights reserved. Keywords: Motorcycles; Consumer demand; Stock adjustment
1. Introduction Over recent decades, motorcycle ownership (which includes scooters and mopeds in this paper) has passed through several peaks and troughs: Fig. 1. The stock measure of the number of motorcycles currently licensed in the UK rose from 729,000 at the end of 1950 to a peak of 1,796,000 at the end of 1960. It then declined to 982,000 by the end of 1972 before rising to a new peak of 1,371,000 in 1981. Motorcycle ownership contracted over subsequent years to reach a record post-1940s low level of 594,000 vehicles in 1995. Since that date, the stock of licensed motorcycles has increased steadily, and by the end of 2001 882,000 motorcycles were licensed for use and 177,100 new registrations were made during the year.1
*
Corresponding author. Department for Transport, Transport Statistics Great Britain: 2002 Edition (available on the web at
1471-4051/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijtm.2005.04.002
Casual empiricism suggests that these trends and cycles in motorcycle ownership must reflect to some extent changes in tastes and preferences over modes of transport in the post-war period. But they are also likely to result from the influence upon demand for motorbikes of economic factors. Thus, the increase in motorcycle ownership in the 1970s is probably related to some extent to the adverse impact on the running costs of cars of the first two oil price shocks, and to the subsequent search by many travellers for alternative, cheaper modes of transport. For the same reason, the use of the fuel duty escalator in the late 1990s may have had a favourable effect on the demand for motorcycles. Rising affluence has undoubtedly increased the demand for cars, but it is not clear a priori what the net effect of rising incomes has been on the motorcycle market. The effect of these economic factors on the demand for motorcycles depends upon the magnitudes of elasticities of demand in this market, but little is known about such matters in this little researched area. This paper reports on an initial attempt to estimate and assess these parameters
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1.75 1.5 1.25 1.00 0.75 0.50 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Fig. 1. Motorcycles, scooters and mopeds: number of vehicles licensed at the end of year (1945–2000), millions.
and the relative contribution of changes in the economic environment and consumer tastes to the evolution over recent decades of motorcycle ownership in the UK. Motor cycle ownership is a stock concept, whereas consumption of the services of motorcycles is a flow variable. In this paper we follow the practice of most previous empirical investigations of demand for consumer durables by focusing on the demand for the stock of motorcycles, rather than the amount of travel that is effected through that mode of transport (motorcycle consumption).2 In fact, though, this decision may make little difference to the general nature of the results obtained. For the flow variable motorcycle traffic, measured by billion vehicle kilometres, has followed a similar pattern to the stock of currently licensed motorcycles over time (especially since the early 1980s): see Broadley (2001, Chart E.2, p. 2). Traffic engineers, motorcycle manufacturers and other parties are motivated to understand the causes of past fluctuations in motorcycle ownership, in so far as this knowledge may help to predict likely future changes in the use of this mode of transport. The more general need is to attempt to anticipate both the growth in total traffic as well as the contributions from alternative modes of transport. However, a complete study of that kind is beyond the scope of the present paper, which is concerned simply with the demand for one particular type of transport, motorcycles. Since the early 1950s, there has occurred a trend movement towards travel by car and away from other modes of transport, including buses, trains and motorcycles. In 1952 cars accounted for only 32% of passenger kilometres, but this proportion had risen to 92% by 2001 (Social Trends, vols. 31–33). However, the rapid growth in car traffic that occurred in the early post-war decades had slowed to a much more modest pace in the 1990s: cars reached the 92% share of total road traffic as early as 1991. This slowdown in the growth of car traffic may represent early signs of a Ôsaturation effectÕ, arising from 2 Although Train (1985) and Jong (1990) present an approach in which the consumption of services and the stock are dealt with jointly.
problems of congestion and other similar constraints. In that case, any future growth in total traffic may be realised largely through other modes of transport, including motorcycles.3 Then the upswing in motorcycle ownership that has occurred since the mid-1990s may continue during future years. An important factor that impinges on the motorcycle market is official policy toward transport, and future initiatives in this area may favour the total demand for powered two-wheel (PTW) vehicles, that is, motorcycles, scooters and mopeds. Thus, many governments have taken action to inhibit motor car use in major cities to relieve congestion4 and it is recognised that increased use of PTWs (and bicycles) can help facilitate this, due to the small size and nimbleness of those vehicles. PTWs and bicycles have the added benefit of making a small contribution to the achievement of official targets for reduced emission of ÔgreenhouseÕ gases. An example of this policy stance can be seen in the UK with the Greater London AuthorityÕs decision to exempt motorcycles from its recently introduced road pricing scheme. The Greater London Authority introduced a Congestion Charge in February 2003. Under this scheme vehicles crossing the ÔboundaryÕ of a zone defined by the Inner Ring Road have to pay a £5 per day toll. The GovernmentÕs ten year transport plan appears to have made little progress towards fulfilment, and congestion is almost certain to go on increasing: The Economist (2002a,b). In a paradoxical way, this may be of benefit to the motorcycle industry. Frustration with public transport and the resultant congestion on the roads, especially in city centres and major motorway complexes, may lead to an increase in two-wheeled vehicle usage: MINTeL (2002). There is growing pressure from the governmentÕs advisers to introduce road charges, particularly on motorways: The Economist (2003). If motorcycles are granted exemption from any future road charging schemes, as in the case of the London Congestion Charge, the incentive to own a motorcycle will increase accordingly. Since the motorcycle may be seen as a partial solution to the problem of traffic congestion in the UK, it is important to estimate and forecast the demand for motorcycles. Although there have been many econometric studies of the demand for car ownership and use in the UK (Romilly et al., 2001; Whelan, 2001; Whelan et al., 2000; Hanley and Dargay, 2000; Dargay and Vythoulkas, 1999; Witt and Johnson, 1986; Button 3 The plateauing of car ownership could also be caused by changes in preferences, in which case there may little or no effect on motorcycle ownership. 4 The GovernmentÕs 10-year plan for transport aims to reduce congestion on BritainÕs roads by 6% by 2010: Department of the Environment, Transport, and the Regions (2000).
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et al., 1982) to our knowledge there has been no published attempt by economists to model the demand for motorcycles in the UK, or indeed in any other country. This paper sets out to rectify this omission.
stant rate, d, per period, so that the logarithmic values of replacement sales in period t are d ln Kt1. On making that assumption, a modified version of Eq. (1) is obtained: ln Qgross ¼ h ln K t þ ðd hÞ ln K t1 ; t
2. Methodology We define net sales of motorcycles in any period t to be identical to the change in the stock of motorcycles between the end of period t 1 and the end of period t, and gross sales are net sales plus ÔdepreciationÕ (that is, purchases to replace vehicles that have been removed from the stock during period t). The specification and estimation of the equation for gross sales proved to be, in some respects, problematic for reasons that are discussed below. These problems are avoided in a model for explaining net sales, although that benefit is achieved at a cost of not accounting for replacement purchases, a significant proportion of total annual sales of new motorcycles in the UK. For the purpose of examining and reporting on these issues, we have estimated, with differing degrees of success, demand functions for both gross sales and net sales of motorcycles. Because we are analysing the demand for a consumer durable, the framework for our investigation is that much-used workhorse of applied studies in this area, the stock adjustment model,5 which is expressed, following the common practice in time series work, in logarithmic form: D ln K t ¼ h½ln K t ln K t1 ;
ð1Þ
where Kt is the stock of motorcycles per head of the population aged 15–606 at the end of period t, the asterisk denotes a desired magnitude, and h represents the average Ôrate of adjustmentÕ during a single period of the actual stock to its desired level. Transaction costs and other factors that induce inertia in consumer behaviour are likely to cause the adjustment of the actual stock to its desired level to be incomplete in a single period, so we expect h to lie in the interval: 0 < h < 1. The left-hand side variable in Eq. (1), the growth rate of the stock of motorcycles, approximates to the net sales of the good (expressed as a proportion of the previous periodÕs outstanding stock), ln Qnet t . We can move to a gross measure of sales if we add estimates of replacement sales to both sides of the equation.7 The easiest way to achieve this adjustment is to introduce an extra assumption: that the stock depreciates at a con-
5
See Chow (1957), Grieves (1983), and Stone and Rowe (1957). Unfortunately data on the population starting at 18 was not available. The next start point after 15 is 20. 7 We must add estimates of replacement sales since, to our knowledge, no direct times series measures of this component have been published. 6
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ð2Þ
where Qgross represents gross purchases of motorcycles t per person per period. The demand for motorcycles is, in fact, a demand for the services of motorcycles. For a given level of intensity of use (as measured by, say, the average number of trips and/or the average trip mileage), a greater demand for motorcycle services implies necessarily a larger desired motorcycle stock. Indicators of intensity of use of motorcycles give conflicting signals. Thus, the number of trips made by motorcycle appears to be falling over time, being 3 per person per year in 1997/99, down from 6 in 1989/91 and 9 in 1985/86: Broadley (2001). On the other hand, the average length of a motorcycle trip has increased from 5.6 miles in 1985/86 to 9.3 miles in 1997/99 (which is 10% longer than the average car trip). In these circumstances (of less but longer motorcycle trips), the assumption of a constant level of intensity of stock use is probably not too unrealistic. We posit that the desired, per capita stock of motorcycles in period t, K t , is determined fundamentally by real per capita disposable income (Yt), a measure of the real cost of motoring (MCt), and a real interest rate term (Rt). We would have liked to relate the desired stock of motorcycles to, inter alia, the relative price of motorcycles, but that was infeasible because of a lack of data on prices. It is hoped that any misspecification bias that may result from that omission is minimised by the inclusion of the index of the real cost of motoring, which is itself a relative price term that could allow for substitution effects in choice of transportation. In this analysis, the desired level of motorcycle services and stock rises (or falls) as people become more affluent. With increased incomes, households revise their plans for commuting and leisure activities, and that impacts on their desired rates of utilisation of various modes of transport. The desired motorcycle stock will also vary inversely with the real cost of using motorcycles, and vary directly with the costs of alternative modes of transport. It must be recognised indeed that in modelling motorcycle ownership and use, it would be good to distinguish between different travel purposes. It may be the case that many motorcycles are bought nowadays primarily for leisure trips, and for such trips they may not be as close substitutes with the car, as they would be for commuting. This is an issue that needs to be borne in mind when developing judgemental assessments of the outlook for market demand for motorcycles, but it could not be investigated further in formal econometric work because of data constraints. The time series data available to the authors are highly aggregate
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in nature, and cannot be used for the purpose of distinguishing, for example, between types of journey. With these comments in mind, the desired stock of motorcycles is modelled in log-linear form as follows: ln K t ¼ a1 ln Y t þ a2 ln MCt þ a3 Rt .
ð3Þ
The income elasticity of demand for the motorcycle stock (a1) may be positive or negative, depending on whether motorcycle services are categorised by the adult population as akin to those of a ÔnormalÕ or ÔinferiorÕ good, respectively. Economic theory suggests that the stock demand for a consumer durable may vary inversely with the user cost of that good: Muellbauer (1981). In this study the user cost of motorcycles is represented approximately by the real interest rate, Rt, and we expect that the interest semi-elasticity of demand for motorcycle stock is non-positive (i.e. a3 6 0). It must be noted that the other elements of the user cost of motorcycles (such as depreciation) have been omitted due to lack of data, and the consequent misspecification and possible bias must be borne in mind when considering the empirical estimates of the model. The statistical measure of motoring costs, MCt, used in this study is dominated by the costs of owning and running a car, which is, of course, an alternative form of transport. When motoring costs rise, the demand for the services of motorcycles may also increase as people reduce their use of cars and switch to other modes of transport. These costs might also decrease, e.g. as a result of increases in fuel efficiency. The elasticity of demand for motorcycle stock with respect to the index of motoring costs is expected to be non-negative (a2 P 0). We substitute (3) into (2) to obtain the estimating form of a demand equation for gross sales of motorcycles: ln Qgross ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b4 ln K t1 ; t
ð4Þ
where bi = hai (i = 1, 2, 3) and b4 = (d h). Since Eq. (4) contains only four coefficients that can be estimated, the five structural parameters h, d, a1, a2, and a3 are not identified. In particular, we cannot unscramble unique estimates of the long-run elasticities a1, a2, and a3 from (4) unless we fix one parameter a priori, such as d: then the long-run elasticities could be calculated as ai = bi/(d b4) (i = 1, 2, 3). Even then, any error in the assumed value of d would translate into erroneous estimates of h, a1, a2, and a3. Subtraction of depreciation from both sides of (4) yields an equation that can be estimated to explain net sales of motorcycles, and that equation is identified exactly: ln Qnet ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b04 ln K t1 ; t
ð5Þ
where bi = hai (i = 1, 2, 3), as defined as below Eq. (4), but b04 ¼ h. In this equation, the lagged stock term, h ln Kt1, allows for the effects of inertia and habit on net sales: by adding ln Kt1 to both sides of (5), we can see that the lower the value of h, the more important are inertia and habits in consumer behaviour, and the more the current, desired stock of motorcycles depends upon the recent, actual stock. The lagged stock term in (4) does, of course, strengthens this relationship between current, desired and actual, lagged stocks by also incorporating replacement sales. The long-run elasticities of demand for motorcycle stock are calculated, in the case of Eq. (5), as the ratio of the short-run elasticities to the coefficient on the lagged stock term, but with the sign reversed: ai ¼ bi =b04 (i = 1, 2, 3). If, and only if, depreciation is a constant proportion of the outstanding stock, will the short-run elasticities bi (i = 1, 2, 3) in (5) be identical to those in (4), whilst the stock elasticities, b4 and b04 will differ. Where the depreciation rate is highly variable, Eq. (4) is suspect since it would then be based on an incorrect assumption about depreciation: Eq. (5) would provide a superior framework, compared to Eq. (4), for the calculation of reliable, unbiased estimates of the short- and long-run elasticities of demand for motorcycles. When working with Eq. (4), we have no firm, statistical information about the rate of depreciation of motorcycles to help us identify the long-run elasticities of demand. However, we can try to estimate d as follows. The logarithmic equation linking gross sales and net sales of motorcycles, with replacement sales expressed as a proportion of the outstanding stock at the beginning of each period, can be written thus: ln Qgross ¼ D ln K t þ dt ln K t1 t
ð6Þ
which yields an estimate of a time-varying rate of depreciation, dt: dt ¼
ln Qgross D ln K t t . ln K t1
In other words, we can use our data on total PTW Þ and stock (Kt) to calculate an implicit rate sales ðQgross t of depreciation. The latter varies over time because it is imputed from time series. The estimate of dt that this process yields is plotted over time in Fig. 2. The chart suggests that replacement sales as a proportion of outstanding stock have varied enormously over the past 60 years, around a sample mean value of 39.5% per annum. This proportion soared to a value of 59% in 1980, but it sank to almost 9% in 1993. The volatility of the implied replacement rate suggests that either, or both, of the following problems may be present: first, that there are deficiencies in the data
M. Duffy, T. Robinson / International Journal of Transport Management 2 (2004) 111–121 0.6
0.5
0.4
0.3
0.2
0.1 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Fig. 2. Estimates of the rate of depreciation of motorcycles in the UK.
(e.g. the errors caused by vehicle duty evasion8) that translate into unrealistic estimates of the implied depreciation rate; and, second, that Eqs. (4) and (6) are based on an unrealistic assumption of a constant rate of depreciation of the stock. As a consequence of these potential errors of measurement and specification, empirical estimates of Eq. (4) may provide a poor fit to the data (and Eq. (6) will yield unreliable estimates of dt). For these reasons, an alternative approach to the estimation of the short- and long-run elasticities of demand for motorcycles is also examined in this paper, namely through the estimation of Eq. (5) for net sales of this vehicle type, which avoids any problems of measurement and specification with respect to replacement sales.9 Returning to the discussion of the specifications of the estimated demand models, it is also worth noting that the sign of the coefficient on ln Kt1 in the gross
8 Broadley (2001, p. 3) reports that ‘‘evidence suggests that 25% of motorcycle stock is evading the VED licence’’. If this proportion is approximately constant over time, then the growth rate of the motorcycle stock D ln Kt will be relatively unaffected by the evasion rate, but the measured stock level will be biased downwards. Then estimates of dt in Eq. (6) will be subject to an error that varies with the size of the measured, lagged stock (but is unaffected by D ln Kt). 9 As suggested by a referee, an alternative way to introduce consumer preferences would be to make the income elasticity (and other coefficients) a function of socio-demographic variables. This could be attempted in various ways. For example, the parameters of the model could be assumed to be linear functions of various sociodemographic variables. That approach, though, leads to loss of degrees of freedom in what is already a small sample size. A parsimonious specification has advantages in that respect (and in terms of estimation and interpretability) over a model that would appear to be unwieldy, since it could involve several interaction terms between socio-demographic and economic factors. In another approach, it would be interesting to use micro-socio-economic panel data in modelling these interactions, but such datasets are not available, as far as we are aware. The influence of socio-demographic variables on the responsiveness of demand for motorcycle stock is beyond the scope of the present paper and is deferred to the agenda for future research.
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sales equation (4) cannot be determined a priori, for it depends upon the unknown, relative magnitudes of the rates of depreciation and adjustment. If d ffi h, the coefficient on ln Kt1 in (4) is approximately zero (and ln Kt1 could be omitted from the estimated form without inducing bias). If d exceeds h, the lagged stock will tend to raise current period sales of motorcycles, whilst the lagged stock will depress total sales of motorcycles in the current period if the rate of adjustment exceeds the rate of depreciation. On the other hand, the coefficient on the lagged stock term in the net sales equation (5) is expected unambiguously to be negative. We also wish to allow for changing tastes and preferences between modes of travel in the model specifications, something which casual empiricism suggests is an important factor. The effect of changes in tastes upon consumer demand for the services of motorcycles (and for other modes of transport), and thence for motorcycle stock, is accounted for by the inclusion among the regressors of a trend. We examine two different specifications of the trend term. In one specification, a deterministic trend is employed. In an alternative approach, we used a variable stochastic trend, although this includes a constant, deterministic trend as a special, limiting case. We are attracted to a stochastic trend (local linear trend) specification because we do not know of any strong a priori reasons for believing that changing tastes in this market have exerted their effects in a constant, steady way. As consumer perceptions of the relative advantages and disadvantages of motorcycle ownership have waxed and waned over the post-war period, it seems equally plausible to suggest that trend changes in tastes and demand have been variable rather than fixed. However, this is an issue that can only be resolved by examining and comparing the empirical performance of the two specifications.9 Eq. (4) augmented by a stochastic trend is: ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b4 ln K t1 ln Qgross t þ lt þ e t ;
ð7Þ
where et is the irregular term, and the stochastic trend term lt is specified as lt ¼ lt1 þ ct1 þ gt ; gt NID 0; r2g ; ð8Þ 2 ð9Þ ct ¼ ct1 þ ft ; ft NID 0; rf ; where ct is the slope or gradient of the trend lt. The irregular et, the level disturbance gt and the slope disturbance ft are mutually uncorrelated. This formulation collapses to a random walk with constant drift if r2f ¼ 0, and to a deterministic trend if r2g ¼ 0 as well. In the latter case, l and b correspond to the constant term and the coefficient on a time trend, respectively, in a conventional OLS regression. If r2g is set to zero when r2f is positive, then the trend is smoothlychanging.
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Prior to estimation, the net sales equation (5) is also augmented by a stochastic trend term: 0 ln Qnet t ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b4 ln K t1 þ lt þ et .
ð10Þ The model comprising Eqs. (7) or (10) with (8) and (9) are specific forms of HarveyÕs (1989) Basic Structural Model (BSM), amended to include explanatory variables. If the disturbances in the models are independently and normally distributed, the hyperparameters r2e , r2g , and r2f (which determine how the irregular and trend components behave over time) may be estimated by maximum likelihood with the recursive equations of the Kalman filter used to update the unobserved components (Harvey, 1989). Then estimates of the trend component may be extracted by a smoothing algorithm as in Koopman (1993) making use of the full set of observations in the sample. For this work, all of these calculations have been made through the use of the STAMP 6.20 package: see Koopman et al. (2000) for details of the estimation algorithms. 3. Data and empirical results The data set consists of 37 annual observations for the UK from 1964 to 2000. We measure the stock of motorcycles, Kt, by the total number of powered twowheeled vehicles with current Vehicle Excise Duty paid, measured during the month of December each year.10 The stock figure is deflated by mid-year estimates of the total population aged 15–60 years (Source: Annual Abstract of Statistics, various issues, and the National Statistics Online website at
Association, and the series was then put on a per capita basis by dividing by the mid-year estimates of the total population aged 15–60 years prior to transformation into logarithmic values. The income term, Yt, is measured as real household disposable income in the UK deflated by mid-year total population estimates, all ages (Sources: Annual Abstract of Statistics, various issues, and the National Statistics Online website at
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Table 1 Basic structural models for motorcycle sales: 1964–1995a Dependent variable Log gross sales (ln Qgross ) t
Log net sales (ln Qnet t ) Stochastic trend
Deterministic trend
Stochastic trend
Deterministic trend
Panel A: Estimated coefficients of the final state vector lnYt (b1) 0.7577 (2.570) ln MCt (b2) 0.3115 (1.473) (b3) 0.0038 (2.385) Rt ln Kt1 (b4) 0.1993 (1.470) Level (l) 2.5278 (1.929) Slope (c) 0.0258 (1.488)
0.9210 (3.050) 0.7100 (3.488) 0.0079 (4.495) 0.0134 (0.238) 5.2736 (4.053) 0.0226 (3.221)
2.1755 (1.381) 1.1558 (1.082) 0.0102 (1.680) 0.4743 (0.569) 2.3063 (0.307) 0.0759 (0.572)
4.0640 (1.595) 4.7991 (2.795) 0.0584 (3.958) 1.4915 (3.140) 34.2140 (3.117) 0.0954 (1.615)
Panel B: Long-run elasticities Income Motoring costs Interest rate
+3.80 +1.56 0.02
n.a. n.a. n.a.
+2.50 1.33 0.01
3.71 4.38 +0.05
6.628 · 104 [1.000] 1.486 · 1012 [0.000] 9.759 · 105 [0.147]
0.0014
0.0000 [0.000]
0.1031
n.a.
0.1327 [1.000]
n.a.
n.a.
0.0073 [0.417]
n.a.
0.56 6.1373 0.0013 4.66 {0.59} 20.22 {0.00} 9.25 {0.10}
0.59 6.3450 0.0012 17.06 {0.01} 9.86 {0.01} 26.63 {0.00}
0.92 3.1115 0.0270 4.85 {0.56} 5.14 {0.08} 4.10 {0.53}
0.74 2.0800 0.0859 25.02 {0.00} 2.37 {0.31} 12.75 {0.03}
Panel C: Hyperparameters Irregular r2e Level
r2g
Slope
r2f
Panel D: Test statistics R2 AIC p.e.v. Q BS PF
Panel A: Figures in parentheses ( ) are t-values. Panel C: The q-ratios in square brackets [ ] are the ratios of the associated variance to the largest hyperparameter variance. Since the variances govern the movements in the components, the q-ratios indicate the relative importance of the irregular, level and slope in that process. Panel D: The numbers in curly brackets { } are p-values. a In this table, R2 is the conventional coefficient of determination. This coefficient is not comparable across the net and gross sales specifications, since the two models use different dependent variables. AIC is the Akaike Information Criterion. The p.e.v. is the variance of the one-step-ahead prediction error. Q is the Box-Ljung statistic, a test for residual serial correlation, which is based on the first 8 residual autocorrelations and tested against a v-square distribution with 6 degrees of freedom. BS is the Bowman–Shenton (1975) test for normality of the residuals, distributed asymptotically as v-square with 2 degrees of freedom. PF is a Chow post-sample predictive ÔfailureÕ test, based on predictions for 1996–2000 (using estimates of the final state vector for the 1964–1995 estimation period). PF is distributed approximately as v2(5). In the specifications which employ deterministic trends, r2g ¼ r2f ¼ 0. The long-run elasticities are calculated by the formulae given in the text, with those for gross sales based on an assumption that the time-varying rate of depreciation reverts to its (sample) mean value of 0.395 in the long-run.
Economists need to assess and discuss all three of these criteria. An insignificant estimate which is of correct size and correct sign is still interesting and informative about the theory that is being tested. For there may be several reasons why the test for significance has failed (eg multicollinearity). The strongest a priori expectations in this context relate to b04 ¼ h in the net sales model. We expect b04 in that model to be negative and to lie in the range 1 6 b04 6 0. The estimates in Table 1 (and Table 2) satisfy those criteria. If the estimate of b04 is insignificantly different from zero, that indicates that a significant stock-adjustment effect has not been identified (which may be consistent with the true position in the motorcycle market). We have presented in Table 1 an estimated rate of adjustment coefficient in the net sales model h = 0.2 indicating that 20% of the gap between
the desired stock of motorcycles and its actual value is closed by net sales in any year on average. On the one hand, that estimate is insignificantly different from zero. On the other hand, the estimate in Table 1 is not significantly different in a t-test from 0.3, the point estimate of h in Table 2, which is significantly different from zero. Our sense of these results is that there are stock adjustment effects present in these data and this market. It is also worth noting that the deterministic trends models consistently yield estimates of the coefficients on the lagged stock terms, b04 , that are positive rather than negative. For the net sales model, this is not plausible, but we cannot say whether the result is plausible or not in the case of the gross sales model since the coefficient is not identified in that case (see above). But even if the negative coefficients on lagged stocks in all of the
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Table 2 Basic structural models for motorcycle sales: 1964–2000
a
Dependent variable Log gross sales (ln Qgross ) t
Log net sales (ln Qnet t ) Stochastic trend
Deterministic trend
Stochastic trend
Deterministic trend
Panel A: Estimated coefficients of the final state vector ln Yt (b1) 0.5362 (1.771) ln MCt (b2) 0.2650 (1.157) (b3) 0.0031 (1.914) Rt ln Kt1 (b4) 0.3100 (2.299) Level (l) 1.4067 (1.036) Slope (c) 0.0186 (0.732)
0.8200 (2.154) 0.7380 (2.821) 0.0074 (3.243) 0.0418 (0.605) 5.0807 (3.026) 0.0196 (2.204)
1.9392 (1.453) 1.1462 (1.185) 0.0095 (1.747) 0.6963 (1.005) 4.5109 (0.714) 0.1847 (1.130)
3.8230 (1.387) 5.1277 (2.706) 0.0558 (3.399) 1.1969 (2.393) 34.5090 (2.839) 0.0855 (1.332)
Panel B: Long-run elasticities Income Motoring costs Interest rate
+1.73 +0.85 0.01
n.a. n.a. n.a.
+1.78 1.05 0.01
4.77 6.39 0.07
5.990 · 104 [1.000] 0.000 [0.000] 2.249 · 104 [0.375]
0.0025
0.0000 [0.000]
0.1288
n.a.
0.0120 [0.974]
n.a.
n.a.
0.0123 [1.000]
n.a.
0.45 5.8391 0.0021 22.17 {0.001} 3.15 {0.21}
0.91 3.1964 0.0265 6.48 {0.37} 3.79 {0.15}
0.64 1.8803 0.1103 24.84 {0.00} 2.307 {0.32}
Panel C: Hyperparameters Irregular r2e Level
r2g
Slope
r2f
Panel D: Test statistics R2 AIC p.e.v. Q BS a
0.59 6.0316 0.0016 2.56 {0.86} 5.70 {0.06}
Notes: Estimation period 1964–2000. See also the notes to Table 1.
stochastic trends models are deemed to be plausible, some may suggest still that aspect constitutes little advantage over the deterministic trends specification for those negative coefficients are insignificantly different from zero. It is certainly true that dynamic effects are not estimated with much precision or reliability in either case, but the stochastic trends specification is preferred nevertheless for the following reasons. First, the lagged stock term does emerge as significant and negative in the full sample period estimates of the net-sales-cum-stochastic-trends model: see Table 2. Second, the incorrect sign on this coefficient in the deterministic trends specification, whilst having no effect, of course, on the short-run demand elasticities, does contribute to the calculation of values for the long-run elasticities of demand that are exceedingly implausible both in terms of sign and magnitude (hence these are not reported). A third advantageous feature of the estimated stochastic trends models is that they pass the post-sample predictive failure tests (indicating that they successfully predict the above-mentioned upswing in motorcycle ownership in the late 1990s), whilst the deterministic trend models fail that test: see the PF statistics in Table 1. This is an important strength of the stochastic trend models: as we argued previously, predictive accuracy is
an acid test of the quality and reliability of any estimated model. In this case, the linear trend models incorrectly extrapolate into the future past trends in consumer preferences away from motorcycles, whilst the flexible, variable, stochastic trend is able to capture the reversal in trend that may have occurred from the mid-1990s onwards. It should be noted though that economic factors, as well as changes in consumer tastes, contributed, no doubt, to the upswing in demand for motorcycles in the late 1990s. Thus, real incomes rebounded as the economy recovered from the recession of the early 1990s, and the real cost of motoring rose steeply at the same time (for example, because of tax increases). The latter may have restrained the demand for cars, and favoured motorcycle sales. On the other hand, real interest rates were at high levels during this period: this may have dampened motorcycle demand (but our estimates suggest that any such effect may have been quite weak and easily offset by the other factors: see below). A fourth advantage of the stochastic trend models is that they do not appear to suffer from autocorrelation in their residuals, whereas the deterministic trend models do have large, significant Box-Ljung statistics (see the Q statistics in Tables 1 and 2). The autocorrelation may be prima facie evidence of misspecification in the deterministic trend models.
M. Duffy, T. Robinson / International Journal of Transport Management 2 (2004) 111–121
For these reasons, we favour using the stochastictrends, rather deterministic trends, formulation in our final analysis. Furthermore, we prefer to work with net sales data rather than gross sales. For we are unable to estimate the coefficients in the final state vector for the gross-sales-cum-stochastic-trends model with any precision: all of the coefficients are insignificantly different from zero (see Tables 1 and 2). This feature of the results may be due to the inexplicably high volatility of replacement sales (see above). In contrast, we enjoyed some success in estimating plausible coefficient estimates that are significantly different from zero, or almost so, in many instances in the net-sales-cum-stochastic-trends models: see Tables 1 and 2. From this point, we will focus our attention on net-sales-cum-stochastic-trends model of motorcycle demand (henceforth, the net sales model, for short). A small point to note is that the estimated hyperparameters in Tables 1 and 2 for the net-salescum-stochastic-trend models (especially the approximately zero value for the estimate of r2g ) suggest that motorcycle demand is subject to a Ôsmooth trendÕ rather than a Ôlocal linear trendÕ: see Koopman et al. (2000). This is a model that achieves a good fit to the data, as evidenced by the coefficients of determination in Tables 1 and 2, as well as the time series plot in Fig. 3 of the actual net sales series and the fitted values from the model estimated over the whole sample period, 1964– 2000. Fig. 3 also contains a plot of the estimated trend in net sales: it clearly shows the secular drift away from motorcycles by consumers, together with the pick-up in trend sales in the late 1990s. It is worth trying to examine the implications of the estimated models for growth prospects in demand for
0.1
Actual
119
motorcycles and for transport policy. Useful concepts to employ in this exercise are the elasticities of motorcycle demand with respect to income, motoring costs and the costs of credit, as well as the underlying changes in consumer tastes and preferences as represented by the stochastic trend. However, it must be noted that our empirical estimates of these parameters are inevitably characterised by some imprecision and uncertainty. This is due to a number of factors. First, there is the unavoidable effect, of course, of sampling variance. Secondly, the stochastic trend is by nature increasingly unpredictable as the forecast horizon is lengthened: extrapolation of the trend element must be largely judgemental. Thirdly, the short and long-run elasticity estimates are surrounded by a significant margin of uncertainty because the evidence relating to the temporal stability of the models is mixed. As already noted, the Chow post-sample predictive failure test statistics reveal no evidence of instability in the stochastic trends models. This is confirmed by construction of confidence intervals from the individual t-ratios in pairwise comparisons of estimated coefficients across Tables 1 and 2. The net sales model is deemed to be stable in all of those tests, but it accommodates, nevertheless, substantial changes (namely, declines of approximately 50%) in the estimated elasticities of demand when the sample period is extended. Furthermore, the estimated coefficients on the income and interest rate terms in Table 1 are significantly different from zero only at the 10%, but not the 5%, level, whilst the motoring cost term is insignificant at both levels. It is unclear whether these instabilities reflect sampling variance, or more fundamental structural changes in the market for motorcycles in the late 1990s. In these
Fitted
0.0 -0.1 1965
1970
1975
1980
1985
1990
1995
2000
1970
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
-0.75 -1.00 Trend
-1.25 -1.50 1965 0.050 Irregular
0.025 0.000 -0.025 1965
1970
Fig. 3. Net sales of motorcycles: actual values, fitted values, trend and irregular (logarithms).
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circumstances, and until further information and market experience become available, it would seem advisable to be prudent in the assessment of elasticities, by giving greater weight to the lower, full-sample estimates. Thus, we err on the side of caution by choosing to view the long-run income elasticity of demand for motorcycle ownership as being in the region of 1.5, compared with a short-run elasticity of about 0.5. Taken on its own, a long-run income elasticity of 1.5 would suggest, on an assumption that long-run income growth remains unchecked, that the medium-to-long-term growth prospects for motorcycle ownership are quite high. The discrepancy in magnitudes of the short-run and longrun income elasticities may be attributed, in the usual way, to the effects of costs of adjustment of desired stock to actual levels. An increase in motoring costs, mainly the expense of buying and running a car, is estimated to have a small, positive but insignificant cross-effect on desired motorcycle ownership in the short-run (Tables 1 and 2). However, the estimates also suggest that this effect may be much larger in the long-run: the estimate of the longrun cross-elasticity from data for 1964–1995 in Table 1 is as high as +1.6, but this falls to +0.85 in the full sample (Table 1). However, statements about the effects of this variable must be made with great caution because of the insignificance of the associated coefficient estimates in Tables 1 and 2. Until further information appears, a reasonable, cautious working assumption in exercises concerned with the forecasting of motorcycle ownership over the long-term may be that a projected increase in motoring costs is likely to raise the desired stock of motorcycles in the same proportion. That is, the longrun cross elasticity could be assumed to be unity. These estimates have an obvious implication for any assessment of the impact of transport policy on the market for motorcycles: namely, any significant increase in road-use charges, which are currently being discussed by policy makers, and providing that they form a significant element of motoring costs, is likely to have a major, beneficial effect on the demand for motorcycles. The real interest rate semi-elasticity in the net sales model is minute in both the short-run and in the longrun: Table 1. In short, motorcycle ownership at any horizon is not very sensitive to changes in the real cost of credit.11
4. Conclusions This paper has reported on an econometric investigation of motorcycle ownership in the UK. The favoured specification was a stock adjustment model augmented by a stochastic trend to allow for changing consumer preferences over modes of transport. It did not prove possible to obtain meaningful estimates of the determinants of gross sales (net additions to the stock plus replacement purchases) because of the large, inexplicable fluctuations in the depreciation component. Greater success was achieved in explaining motorcycle sales net of replacement purchases. Empirical estimates of the net sales model suggest that the future growth prospects for motorcycles may be quite good. This tentative conclusion follows primarily from what appears to be a significant, relatively high, long-run income elasticity of demand for motorcycles, combined with a high cross-elasticity of substitution effect with regard to the cost of motoring. If the long-run expansion of real incomes continues apace in the future, the demand for cars will increase, as will the demand for other modes of transport including motorcycles. The general expansion in demand for transport may favour cars more than other modes, but this could be offset somewhat by other factors. Thus, the likely effect of further increases in the cost of running cars through policy initiatives (eg increases in ÔgreenÕ taxes on petrol and emissions, car tax, road-use charges, etc) will be a significant expansion in demand for noncar modes of transport, including motorcycles. At the same time, our estimates have indicated that these effects are subject to a countervailing tendency, represented by an on-going change in the publicÕs preferences away from motorcycles towards other modes of transport. Which of these tendencies will dominate in the motorcycle market over the next few years remains to be seen.
Acknowledgements The authors would like to acknowledge the very helpful comments and suggestions made by the editor and two, anonymous referees which helped to improve the paper. The usual disclaimer applies.
References 11
Several other possible determinants of motorcycle demand were investigated but without success. Thus, the influence of demographic changes was examined by the inclusion in the model of the logarithm of the proportion of the total population that is aged between 15 and 65 years. This admittedly crude measure of demographic changes in the age structure of the population was always estimated to have an insignificant effect on the desired stock of motorcycles. Similarly, a simple measure of the amount of congestion on the roads in the UK (distance travelled by motor vehicles divided by road length) had no apparent, significant effect on the desired stock of motorcycles.
Bowman, K.O., Shenton, L.R., 1975. Omnibus test contours for pffiffiffiffiffi departures from normality based on b1 and b2 . Biometrika 62, 243–250. Broadley, S., 2001. Motorcycling in Great Britain, Transport Statistics. Transport Trends. 2001 Edition, Department of the Environment, Transport and the Regions (available on the web at). Button, K.J., Pearman, A.D., Fowkes, A.S., 1982. Car Ownership Modelling and Forecasting. Gower Press, Aldershot.
M. Duffy, T. Robinson / International Journal of Transport Management 2 (2004) 111–121 Chow, G., 1957. Demand for Automobiles in the U.S.: A Study in Consumer Durables. North Holland, Amsterdam. Dargay, J.M., Vythoulkas, P.C., 1999. Estimation of a dynamic car ownership model: A pseudo panel approach. Journal of Transport Economics and Policy 33-3, 287–302. Department of the Environment, Transport, and the Regions, 2000. Transport 2010: The 10 Year PlanÕ (available on the web at). Grieves, R., 1983. The demand for consumer durables. Journal of Money, Credit, and Banking 15 (3), 316–326. Hanley, M., Dargay, J.M., 2000. Car ownership in Great Britain–a panel data analysis. ESRC Transport Studies Unit, University College London. Harvey, A., 1989. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge. Jong, G.C. de, 1990. An indirect utility model of car ownership and use. European Economic Review 34, 971–985. Koopman, S.J., 1993. Disturbance smoother for state space models. Biometrika 80, 117–126. Koopman, S.J., Harvey, A.C., Doornik, J.A., Shephard, N., 2000. Stamp: Structural Time Series Analyser, Modeller and Predictor. Timberlake Consultants Press, London. Ledger, A., 2001. The Use and Characteristics of Vehicle Stock DataÕ, Transport Statistics. Transport Trends. 2001 Edition, Department of the Environment, Transport and the Regions (available on the web at ).
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MINTeL, 2002. Motorcycles, Market Intelligence, June, Mintel International Group Ltd.: London. Muellbauer, J., 1981. Testing Neoclassical Models of the Demand for Consumer Durables. In: Deaton, A. (Ed.), Essays in the Theory and Measurement of Consumer Behaviour. Cambridge University Press, Cambridge, UK. Romilly, P., Song, H., Liu, X., 2001. Car ownership and use in Britian: A comparison of the empirical results of alternative cointegration estimation methods and forecasts. Applied Economics 33, 1803– 1818. Stone, R., Rowe, D.A., 1957. The market demand for durable goods. Econometrica 25, 423–443. The Economist, 2002a. Jam, Darling? October 10. The Economist, 2002b, ÔGridlocked BritainÕ, December 12. The Economist, 2003, ÔShush, DarlingÕ, April 3. Train, K., 1985. Qualitative Choice Models. The MIT Press, Cambridge MA. Whelan, G., 2001. Methodological advances in modelling and forecasting car ownership in Great Britain. Paper Presented at the European Transport Conference 2000, PTRC, Cambridge. Whelan, G., Wardman, M., Daly, A., 2000. Is there a limit to car ownership growth? An exploration of household saturation levels using two novel approaches. Paper Presented at the European Transport Conference 2000, PTRC, Cambridge. Witt, S., Johnson, S.R., 1986. An econometric model of new-car demand in the UK. Managerial and Decision Economics 7, 19–23.
An econometric analysis of motorcycle ownership in the UK Martyn Duffy, Terry Robinson
*
Manchester Business School, The University of Manchester, Booth Street West, Manchester M15 6PB, UK Received 1 April 2004; received in revised form 1 March 2005; accepted 1 April 2005
Abstract This paper reports on an econometric investigation of motorcycle ownership in the UK. The favoured specification is a stock adjustment model augmented by a stochastic trend to allow for changing consumer preferences over modes of transport. Empirical estimates suggest that the future growth prospects for motorcycles may be quite good. This tentative conclusion follows primarily from what appears to be a significant, relatively high, long-run income elasticity of demand for motorcycles, combined with a high cross-elasticity of substitution effect with regard to a measure of the cost of motoring, which is dominated by the costs of buying and running a car. At the same time, our estimates indicate that these effects are subject to a countervailing tendency, represented by an on-going change in the publicÕs preferences away from motorcycles towards other modes of transport. Which of these tendencies will dominate in the motorcycle market over the next few years remains to be seen. 2005 Elsevier Ltd. All rights reserved. Keywords: Motorcycles; Consumer demand; Stock adjustment
1. Introduction Over recent decades, motorcycle ownership (which includes scooters and mopeds in this paper) has passed through several peaks and troughs: Fig. 1. The stock measure of the number of motorcycles currently licensed in the UK rose from 729,000 at the end of 1950 to a peak of 1,796,000 at the end of 1960. It then declined to 982,000 by the end of 1972 before rising to a new peak of 1,371,000 in 1981. Motorcycle ownership contracted over subsequent years to reach a record post-1940s low level of 594,000 vehicles in 1995. Since that date, the stock of licensed motorcycles has increased steadily, and by the end of 2001 882,000 motorcycles were licensed for use and 177,100 new registrations were made during the year.1
*
Corresponding author. Department for Transport, Transport Statistics Great Britain: 2002 Edition (available on the web at
1471-4051/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijtm.2005.04.002
Casual empiricism suggests that these trends and cycles in motorcycle ownership must reflect to some extent changes in tastes and preferences over modes of transport in the post-war period. But they are also likely to result from the influence upon demand for motorbikes of economic factors. Thus, the increase in motorcycle ownership in the 1970s is probably related to some extent to the adverse impact on the running costs of cars of the first two oil price shocks, and to the subsequent search by many travellers for alternative, cheaper modes of transport. For the same reason, the use of the fuel duty escalator in the late 1990s may have had a favourable effect on the demand for motorcycles. Rising affluence has undoubtedly increased the demand for cars, but it is not clear a priori what the net effect of rising incomes has been on the motorcycle market. The effect of these economic factors on the demand for motorcycles depends upon the magnitudes of elasticities of demand in this market, but little is known about such matters in this little researched area. This paper reports on an initial attempt to estimate and assess these parameters
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1.75 1.5 1.25 1.00 0.75 0.50 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Fig. 1. Motorcycles, scooters and mopeds: number of vehicles licensed at the end of year (1945–2000), millions.
and the relative contribution of changes in the economic environment and consumer tastes to the evolution over recent decades of motorcycle ownership in the UK. Motor cycle ownership is a stock concept, whereas consumption of the services of motorcycles is a flow variable. In this paper we follow the practice of most previous empirical investigations of demand for consumer durables by focusing on the demand for the stock of motorcycles, rather than the amount of travel that is effected through that mode of transport (motorcycle consumption).2 In fact, though, this decision may make little difference to the general nature of the results obtained. For the flow variable motorcycle traffic, measured by billion vehicle kilometres, has followed a similar pattern to the stock of currently licensed motorcycles over time (especially since the early 1980s): see Broadley (2001, Chart E.2, p. 2). Traffic engineers, motorcycle manufacturers and other parties are motivated to understand the causes of past fluctuations in motorcycle ownership, in so far as this knowledge may help to predict likely future changes in the use of this mode of transport. The more general need is to attempt to anticipate both the growth in total traffic as well as the contributions from alternative modes of transport. However, a complete study of that kind is beyond the scope of the present paper, which is concerned simply with the demand for one particular type of transport, motorcycles. Since the early 1950s, there has occurred a trend movement towards travel by car and away from other modes of transport, including buses, trains and motorcycles. In 1952 cars accounted for only 32% of passenger kilometres, but this proportion had risen to 92% by 2001 (Social Trends, vols. 31–33). However, the rapid growth in car traffic that occurred in the early post-war decades had slowed to a much more modest pace in the 1990s: cars reached the 92% share of total road traffic as early as 1991. This slowdown in the growth of car traffic may represent early signs of a Ôsaturation effectÕ, arising from 2 Although Train (1985) and Jong (1990) present an approach in which the consumption of services and the stock are dealt with jointly.
problems of congestion and other similar constraints. In that case, any future growth in total traffic may be realised largely through other modes of transport, including motorcycles.3 Then the upswing in motorcycle ownership that has occurred since the mid-1990s may continue during future years. An important factor that impinges on the motorcycle market is official policy toward transport, and future initiatives in this area may favour the total demand for powered two-wheel (PTW) vehicles, that is, motorcycles, scooters and mopeds. Thus, many governments have taken action to inhibit motor car use in major cities to relieve congestion4 and it is recognised that increased use of PTWs (and bicycles) can help facilitate this, due to the small size and nimbleness of those vehicles. PTWs and bicycles have the added benefit of making a small contribution to the achievement of official targets for reduced emission of ÔgreenhouseÕ gases. An example of this policy stance can be seen in the UK with the Greater London AuthorityÕs decision to exempt motorcycles from its recently introduced road pricing scheme. The Greater London Authority introduced a Congestion Charge in February 2003. Under this scheme vehicles crossing the ÔboundaryÕ of a zone defined by the Inner Ring Road have to pay a £5 per day toll. The GovernmentÕs ten year transport plan appears to have made little progress towards fulfilment, and congestion is almost certain to go on increasing: The Economist (2002a,b). In a paradoxical way, this may be of benefit to the motorcycle industry. Frustration with public transport and the resultant congestion on the roads, especially in city centres and major motorway complexes, may lead to an increase in two-wheeled vehicle usage: MINTeL (2002). There is growing pressure from the governmentÕs advisers to introduce road charges, particularly on motorways: The Economist (2003). If motorcycles are granted exemption from any future road charging schemes, as in the case of the London Congestion Charge, the incentive to own a motorcycle will increase accordingly. Since the motorcycle may be seen as a partial solution to the problem of traffic congestion in the UK, it is important to estimate and forecast the demand for motorcycles. Although there have been many econometric studies of the demand for car ownership and use in the UK (Romilly et al., 2001; Whelan, 2001; Whelan et al., 2000; Hanley and Dargay, 2000; Dargay and Vythoulkas, 1999; Witt and Johnson, 1986; Button 3 The plateauing of car ownership could also be caused by changes in preferences, in which case there may little or no effect on motorcycle ownership. 4 The GovernmentÕs 10-year plan for transport aims to reduce congestion on BritainÕs roads by 6% by 2010: Department of the Environment, Transport, and the Regions (2000).
M. Duffy, T. Robinson / International Journal of Transport Management 2 (2004) 111–121
et al., 1982) to our knowledge there has been no published attempt by economists to model the demand for motorcycles in the UK, or indeed in any other country. This paper sets out to rectify this omission.
stant rate, d, per period, so that the logarithmic values of replacement sales in period t are d ln Kt1. On making that assumption, a modified version of Eq. (1) is obtained: ln Qgross ¼ h ln K t þ ðd hÞ ln K t1 ; t
2. Methodology We define net sales of motorcycles in any period t to be identical to the change in the stock of motorcycles between the end of period t 1 and the end of period t, and gross sales are net sales plus ÔdepreciationÕ (that is, purchases to replace vehicles that have been removed from the stock during period t). The specification and estimation of the equation for gross sales proved to be, in some respects, problematic for reasons that are discussed below. These problems are avoided in a model for explaining net sales, although that benefit is achieved at a cost of not accounting for replacement purchases, a significant proportion of total annual sales of new motorcycles in the UK. For the purpose of examining and reporting on these issues, we have estimated, with differing degrees of success, demand functions for both gross sales and net sales of motorcycles. Because we are analysing the demand for a consumer durable, the framework for our investigation is that much-used workhorse of applied studies in this area, the stock adjustment model,5 which is expressed, following the common practice in time series work, in logarithmic form: D ln K t ¼ h½ln K t ln K t1 ;
ð1Þ
where Kt is the stock of motorcycles per head of the population aged 15–606 at the end of period t, the asterisk denotes a desired magnitude, and h represents the average Ôrate of adjustmentÕ during a single period of the actual stock to its desired level. Transaction costs and other factors that induce inertia in consumer behaviour are likely to cause the adjustment of the actual stock to its desired level to be incomplete in a single period, so we expect h to lie in the interval: 0 < h < 1. The left-hand side variable in Eq. (1), the growth rate of the stock of motorcycles, approximates to the net sales of the good (expressed as a proportion of the previous periodÕs outstanding stock), ln Qnet t . We can move to a gross measure of sales if we add estimates of replacement sales to both sides of the equation.7 The easiest way to achieve this adjustment is to introduce an extra assumption: that the stock depreciates at a con-
5
See Chow (1957), Grieves (1983), and Stone and Rowe (1957). Unfortunately data on the population starting at 18 was not available. The next start point after 15 is 20. 7 We must add estimates of replacement sales since, to our knowledge, no direct times series measures of this component have been published. 6
113
ð2Þ
where Qgross represents gross purchases of motorcycles t per person per period. The demand for motorcycles is, in fact, a demand for the services of motorcycles. For a given level of intensity of use (as measured by, say, the average number of trips and/or the average trip mileage), a greater demand for motorcycle services implies necessarily a larger desired motorcycle stock. Indicators of intensity of use of motorcycles give conflicting signals. Thus, the number of trips made by motorcycle appears to be falling over time, being 3 per person per year in 1997/99, down from 6 in 1989/91 and 9 in 1985/86: Broadley (2001). On the other hand, the average length of a motorcycle trip has increased from 5.6 miles in 1985/86 to 9.3 miles in 1997/99 (which is 10% longer than the average car trip). In these circumstances (of less but longer motorcycle trips), the assumption of a constant level of intensity of stock use is probably not too unrealistic. We posit that the desired, per capita stock of motorcycles in period t, K t , is determined fundamentally by real per capita disposable income (Yt), a measure of the real cost of motoring (MCt), and a real interest rate term (Rt). We would have liked to relate the desired stock of motorcycles to, inter alia, the relative price of motorcycles, but that was infeasible because of a lack of data on prices. It is hoped that any misspecification bias that may result from that omission is minimised by the inclusion of the index of the real cost of motoring, which is itself a relative price term that could allow for substitution effects in choice of transportation. In this analysis, the desired level of motorcycle services and stock rises (or falls) as people become more affluent. With increased incomes, households revise their plans for commuting and leisure activities, and that impacts on their desired rates of utilisation of various modes of transport. The desired motorcycle stock will also vary inversely with the real cost of using motorcycles, and vary directly with the costs of alternative modes of transport. It must be recognised indeed that in modelling motorcycle ownership and use, it would be good to distinguish between different travel purposes. It may be the case that many motorcycles are bought nowadays primarily for leisure trips, and for such trips they may not be as close substitutes with the car, as they would be for commuting. This is an issue that needs to be borne in mind when developing judgemental assessments of the outlook for market demand for motorcycles, but it could not be investigated further in formal econometric work because of data constraints. The time series data available to the authors are highly aggregate
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in nature, and cannot be used for the purpose of distinguishing, for example, between types of journey. With these comments in mind, the desired stock of motorcycles is modelled in log-linear form as follows: ln K t ¼ a1 ln Y t þ a2 ln MCt þ a3 Rt .
ð3Þ
The income elasticity of demand for the motorcycle stock (a1) may be positive or negative, depending on whether motorcycle services are categorised by the adult population as akin to those of a ÔnormalÕ or ÔinferiorÕ good, respectively. Economic theory suggests that the stock demand for a consumer durable may vary inversely with the user cost of that good: Muellbauer (1981). In this study the user cost of motorcycles is represented approximately by the real interest rate, Rt, and we expect that the interest semi-elasticity of demand for motorcycle stock is non-positive (i.e. a3 6 0). It must be noted that the other elements of the user cost of motorcycles (such as depreciation) have been omitted due to lack of data, and the consequent misspecification and possible bias must be borne in mind when considering the empirical estimates of the model. The statistical measure of motoring costs, MCt, used in this study is dominated by the costs of owning and running a car, which is, of course, an alternative form of transport. When motoring costs rise, the demand for the services of motorcycles may also increase as people reduce their use of cars and switch to other modes of transport. These costs might also decrease, e.g. as a result of increases in fuel efficiency. The elasticity of demand for motorcycle stock with respect to the index of motoring costs is expected to be non-negative (a2 P 0). We substitute (3) into (2) to obtain the estimating form of a demand equation for gross sales of motorcycles: ln Qgross ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b4 ln K t1 ; t
ð4Þ
where bi = hai (i = 1, 2, 3) and b4 = (d h). Since Eq. (4) contains only four coefficients that can be estimated, the five structural parameters h, d, a1, a2, and a3 are not identified. In particular, we cannot unscramble unique estimates of the long-run elasticities a1, a2, and a3 from (4) unless we fix one parameter a priori, such as d: then the long-run elasticities could be calculated as ai = bi/(d b4) (i = 1, 2, 3). Even then, any error in the assumed value of d would translate into erroneous estimates of h, a1, a2, and a3. Subtraction of depreciation from both sides of (4) yields an equation that can be estimated to explain net sales of motorcycles, and that equation is identified exactly: ln Qnet ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b04 ln K t1 ; t
ð5Þ
where bi = hai (i = 1, 2, 3), as defined as below Eq. (4), but b04 ¼ h. In this equation, the lagged stock term, h ln Kt1, allows for the effects of inertia and habit on net sales: by adding ln Kt1 to both sides of (5), we can see that the lower the value of h, the more important are inertia and habits in consumer behaviour, and the more the current, desired stock of motorcycles depends upon the recent, actual stock. The lagged stock term in (4) does, of course, strengthens this relationship between current, desired and actual, lagged stocks by also incorporating replacement sales. The long-run elasticities of demand for motorcycle stock are calculated, in the case of Eq. (5), as the ratio of the short-run elasticities to the coefficient on the lagged stock term, but with the sign reversed: ai ¼ bi =b04 (i = 1, 2, 3). If, and only if, depreciation is a constant proportion of the outstanding stock, will the short-run elasticities bi (i = 1, 2, 3) in (5) be identical to those in (4), whilst the stock elasticities, b4 and b04 will differ. Where the depreciation rate is highly variable, Eq. (4) is suspect since it would then be based on an incorrect assumption about depreciation: Eq. (5) would provide a superior framework, compared to Eq. (4), for the calculation of reliable, unbiased estimates of the short- and long-run elasticities of demand for motorcycles. When working with Eq. (4), we have no firm, statistical information about the rate of depreciation of motorcycles to help us identify the long-run elasticities of demand. However, we can try to estimate d as follows. The logarithmic equation linking gross sales and net sales of motorcycles, with replacement sales expressed as a proportion of the outstanding stock at the beginning of each period, can be written thus: ln Qgross ¼ D ln K t þ dt ln K t1 t
ð6Þ
which yields an estimate of a time-varying rate of depreciation, dt: dt ¼
ln Qgross D ln K t t . ln K t1
In other words, we can use our data on total PTW Þ and stock (Kt) to calculate an implicit rate sales ðQgross t of depreciation. The latter varies over time because it is imputed from time series. The estimate of dt that this process yields is plotted over time in Fig. 2. The chart suggests that replacement sales as a proportion of outstanding stock have varied enormously over the past 60 years, around a sample mean value of 39.5% per annum. This proportion soared to a value of 59% in 1980, but it sank to almost 9% in 1993. The volatility of the implied replacement rate suggests that either, or both, of the following problems may be present: first, that there are deficiencies in the data
M. Duffy, T. Robinson / International Journal of Transport Management 2 (2004) 111–121 0.6
0.5
0.4
0.3
0.2
0.1 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Fig. 2. Estimates of the rate of depreciation of motorcycles in the UK.
(e.g. the errors caused by vehicle duty evasion8) that translate into unrealistic estimates of the implied depreciation rate; and, second, that Eqs. (4) and (6) are based on an unrealistic assumption of a constant rate of depreciation of the stock. As a consequence of these potential errors of measurement and specification, empirical estimates of Eq. (4) may provide a poor fit to the data (and Eq. (6) will yield unreliable estimates of dt). For these reasons, an alternative approach to the estimation of the short- and long-run elasticities of demand for motorcycles is also examined in this paper, namely through the estimation of Eq. (5) for net sales of this vehicle type, which avoids any problems of measurement and specification with respect to replacement sales.9 Returning to the discussion of the specifications of the estimated demand models, it is also worth noting that the sign of the coefficient on ln Kt1 in the gross
8 Broadley (2001, p. 3) reports that ‘‘evidence suggests that 25% of motorcycle stock is evading the VED licence’’. If this proportion is approximately constant over time, then the growth rate of the motorcycle stock D ln Kt will be relatively unaffected by the evasion rate, but the measured stock level will be biased downwards. Then estimates of dt in Eq. (6) will be subject to an error that varies with the size of the measured, lagged stock (but is unaffected by D ln Kt). 9 As suggested by a referee, an alternative way to introduce consumer preferences would be to make the income elasticity (and other coefficients) a function of socio-demographic variables. This could be attempted in various ways. For example, the parameters of the model could be assumed to be linear functions of various sociodemographic variables. That approach, though, leads to loss of degrees of freedom in what is already a small sample size. A parsimonious specification has advantages in that respect (and in terms of estimation and interpretability) over a model that would appear to be unwieldy, since it could involve several interaction terms between socio-demographic and economic factors. In another approach, it would be interesting to use micro-socio-economic panel data in modelling these interactions, but such datasets are not available, as far as we are aware. The influence of socio-demographic variables on the responsiveness of demand for motorcycle stock is beyond the scope of the present paper and is deferred to the agenda for future research.
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sales equation (4) cannot be determined a priori, for it depends upon the unknown, relative magnitudes of the rates of depreciation and adjustment. If d ffi h, the coefficient on ln Kt1 in (4) is approximately zero (and ln Kt1 could be omitted from the estimated form without inducing bias). If d exceeds h, the lagged stock will tend to raise current period sales of motorcycles, whilst the lagged stock will depress total sales of motorcycles in the current period if the rate of adjustment exceeds the rate of depreciation. On the other hand, the coefficient on the lagged stock term in the net sales equation (5) is expected unambiguously to be negative. We also wish to allow for changing tastes and preferences between modes of travel in the model specifications, something which casual empiricism suggests is an important factor. The effect of changes in tastes upon consumer demand for the services of motorcycles (and for other modes of transport), and thence for motorcycle stock, is accounted for by the inclusion among the regressors of a trend. We examine two different specifications of the trend term. In one specification, a deterministic trend is employed. In an alternative approach, we used a variable stochastic trend, although this includes a constant, deterministic trend as a special, limiting case. We are attracted to a stochastic trend (local linear trend) specification because we do not know of any strong a priori reasons for believing that changing tastes in this market have exerted their effects in a constant, steady way. As consumer perceptions of the relative advantages and disadvantages of motorcycle ownership have waxed and waned over the post-war period, it seems equally plausible to suggest that trend changes in tastes and demand have been variable rather than fixed. However, this is an issue that can only be resolved by examining and comparing the empirical performance of the two specifications.9 Eq. (4) augmented by a stochastic trend is: ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b4 ln K t1 ln Qgross t þ lt þ e t ;
ð7Þ
where et is the irregular term, and the stochastic trend term lt is specified as lt ¼ lt1 þ ct1 þ gt ; gt NID 0; r2g ; ð8Þ 2 ð9Þ ct ¼ ct1 þ ft ; ft NID 0; rf ; where ct is the slope or gradient of the trend lt. The irregular et, the level disturbance gt and the slope disturbance ft are mutually uncorrelated. This formulation collapses to a random walk with constant drift if r2f ¼ 0, and to a deterministic trend if r2g ¼ 0 as well. In the latter case, l and b correspond to the constant term and the coefficient on a time trend, respectively, in a conventional OLS regression. If r2g is set to zero when r2f is positive, then the trend is smoothlychanging.
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Prior to estimation, the net sales equation (5) is also augmented by a stochastic trend term: 0 ln Qnet t ¼ b1 ln Y t þ b2 ln MCt þ b3 Rt þ b4 ln K t1 þ lt þ et .
ð10Þ The model comprising Eqs. (7) or (10) with (8) and (9) are specific forms of HarveyÕs (1989) Basic Structural Model (BSM), amended to include explanatory variables. If the disturbances in the models are independently and normally distributed, the hyperparameters r2e , r2g , and r2f (which determine how the irregular and trend components behave over time) may be estimated by maximum likelihood with the recursive equations of the Kalman filter used to update the unobserved components (Harvey, 1989). Then estimates of the trend component may be extracted by a smoothing algorithm as in Koopman (1993) making use of the full set of observations in the sample. For this work, all of these calculations have been made through the use of the STAMP 6.20 package: see Koopman et al. (2000) for details of the estimation algorithms. 3. Data and empirical results The data set consists of 37 annual observations for the UK from 1964 to 2000. We measure the stock of motorcycles, Kt, by the total number of powered twowheeled vehicles with current Vehicle Excise Duty paid, measured during the month of December each year.10 The stock figure is deflated by mid-year estimates of the total population aged 15–60 years (Source: Annual Abstract of Statistics, various issues, and the National Statistics Online website at
Association, and the series was then put on a per capita basis by dividing by the mid-year estimates of the total population aged 15–60 years prior to transformation into logarithmic values. The income term, Yt, is measured as real household disposable income in the UK deflated by mid-year total population estimates, all ages (Sources: Annual Abstract of Statistics, various issues, and the National Statistics Online website at
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Table 1 Basic structural models for motorcycle sales: 1964–1995a Dependent variable Log gross sales (ln Qgross ) t
Log net sales (ln Qnet t ) Stochastic trend
Deterministic trend
Stochastic trend
Deterministic trend
Panel A: Estimated coefficients of the final state vector lnYt (b1) 0.7577 (2.570) ln MCt (b2) 0.3115 (1.473) (b3) 0.0038 (2.385) Rt ln Kt1 (b4) 0.1993 (1.470) Level (l) 2.5278 (1.929) Slope (c) 0.0258 (1.488)
0.9210 (3.050) 0.7100 (3.488) 0.0079 (4.495) 0.0134 (0.238) 5.2736 (4.053) 0.0226 (3.221)
2.1755 (1.381) 1.1558 (1.082) 0.0102 (1.680) 0.4743 (0.569) 2.3063 (0.307) 0.0759 (0.572)
4.0640 (1.595) 4.7991 (2.795) 0.0584 (3.958) 1.4915 (3.140) 34.2140 (3.117) 0.0954 (1.615)
Panel B: Long-run elasticities Income Motoring costs Interest rate
+3.80 +1.56 0.02
n.a. n.a. n.a.
+2.50 1.33 0.01
3.71 4.38 +0.05
6.628 · 104 [1.000] 1.486 · 1012 [0.000] 9.759 · 105 [0.147]
0.0014
0.0000 [0.000]
0.1031
n.a.
0.1327 [1.000]
n.a.
n.a.
0.0073 [0.417]
n.a.
0.56 6.1373 0.0013 4.66 {0.59} 20.22 {0.00} 9.25 {0.10}
0.59 6.3450 0.0012 17.06 {0.01} 9.86 {0.01} 26.63 {0.00}
0.92 3.1115 0.0270 4.85 {0.56} 5.14 {0.08} 4.10 {0.53}
0.74 2.0800 0.0859 25.02 {0.00} 2.37 {0.31} 12.75 {0.03}
Panel C: Hyperparameters Irregular r2e Level
r2g
Slope
r2f
Panel D: Test statistics R2 AIC p.e.v. Q BS PF
Panel A: Figures in parentheses ( ) are t-values. Panel C: The q-ratios in square brackets [ ] are the ratios of the associated variance to the largest hyperparameter variance. Since the variances govern the movements in the components, the q-ratios indicate the relative importance of the irregular, level and slope in that process. Panel D: The numbers in curly brackets { } are p-values. a In this table, R2 is the conventional coefficient of determination. This coefficient is not comparable across the net and gross sales specifications, since the two models use different dependent variables. AIC is the Akaike Information Criterion. The p.e.v. is the variance of the one-step-ahead prediction error. Q is the Box-Ljung statistic, a test for residual serial correlation, which is based on the first 8 residual autocorrelations and tested against a v-square distribution with 6 degrees of freedom. BS is the Bowman–Shenton (1975) test for normality of the residuals, distributed asymptotically as v-square with 2 degrees of freedom. PF is a Chow post-sample predictive ÔfailureÕ test, based on predictions for 1996–2000 (using estimates of the final state vector for the 1964–1995 estimation period). PF is distributed approximately as v2(5). In the specifications which employ deterministic trends, r2g ¼ r2f ¼ 0. The long-run elasticities are calculated by the formulae given in the text, with those for gross sales based on an assumption that the time-varying rate of depreciation reverts to its (sample) mean value of 0.395 in the long-run.
Economists need to assess and discuss all three of these criteria. An insignificant estimate which is of correct size and correct sign is still interesting and informative about the theory that is being tested. For there may be several reasons why the test for significance has failed (eg multicollinearity). The strongest a priori expectations in this context relate to b04 ¼ h in the net sales model. We expect b04 in that model to be negative and to lie in the range 1 6 b04 6 0. The estimates in Table 1 (and Table 2) satisfy those criteria. If the estimate of b04 is insignificantly different from zero, that indicates that a significant stock-adjustment effect has not been identified (which may be consistent with the true position in the motorcycle market). We have presented in Table 1 an estimated rate of adjustment coefficient in the net sales model h = 0.2 indicating that 20% of the gap between
the desired stock of motorcycles and its actual value is closed by net sales in any year on average. On the one hand, that estimate is insignificantly different from zero. On the other hand, the estimate in Table 1 is not significantly different in a t-test from 0.3, the point estimate of h in Table 2, which is significantly different from zero. Our sense of these results is that there are stock adjustment effects present in these data and this market. It is also worth noting that the deterministic trends models consistently yield estimates of the coefficients on the lagged stock terms, b04 , that are positive rather than negative. For the net sales model, this is not plausible, but we cannot say whether the result is plausible or not in the case of the gross sales model since the coefficient is not identified in that case (see above). But even if the negative coefficients on lagged stocks in all of the
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Table 2 Basic structural models for motorcycle sales: 1964–2000
a
Dependent variable Log gross sales (ln Qgross ) t
Log net sales (ln Qnet t ) Stochastic trend
Deterministic trend
Stochastic trend
Deterministic trend
Panel A: Estimated coefficients of the final state vector ln Yt (b1) 0.5362 (1.771) ln MCt (b2) 0.2650 (1.157) (b3) 0.0031 (1.914) Rt ln Kt1 (b4) 0.3100 (2.299) Level (l) 1.4067 (1.036) Slope (c) 0.0186 (0.732)
0.8200 (2.154) 0.7380 (2.821) 0.0074 (3.243) 0.0418 (0.605) 5.0807 (3.026) 0.0196 (2.204)
1.9392 (1.453) 1.1462 (1.185) 0.0095 (1.747) 0.6963 (1.005) 4.5109 (0.714) 0.1847 (1.130)
3.8230 (1.387) 5.1277 (2.706) 0.0558 (3.399) 1.1969 (2.393) 34.5090 (2.839) 0.0855 (1.332)
Panel B: Long-run elasticities Income Motoring costs Interest rate
+1.73 +0.85 0.01
n.a. n.a. n.a.
+1.78 1.05 0.01
4.77 6.39 0.07
5.990 · 104 [1.000] 0.000 [0.000] 2.249 · 104 [0.375]
0.0025
0.0000 [0.000]
0.1288
n.a.
0.0120 [0.974]
n.a.
n.a.
0.0123 [1.000]
n.a.
0.45 5.8391 0.0021 22.17 {0.001} 3.15 {0.21}
0.91 3.1964 0.0265 6.48 {0.37} 3.79 {0.15}
0.64 1.8803 0.1103 24.84 {0.00} 2.307 {0.32}
Panel C: Hyperparameters Irregular r2e Level
r2g
Slope
r2f
Panel D: Test statistics R2 AIC p.e.v. Q BS a
0.59 6.0316 0.0016 2.56 {0.86} 5.70 {0.06}
Notes: Estimation period 1964–2000. See also the notes to Table 1.
stochastic trends models are deemed to be plausible, some may suggest still that aspect constitutes little advantage over the deterministic trends specification for those negative coefficients are insignificantly different from zero. It is certainly true that dynamic effects are not estimated with much precision or reliability in either case, but the stochastic trends specification is preferred nevertheless for the following reasons. First, the lagged stock term does emerge as significant and negative in the full sample period estimates of the net-sales-cum-stochastic-trends model: see Table 2. Second, the incorrect sign on this coefficient in the deterministic trends specification, whilst having no effect, of course, on the short-run demand elasticities, does contribute to the calculation of values for the long-run elasticities of demand that are exceedingly implausible both in terms of sign and magnitude (hence these are not reported). A third advantageous feature of the estimated stochastic trends models is that they pass the post-sample predictive failure tests (indicating that they successfully predict the above-mentioned upswing in motorcycle ownership in the late 1990s), whilst the deterministic trend models fail that test: see the PF statistics in Table 1. This is an important strength of the stochastic trend models: as we argued previously, predictive accuracy is
an acid test of the quality and reliability of any estimated model. In this case, the linear trend models incorrectly extrapolate into the future past trends in consumer preferences away from motorcycles, whilst the flexible, variable, stochastic trend is able to capture the reversal in trend that may have occurred from the mid-1990s onwards. It should be noted though that economic factors, as well as changes in consumer tastes, contributed, no doubt, to the upswing in demand for motorcycles in the late 1990s. Thus, real incomes rebounded as the economy recovered from the recession of the early 1990s, and the real cost of motoring rose steeply at the same time (for example, because of tax increases). The latter may have restrained the demand for cars, and favoured motorcycle sales. On the other hand, real interest rates were at high levels during this period: this may have dampened motorcycle demand (but our estimates suggest that any such effect may have been quite weak and easily offset by the other factors: see below). A fourth advantage of the stochastic trend models is that they do not appear to suffer from autocorrelation in their residuals, whereas the deterministic trend models do have large, significant Box-Ljung statistics (see the Q statistics in Tables 1 and 2). The autocorrelation may be prima facie evidence of misspecification in the deterministic trend models.
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For these reasons, we favour using the stochastictrends, rather deterministic trends, formulation in our final analysis. Furthermore, we prefer to work with net sales data rather than gross sales. For we are unable to estimate the coefficients in the final state vector for the gross-sales-cum-stochastic-trends model with any precision: all of the coefficients are insignificantly different from zero (see Tables 1 and 2). This feature of the results may be due to the inexplicably high volatility of replacement sales (see above). In contrast, we enjoyed some success in estimating plausible coefficient estimates that are significantly different from zero, or almost so, in many instances in the net-sales-cum-stochastic-trends models: see Tables 1 and 2. From this point, we will focus our attention on net-sales-cum-stochastic-trends model of motorcycle demand (henceforth, the net sales model, for short). A small point to note is that the estimated hyperparameters in Tables 1 and 2 for the net-salescum-stochastic-trend models (especially the approximately zero value for the estimate of r2g ) suggest that motorcycle demand is subject to a Ôsmooth trendÕ rather than a Ôlocal linear trendÕ: see Koopman et al. (2000). This is a model that achieves a good fit to the data, as evidenced by the coefficients of determination in Tables 1 and 2, as well as the time series plot in Fig. 3 of the actual net sales series and the fitted values from the model estimated over the whole sample period, 1964– 2000. Fig. 3 also contains a plot of the estimated trend in net sales: it clearly shows the secular drift away from motorcycles by consumers, together with the pick-up in trend sales in the late 1990s. It is worth trying to examine the implications of the estimated models for growth prospects in demand for
0.1
Actual
119
motorcycles and for transport policy. Useful concepts to employ in this exercise are the elasticities of motorcycle demand with respect to income, motoring costs and the costs of credit, as well as the underlying changes in consumer tastes and preferences as represented by the stochastic trend. However, it must be noted that our empirical estimates of these parameters are inevitably characterised by some imprecision and uncertainty. This is due to a number of factors. First, there is the unavoidable effect, of course, of sampling variance. Secondly, the stochastic trend is by nature increasingly unpredictable as the forecast horizon is lengthened: extrapolation of the trend element must be largely judgemental. Thirdly, the short and long-run elasticity estimates are surrounded by a significant margin of uncertainty because the evidence relating to the temporal stability of the models is mixed. As already noted, the Chow post-sample predictive failure test statistics reveal no evidence of instability in the stochastic trends models. This is confirmed by construction of confidence intervals from the individual t-ratios in pairwise comparisons of estimated coefficients across Tables 1 and 2. The net sales model is deemed to be stable in all of those tests, but it accommodates, nevertheless, substantial changes (namely, declines of approximately 50%) in the estimated elasticities of demand when the sample period is extended. Furthermore, the estimated coefficients on the income and interest rate terms in Table 1 are significantly different from zero only at the 10%, but not the 5%, level, whilst the motoring cost term is insignificant at both levels. It is unclear whether these instabilities reflect sampling variance, or more fundamental structural changes in the market for motorcycles in the late 1990s. In these
Fitted
0.0 -0.1 1965
1970
1975
1980
1985
1990
1995
2000
1970
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
-0.75 -1.00 Trend
-1.25 -1.50 1965 0.050 Irregular
0.025 0.000 -0.025 1965
1970
Fig. 3. Net sales of motorcycles: actual values, fitted values, trend and irregular (logarithms).
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circumstances, and until further information and market experience become available, it would seem advisable to be prudent in the assessment of elasticities, by giving greater weight to the lower, full-sample estimates. Thus, we err on the side of caution by choosing to view the long-run income elasticity of demand for motorcycle ownership as being in the region of 1.5, compared with a short-run elasticity of about 0.5. Taken on its own, a long-run income elasticity of 1.5 would suggest, on an assumption that long-run income growth remains unchecked, that the medium-to-long-term growth prospects for motorcycle ownership are quite high. The discrepancy in magnitudes of the short-run and longrun income elasticities may be attributed, in the usual way, to the effects of costs of adjustment of desired stock to actual levels. An increase in motoring costs, mainly the expense of buying and running a car, is estimated to have a small, positive but insignificant cross-effect on desired motorcycle ownership in the short-run (Tables 1 and 2). However, the estimates also suggest that this effect may be much larger in the long-run: the estimate of the longrun cross-elasticity from data for 1964–1995 in Table 1 is as high as +1.6, but this falls to +0.85 in the full sample (Table 1). However, statements about the effects of this variable must be made with great caution because of the insignificance of the associated coefficient estimates in Tables 1 and 2. Until further information appears, a reasonable, cautious working assumption in exercises concerned with the forecasting of motorcycle ownership over the long-term may be that a projected increase in motoring costs is likely to raise the desired stock of motorcycles in the same proportion. That is, the longrun cross elasticity could be assumed to be unity. These estimates have an obvious implication for any assessment of the impact of transport policy on the market for motorcycles: namely, any significant increase in road-use charges, which are currently being discussed by policy makers, and providing that they form a significant element of motoring costs, is likely to have a major, beneficial effect on the demand for motorcycles. The real interest rate semi-elasticity in the net sales model is minute in both the short-run and in the longrun: Table 1. In short, motorcycle ownership at any horizon is not very sensitive to changes in the real cost of credit.11
4. Conclusions This paper has reported on an econometric investigation of motorcycle ownership in the UK. The favoured specification was a stock adjustment model augmented by a stochastic trend to allow for changing consumer preferences over modes of transport. It did not prove possible to obtain meaningful estimates of the determinants of gross sales (net additions to the stock plus replacement purchases) because of the large, inexplicable fluctuations in the depreciation component. Greater success was achieved in explaining motorcycle sales net of replacement purchases. Empirical estimates of the net sales model suggest that the future growth prospects for motorcycles may be quite good. This tentative conclusion follows primarily from what appears to be a significant, relatively high, long-run income elasticity of demand for motorcycles, combined with a high cross-elasticity of substitution effect with regard to the cost of motoring. If the long-run expansion of real incomes continues apace in the future, the demand for cars will increase, as will the demand for other modes of transport including motorcycles. The general expansion in demand for transport may favour cars more than other modes, but this could be offset somewhat by other factors. Thus, the likely effect of further increases in the cost of running cars through policy initiatives (eg increases in ÔgreenÕ taxes on petrol and emissions, car tax, road-use charges, etc) will be a significant expansion in demand for noncar modes of transport, including motorcycles. At the same time, our estimates have indicated that these effects are subject to a countervailing tendency, represented by an on-going change in the publicÕs preferences away from motorcycles towards other modes of transport. Which of these tendencies will dominate in the motorcycle market over the next few years remains to be seen.
Acknowledgements The authors would like to acknowledge the very helpful comments and suggestions made by the editor and two, anonymous referees which helped to improve the paper. The usual disclaimer applies.
References 11
Several other possible determinants of motorcycle demand were investigated but without success. Thus, the influence of demographic changes was examined by the inclusion in the model of the logarithm of the proportion of the total population that is aged between 15 and 65 years. This admittedly crude measure of demographic changes in the age structure of the population was always estimated to have an insignificant effect on the desired stock of motorcycles. Similarly, a simple measure of the amount of congestion on the roads in the UK (distance travelled by motor vehicles divided by road length) had no apparent, significant effect on the desired stock of motorcycles.
Bowman, K.O., Shenton, L.R., 1975. Omnibus test contours for pffiffiffiffiffi departures from normality based on b1 and b2 . Biometrika 62, 243–250. Broadley, S., 2001. Motorcycling in Great Britain, Transport Statistics. Transport Trends. 2001 Edition, Department of the Environment, Transport and the Regions (available on the web at
M. Duffy, T. Robinson / International Journal of Transport Management 2 (2004) 111–121 Chow, G., 1957. Demand for Automobiles in the U.S.: A Study in Consumer Durables. North Holland, Amsterdam. Dargay, J.M., Vythoulkas, P.C., 1999. Estimation of a dynamic car ownership model: A pseudo panel approach. Journal of Transport Economics and Policy 33-3, 287–302. Department of the Environment, Transport, and the Regions, 2000. Transport 2010: The 10 Year PlanÕ (available on the web at
121
MINTeL, 2002. Motorcycles, Market Intelligence, June, Mintel International Group Ltd.: London. Muellbauer, J., 1981. Testing Neoclassical Models of the Demand for Consumer Durables. In: Deaton, A. (Ed.), Essays in the Theory and Measurement of Consumer Behaviour. Cambridge University Press, Cambridge, UK. Romilly, P., Song, H., Liu, X., 2001. Car ownership and use in Britian: A comparison of the empirical results of alternative cointegration estimation methods and forecasts. Applied Economics 33, 1803– 1818. Stone, R., Rowe, D.A., 1957. The market demand for durable goods. Econometrica 25, 423–443. The Economist, 2002a. Jam, Darling? October 10. The Economist, 2002b, ÔGridlocked BritainÕ, December 12. The Economist, 2003, ÔShush, DarlingÕ, April 3. Train, K., 1985. Qualitative Choice Models. The MIT Press, Cambridge MA. Whelan, G., 2001. Methodological advances in modelling and forecasting car ownership in Great Britain. Paper Presented at the European Transport Conference 2000, PTRC, Cambridge. Whelan, G., Wardman, M., Daly, A., 2000. Is there a limit to car ownership growth? An exploration of household saturation levels using two novel approaches. Paper Presented at the European Transport Conference 2000, PTRC, Cambridge. Witt, S., Johnson, S.R., 1986. An econometric model of new-car demand in the UK. Managerial and Decision Economics 7, 19–23.