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A dynamic panel analysis of urban metro demand
Transportation Research Part E 45 (2009) 787–794
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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre
A dynamic panel analysis of urban metro demand Daniel J. Graham *, Amado Crotte, Richard J. Anderson Imperial College London, Railway and Transport Strategy Centre, Centre for Transport Studies, Department of Civil and Environmental Engineering, London SW7 2AZ, UK
a r t i c l e
i n f o
Article history: Received 23 July 2008 Received in revised form 23 January 2009 Accepted 24 January 2009
Keywords: Urban metro Demand Dynamic panel GMM
a b s t r a c t A dynamic panel model is used to estimate the effect that fares, income and quality of service have on demand for a sample of 22 urban metros. The estimated price elasticity is 0.05 in the short run and 0.33 in the long run. The estimated long run income elasticity is small but positive (0.18), indicating that metros are perceived as normal goods. The quality of service elasticities are positive and substantially higher than the absolute value of fare elasticities. The implication is that quality of service improvements, rather than fare reductions, may be more effective in increasing metro patronage. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Public transport performance benchmarking offers operators a means to gauge their own performance, relative to that of other providers, when there are few similar operators in their own immediate environment. Such inter-system comparative analyses can be particularly valuable for urban metros because there typically tends to be only one metro system operating in any city, and therefore, limited opportunities to obtain performance comparisons at the local level. Benchmarking analyses cover a diverse range of different activities, from ‘qualitative’ comparisons of best practice to quantitative analyses of different performance based measures. From the quantitative analyses, operators seek to get some idea of how the performance of their metro compares to that of others, typically by constructing rankings or by using deviations from some measure of central tendency derived from a sample of firms. In this paper, we use data on urban metros collected for the CoMET and Nova benchmarking groups, which are facilitated by the Railway and Transport Strategy Centre (RTSC) at Imperial College London, to analyse the demand for metro services. We derive a set of elasticities that describe the effect that fares, income and quality of service have on metro demand, and we then show how passenger demand for each metro within the sample compares to this evidence generated across the range of different systems. In estimating urban metro demand we are faced with a number of difficult empirical issues. The use of cross-sectional data, which tend to be readily available, is problematic due to the potential for omitted variable bias or confounding, the need to find a vast array of variables that can adequately characterise demand, and because many of the variables that should be included in the demand function are potentially endogenous but obvious external instruments may not be available. Of course, cross-sectional models also suffer from the disadvantage that they do not allow for any period of adjustment in the demand relationships. The use of time series data, taken one system at time, provides a potential solution to problems of
* Corresponding author. Tel.: +44 0 20 7594 6088; fax: +44 0 20 7594 6102. E-mail address: [email protected] (D.J. Graham). 1366-5545/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2009.01.001
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endogeneity and dynamics, but still cannot tell us much about the effect of individual heterogeneity on demand and also tend to be plagued with multicollinearity which can prevent proper identification of the demand function. Estimation of demand using panel data offers a number of advantages. It tends to provide more variance than contained in time series alone, it allows for individual system specific heterogeneity and thus a potential solution to the problem of omitted variables bias, and it can reduce the potential for multicollinearity and aid identification. Furthermore, dynamic panel data techniques allow us to study the temporal adjustment of demand and can accommodate endogenous regressors. But crucially, for the purposes of this paper, a key benefit of panel data is that it allows us to derive some intuition about the key drivers of demand from across a range of systems while also allowing us to model system specific effects. We can then use this intuition to make some comparisons of actual metro performance compared to average sample performance. In this paper, we use dynamic panel data techniques to estimate the effect that fares, income and quality of service have on the demand for medium sized and large urban metros from around the world. Our statistical approach allows for system specific heterogeneity, dynamic adjustment of the demand function, and can also accommodate endogenous regressors; an important concern when modelling quality of service. The paper is divided into five sections. Section 2 reviews previous literature on public transport demand. Section 3 describes the data available for estimation and outlines the Generalised Method of Moments (GMM) estimator for dynamic panel data. The Section 4 presents our results, and conclusions are then drawn in the final section of the paper. 2. Previous research There are a number of excellent surveys of the empirical literature on public transport demand (see in particular Pham and Linsalata, 1991; Oum et al., 1992; Goodwin, 1992; Luk and Hepburn, 1993; TRACE, 1999; TRL, 2004; McCollom and Pratt, 2004; Paulley et al., 2006). There is, therefore, no contribution to be made by providing an extensive literature survey here. However, it is worth reviewing some of the main findings from previous research to provide a context for the empirical work of this paper. The major survey articles cited above review results on the responsiveness of demand to changes in fares, income, quality of service, the price of competitive modes, and other factors. They show that there is a great deal of variation across studies in the magnitude of the relevant public transport demand elasticity estimates. This is mainly due to six key study characteristics: (1) type of data used (aggregate or disaggregate), (2) time frame analysed (month, quarter, year), (3) model structure (static and dynamic), (4) econometric technique used, (5) specification of the dependent variable (travel volume, modal choice or route choice), and (6) demand specification. The influence of these characteristics limits our ability to make direct comparisons of results from one particular study to those of another. In fact, the survey articles show that elasticity estimates can still vary substantially between studies even when the six key elements are consistent. This is due to the influence of certain country-specific characteristics such as natural circumstances, travel distances, and cultural differences that determine the level of competitiveness between transport modes. Thus, to some extent one of the key messages from the literature surveys is that the evidence on the magnitude of demand elasticities can be divergent and consequently direct comparisons may not be useful. That said, the reviews also point towards some basic generalisations about the responsiveness of demand to changes in price, income, service quality and price of competing modes. These are as follows. With regards to fare elasticities, the difference between estimates can be largely explained by four factors. First, rural areas in general have greater fares elasticities than urban areas, reflecting greater feasibility of using a car as an alternative mode due to less congestion and cheaper parking. Second, public transport choice or discretionary users that can choose to make a trip by car tend to be more responsive to fare changes than captive users who do not have the alternative of the car. Third, non-commute trips such as shopping and leisure are more elastic than work trips while off-peak trips have larger fare elasticities than peak-time values, mainly because peak-hour trips are work related. Finally, public transport fare elasticities depend on the type of transit analysed. In general, metros seem to have less sensitivity to fare changes than buses, possibly due to higher speeds and lower travel time particularly for longer journeys. Regarding income elasticities, some studies estimate negative coefficients perhaps indicating that public transport is an inferior good (e.g. Dargay and Hanly, 2002), while some studies show that the relationship is positive (e.g. Romilly, 2001) suggesting that as incomes grow and wealth increases people engage in activities that require more transportation services since transport is a derived demand. The literature shows that in general, income elasticities are found to be positive when vehicle ownership is included in the model, however, when it is excluded income picks up the negative effect that vehicle stock has on public transport demand. In fact, not many studies have included both variables in the same model due to problems of multicollinearity. Some authors believe that the inclusion of a time trend can improve estimation, arguing that if the trend coefficient is negative it accounts for vehicle ownership, while if it is positive it accounts for other unobservable or difficult to measure factors, such as traffic, car journey times and other car costs. In general, the literature surveys caution great care in interpreting the income elasticities since they depend on the variables selected for inclusion in the model. Some generalisations are also possible with regards to quality of service elasticities. Quality of service is a difficult characteristic to measure and while there is no consensus within the literature on a single appropriate proxy variable, we can define three approaches that are most commonly used: (1) number of vehicles/trains in operation and train kilometres operated (as these figures increase per passenger or per route length, service frequency also increases and there is less crowding),
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(2) some measure of time or money (for instance in vehicle time or waiting time through a value of time factor), and (3) other quality factors that are not directly measurable in terms of time or money (such as service reliability, infrastructure quality, and ventilation). As with fare elasticities, the main factors that give rise to variance in service quality elasticity values include city size, type of trip, type of user and type of mode. For instance, larger cities tend to have higher service elasticities than price elasticities, while smaller cities have comparable values. Rural areas have higher service elasticities because improvements to a poorer service have a greater impact. Another important point about the service quality variables is that they may be simultaneously determined with demand, but their potentially endogenous nature is often not addressed in empirical work. With regards to cross elasticities no general guidelines can be drawn. Oum et al. (1992) argue that the specification of the demand for public transport should include prices and service quality factors of competing modes to truly capture the effect of public transport markets. However, such cross elasticities are not directly transferable across time and space because they depend on the relative size of the two markets represented (Acutt and Dodgson, 1996). Oum et al. (1992) show that the estimated cross-elasticity of transit with respect to fuel prices ranges between studies from as little as 0.01 up to 1.32. In this section we have briefly summarised some of the key influences, both theorised and estimated, that affect the demand for public transport, as reported in the literature. The results reviewed in this literature have been derived for different modes in a variety of different empirical contexts. In this paper, we focus on the demand for urban metro services using a dynamic panel data approach which provides elasticities net of system or city specific characteristics. In this way we hope to be able to provide some general guidance about the characteristics of demand for this mode. 3. Data and model estimation The data we have available for estimation are for an unbalanced panel of 22 urban metros over a 13 year period. These data are collected by the Railway and Transport Strategy Centre (RTSC) at Imperial College London and used for their two urban metro benchmarking exercises CoMET and NOVA.1 We also have data on the Helsinki metro for the sample period. The panel data include the annual number of passengers per metro normalised by population, and a proxy for metro fares is estimated for each metro system with annual revenue from fares divided by annual number of passengers. We also have information on inflation and currency factors that allows us to transform the data into real comparable figures in US dollars. National GDP per capita is used as a proxy for local income and was obtained from the World Bank website as was annual national population. All financial quantities are converted into real US Dollars using Purchasing Power Parities, again published by the World Bank. The data available allow for five different specifications to measure quality of service. The data include rail car kilometres travelled and rail car operating hours. Both variables capture the effect of changes in metro supply as a result of line extensions, changes in frequency, and changes in hours of operation of the service. Ceteris paribus, changes in any of these three elements imply changes in both rail car kilometres travelled and rail car operating hours. Both variables can be normalised by metro passengers, to capture crowding and comfort, or by metro network length, to capture the same effect net of line extensions. The fifth specification includes rail car kilometres normalised by rail car operating hours, which would capture changes in speed. As mentioned in Section 2 above quality of service is a difficult attribute to quantify. With the data we have available we are only really able to represent those characteristics of quality of service which are related to supply, for instance, frequency, hours of service, and speeds. We do not include other potentially important aspects of service quality such as station and vehicle cleanliness, crowding, security, temperature control, and the availability of station facilities (see Litman 2007). Estimation with panel data does allow for the inclusion of individual effects which provide a means of capturing differences between metros in quality of service as well as other characteristics. Nonetheless, it is worth emphasising that we look explicitly at only a subset of quality of service variables and consequently the results do not have relevance over the broader definition discussed by Litman (2007). Given the dimensions of the panel, particularly the small number of annual observations relative to cross-sectional units, dynamic panel estimation should proceed with GMM rather than panel cointegration2. The main issue to be addressed in the context of dynamic panel estimation is correlation between the lagged endogenous terms and the unobserved cross-section individual effects. For instance, consider the autoregressive distributed lag (ADL) dynamic panel model
yit ¼ ayit1 þ bxit þ ðgi þ eit Þ
ð1Þ
1 The CoMET (Community of Metros) data include a consortium of twelve of the world’s largest metropolitan metros: Berlin BVG, Hong Kong MTR, London Underground Ltd, Metro de Madrid, Mexico City STC, Moscow MoM, Paris Metro (RATP), Paris RER, New York City Transit, Metro de Santiago, São Paulo MSP and Shanghai SMOC. The Nova group is a consortium of fifteen small to medium sized metros: Bangkok BMCL, Barcelona TMB, Buenos Aires Metrovías, Delhi DMRC, Glasgow SPT, Metropolitano de Lisboa, Milan ATM, Montréal STM, MetroNapoli, Newcastle Nexus, Metro Rio, Singapore SMRT, Taipei TRTC, Toronto TTC and Sydney CityRail, We have not been able to include data on the Delhi, Hong Kong (KCW), Lisbon, Milan, Taipei and Toronto metros in the model due to the small number of annual observations currently available. 2 Although the literature does not explicitly suggest the minimum number of annual observations needed for estimation of elasticities with a panel cointegration approach, most studies use at least from 20 to 25 annual observations.
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where y is the dependent variable, xit can be a vector of current and lagged values of the independent variables, the term gi is an unobserved time-invariant individual specific effect, and eit IID(0, r2) is a serially uncorrelated error term. Clearly there is a correlation between yit1 and gi. Furthermore, this correlation cannot be purged through the within transformation of the fixed effects estimator, that would effectively remove the individual effect gi, but would still result in correlation between the transformed regressors and the transformed errors with the consistency of the estimator dependent on having a large T dimension (e.g. Nickell, 1981). A similar problem prevents application of the quasi-demeaned GLS random effects estimator which still gives biased and inconsistent estimates for dynamic panel data models. When the assumption of zero conditional mean of the error term given the regressors is not satisfied, the GMM estimator provides a potential solution. The principle underpinning GMM is that, given a set of exogenous instrumental variables which are correlated with the regressors but orthogonal to the errors, we can define and solve a set of moment conditions which will be satisfied at the true value of the parameters to be estimated. In the context of dynamic panel data models the time series nature of the data is used to derive these instruments and establish the moment conditions (e.g. Arellano and Bond, 1991; Arellano and Bover, 1995; Blundell and Bond, 1998). For instance, given 1 the GMM estimator proceeds by taking first differences to eliminate the individual effects
yit yit1 ¼ ayit1 yit2 þ bxit bxit1 þ ðeit eit1 Þ:
ð2Þ
The correlation between yit1 and eit1 in 2 implies that OLS estimation will be inconsistent. Drawing on the panel nature of the data, however, we can derive a set of instruments which are both correlated with Dyit1 and orthogonal to Deit1. For instance, in the absence of serial autocorrelation, the lagged level yit2 will be correlated with Dyit1 but uncorrelated with Deit1. Following this line of reasoning, if T P 3 we also have yit3 available as an instrument, and so on, such that with each additional time period we can add an extra valid instrument. Similarly, this can be done for any other endogenous explanatory variables in the model giving rise to an instrument matrix denoted Zi = (yi, xi). The moment conditions are
E Z 0i Dei ¼ 0
ð3Þ
where Dei = (De3, De4,. . ., DeT)’, and the GMM estimator based on these moment conditions minimizes
qN ¼
n
1
n X
!
0 i Zi
De
1
WN n
n X
i¼1
!
Z 0i D i
e ;
ð4Þ
i¼1
where WN is the weight matrix
" W N ¼ n1
n X
Z 0i Dei De0i Z
#1 :
ð5Þ
i¼1
The GMM estimator can be derived in two steps by substituting the differences residuals from an initial estimation for Dei in (5). This so called difference GMM estimator (e.g. Arellano and Bond, 1991), therefore, has two attractive properties. First, it permits unobserved heterogeneity in the means of the yit series across individuals; and second, it accommodates the use of endogenous or stochastic regressors. In practice however the difference GMM estimator has been shown to perform poorly on data with persistent series. The main reason for this is that under these circumstances, the lagged levels of variables will sometimes tend to have only weak correlations with the first-difference equations. In particular, it has been shown that when the series have near unit roots the lag variable instruments tend to contain little information about the endogenous variables in first differences. The proposed solution to this problem gave rise to the development of the so called system GMM estimator, which uses lagged first differences as instruments for equations in levels as well as the lag variable instruments for first-difference equations (e.g. Arellano and Bover, 1995; Blundell and Bond, 1998; Blundell and Bond, 2000; Blundell et al., 2000). The validity of the extended system GMM estimator in the ADL context rests on the assumption that the (yit, xit) series each satisfy a mean stationarity assumption, yielding the additional moment conditions
E½DZ it1 ðgi þ eit Þ ¼ 0:
ð6Þ
Using both sets of moment conditions together, 3 and 6, gives rise to a system GMM estimator with first-differenced and levels equations. This estimator has been shown to offer much increased efficiency and less finite sample bias compared to the difference GMM estimator3. The consistency of the GMM estimator relies on the assumptions that there is no first-order serial autocorrelation in the errors of the level equation 1, and that the instrument matrix is truly exogenous and therefore valid to define the moment conditions. The Arellano and Bond test for serial autocorrelation (Arellano and Bond, 1991) tests the hypothesis that there is no second-order serial correlation in the first differenced residuals, which in turn implies that the errors from the levels equations are serially uncorrelated. The standard test for validity of the instrument matrix is the Sargan/Hansen test of
3
A good summary of this literature is given in Baltagi, 2005.
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overidentifying restrictions. The assumption of exogeneity of the instruments implies that we have a set of moment conditions which will be satisfied at the true value of our parameter estimates. If the model is overidentified (i.e. if there are more moment conditions than there are parameters to be estimated) the GMM framework allows us to test the validity of the additional moment conditions (overidentifying restrictions) in terms of whether they are set close enough to zero at the optimal GMM parameter estimates. Essentially, this is akin to testing for correlation between the model residuals and a subset of the instruments used. The Difference Sargan test is used to compare the results from difference and system GMM. The drawback of the Sargan test is that apart from detecting serial correlation, it can reject the restrictions if the model is miss-specified. Imbens et al. (1998) show that the Sargan test has poor size properties and propose alternative Tilting Parameter tests of overidentifying restrictions, however, Bowsher (2002) finds that the Tilting Parameter is only preferred to the Sargan test when few moment conditions are tested, which applies with panels with small T, or when few variables are treated as predetermined or strictly exogenous. The results from the Sargan test should therefore be interpreted with care. GMM estimation in the context of dynamic panel data models offers a means of obtaining consistent parameter estimates when regressors are potentially endogenous and where measurement error may be present. It also allows for unobserved individual heterogeneity and a period of adjustment in the demand relationships. For all of these reasons, it is highly suited to the estimation of metro demand functions given the available data. The dynamic demand model we estimate has the following form:
ln M it ¼ ci þ a ln Mi;t1 þ b0 ln P it þ b1 ln Y it þ b0 ln QoSit þ eit
ð7Þ
for i = 1,. . .,22 and t = 1,. . .,T (Ti is the number of annual observation for metro i), where Mit, Pit, Yit and QoSit denote metro patronage per capita, real fares in US dollars, real income per capita in US dollars, and quality of service, respectively, all expressed in logarithmic form. ci denotes the unobserved system specific effects that capture a whole range of individual characteristics such as city size, metro network coverage, and the supply and price of other modes and eit IID(0, r2) is the disturbance term. For comparative purposes, we also present estimates obtained by applying pooled OLS and fixed effects estimators to a dynamic demand model. 4. Results The demand model was first tested using each of the five possible quality of service variables and also with various combinations of these variables. The coefficient on the proxy for metro speed (rail car kilometres divided by rail car operating hours) was consistently found to be statistically insignificant and this variable was therefore excluded from the analysis. For the remaining variables, the results of diagnostic tests showed a significant improvement in fit when the quality of service variable was normalised by route length rather than by number of passengers. In fact, we found that normalisation by the number of passengers produced high correlation with the lagged dependent variable. The results also showed that the inclusion of more than one quality of service variable gives multicollinearity. We therefore found that the viable options for quality of service proxies include either rail car kilometres or rail car operating hours, both normalised by route length. The four columns of Table 1 report the results using OLS levels, Within Groups, difference GMM, and system GMM, respectively, for the model that uses rail car kilometres travelled normalised by network length as a proxy for quality of service. For the GMM estimators, several specifications were tested with regards to the endogeneity of the variables. The choice of model was based on the significance of the estimates, as well as the Arellano-Bond tests for AR(1) and AR(2) in first differences, the Sargan and Hansen tests of overidentifying restrictions, and the Difference-in-Hansen tests of exogeneity of instrument subsets. The most appropriate difference GMM model treats quality of service as endogenous, prices as predetermined but not strictly exogenous, and income as strictly exogenous. The results from both difference and system GMM pass the instrument validity tests, however, the estimate of the autoregressive term in the system GMM model is larger than that of OLS levels, which suggests the estimates are biased. System GMM also produces insignificant estimates with counterintuitive signs. The difference Sargan test statistic for system GMM appears unusually large, which may indicate failure of the model to satisfy the necessary condition for system GMM that the lagged differences are uncorrelated with the individual effects (Blundell and Bond 1998). A key problem here is that when the number of moment conditions is large relative to the number of cross-sectional units, the system GMM estimator increases potential for finite sample bias while at the same time weakening the ability of the Sargan tests to detect an invalid specification. It is well known that problems can arise with system GMM estimation in samples with a small number of cross-sectional relative to temporal units, as is the case with our data (N = 22, T 6 13). When the instruments used in the difference GMM estimator are not weak, the additional instruments employed in system GMM can overfit the endogenous variables and are themselves potentially endogenous unless some rather strict conditions are satisfied (see Roodman 2008). For these reasons, we believe the difference GMM specification is probably more appropriate for our data. Table 2 presents the results of the model with rail car operating hours normalised by route length as a proxy for quality of service, which also measures frequency of service and metro operating hours net of the effect of line extensions or construction of new lines4. Again, both difference and system GMM models pass the instrument validity tests, however, the estimate of
4 The number of observations for the regressions in Table 2 is less than in Table 1 because some of our metros did not report rail car hours operated for certain years.
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Table 1 Results of the dynamic panel model with quality of service measured as rail car kilometres per route kilometre. Dependent variable: metro patronage per capita (lnM). Variable
OLS levels
Within groups
Diff GMM
Sys GMM
lnP
0.010 (0.006) 0.007 (0.006) 0.010 (0.010) 0.999* (0.003) – – – – – 0.99 192
0.088* (0.016) 0.074* (0.018) 0.015 (0.040) 0.816* (0.038) – – – – – 0.99 192
0.047* (0.011) 0.026* (0.008) 0.072* (0.005) 0.858* (0.045) 0.001 0.445 0.242 0.246 34 – 170
0.043 (0.046) 0.067 (0.087) 0.187 (0.100) 1.003* (0.031) 0.008 0.533 0.124 1.000 50 – 192
lnY lnQoS (rail car kms/route km) lnMt1 AB AR (1) AB AR (2) Sargan Dif Sargan no. Instruments Adj. R2 No. observations
All variables are expressed in logarithmic form. Real Income (lnY) is in per capita terms, quality of service (lnQoS) is measured as rail car kilometres normalised by route kilometres, fares (lnP) and income (lnY) were converted into real terms and are expressed in 2006 US dollars. * denotes significance at the 1% level. The estimated coefficients without a* are not statistically significant at a level lower than 10%. Standard errors in parenthesis.
Table 2 Results of the dynamic panel model with quality of service measured as rail car hours per route kilometre. Dependent variable: metro patronage per capita (lnM). Variable
OLS levels
Within groups
Diff GMM
Sys GMM
lnP
0.009 (0.006) 0.007 (0.006) 0.015 (0.011) 0.998* (0.003) – – – – – 0.99 182
0.096* (0.017) 0.082* (0.018) 0.044* (0.035) 0.850* (0.043) – – – – – 0.99 182
0.048* (0.024) 0.024* (0.009) 0.053* (0.021) 0.852* (0.050) 0.015 0.944 0.557 0.339 35 – 160
0.047 (0.031) 0.063 (0.033) 0.203* (0.079) 0.999* (0.039) 0.019 0.957 0.243 0.970 39 – 182
lnY lnQoS (rail car hrs/route km) lnMt1 AB AR(1) AB AR(2) Sargan Dif Sargan no. Instruments Adj. R2 No. Observations
All variables are expressed in logarithmic form. Real Income (lnY) is in per capita terms, quality of service (lnQoS) is measured as rail car operating hours normalised by route kilometres, fares (lnP) and income (lnY) were converted into real terms and are expressed in 2006 US dollars. denotes significance at the 1% level. The estimated coefficients without a * are not statistically significant at a level lower than 10%. Standard errors in parenthesis. *
the autoregressive term,a, appears too close to that of Within Groups in the difference GMM specification, and does not lie between the corresponding OLS levels and Within Groups estimates in the system GMM specification. This suggests that for the panel of metros analysed the instruments may be weak and the coefficients may be downward biased. Comparing the results shown in Tables 1 and 2, we can see that although both difference GMM specifications produce almost identical price and income coefficients, the quality of service coefficient is much smaller in the second model. This is not surprising as rail car operating hours can increase even if hours of operation or frequency do not change, for instance if trains spend more time at platforms to allow passengers to get on and off, or due to signalling problems. The interesting result, however, is that in both models the coefficient of the quality of service proxy is larger in absolute value than the price elasticity, which suggests that quality of service improvements, rather than fares reductions, may offer a more effective way of attracting metro passengers. Table 3 shows the short and long run price, income and service elasticities derived using difference GMM and the two different definitions of quality of service. These results indicate a price elasticity of 0.05 in the short run and 0.33 in the long run. Income elasticities are positive, which suggests metros are perceived as normal goods, with a short run elasticity of 0.03 and a long run elasticity of 0.18. The results also show that service elasticities, either measured by rail car kilometres travelled per route kilometre or rail car operating hours normalised by route length, are positive and higher than the absolute value or fare elasticities, which suggests that quality of service improvements, rather than fares reductions, may be more
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D.J. Graham et al. / Transportation Research Part E 45 (2009) 787–794 Table 3 Summary of elasticity estimates from difference GMM models. Variable
P Y KM
Quality of service (rail car kms per route km)
Quality of service (rail car hrs per route km)
Short run
Long run
Short run
Long run
0.047 0.026 0.072
0.331 0.183 0.507
0.048 0.024 0.053
0.325 0.162 0.358
30% 20% 10% 0% -10% -20%
Asia 5 Europe 8 Europe 3 Europe 10 Europe 7 Europe 5 Europe 1 Europe 2 Europe 9 Europe 4 Europe 6
-40%
Americas 5 Americas 7 Americas 2 Americas 1 Americas 6 Americas 3 Americas 4 Asia 3 Asia 4 Asia 2 Asia 1
-30%
Fig. 1. Forecast error for the most recent year of data.
effective in attracting additional metro passengers. The results indicate a supply or ‘quality of service’ elasticity of 0.07 in the short run and 0.50 in the long run. The estimated elasticities provide intuition about the key drivers of demand from across a range of systems, and we can think of these estimates as representing the weighted average responsiveness across the sample. How does the demand experience of the individual metro systems compare to these sample average parameters? Fig. 1 shows the forecast error of the first model specification for each of the metros included in the analysis. The forecast error is computed as the percentage difference between the actual level of patronage and the forecasted value for the most recent year of data. Given differences between metros and cities such as network coverage, mode share, interaction between modes, and size of the markets analysed, such forecast errors are inevitable5. However, it is interesting to note that the error is less than 20% in 18 of the 22 metros analysed. This indicates that the parameters from the demand model are reasonably effective in explaining variation in the demand for metro services and that these elasticities could therefore serve as useful parameters in metro benchmarking. As our dynamic panel model allows for different levels of heterogeneity among metros, the individual metro characteristics shift each metro regression line up or down. Therefore, the difference in forecast errors between metros also shows that, for some metros, those individual characteristics play a more important role in determining patronage levels. For instance, the fact that four of the five Asian metros have similar forecast errors, but most European metros present various levels of forecasting error, perhaps shows that individual city and metro characteristics tend to be more homogeneous in Asian than in European metro systems. 5. Conclusions This paper uses panel data on metros from around the world to estimate the responsiveness of demand to changes in fares, incomes and quality of service. The data allow for dynamic panel estimation which accommodates individual system specific heterogeneity, endogenous regressors, and measurement error. The results distinguish between short and long run demand responses. Litman (2004) suggests that in general short run fare elasticities of demand for public transport are between 0.2 and 0.5, while long run elasticities are between 0.6 and 0.9. Compared to these results our price estimates for urban metros are quite low, particularly in the short run. There are two important characteristics of metros that could explain this difference. First, metros in large or dense cities often have a degree of monopoly power in the market for mass transit, particularly 5
Due to the need to respect confidentiality it is not possible to reveal the name of the metro system.
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when there is traffic congestion or some other restrictions that adversely affect the speed or generalised cost of road transport. Second, historically metro fares have been set well below their revenue maximising fare for social, political and economic reasons. At any rate, the magnitude of the elasticities we estimate are consistent with the rule-of-thumb frequently used in the past that (in the long run) a 10% increase in fares will reduce patronage by around 3%. Thus, if the aim is to improve the finances of the metro systems, fare increases (at least at the margin) will lead to higher revenue without substantial negative effects on patronage in the short run. We also find that the effect of a 10 per cent increase in service quality tends to be more effective in attracting additional metro passengers than a 10 per cent fare reduction. It seems, therefore, that changes in frequency of service where viable could have a greater impact on demand than changes in fares. The long-term elasticity of demand with respect to service quality (measured as rail car kilometres per route kilometre) is 0.51. Thus, by increasing service frequencies we can expect to generate additional passenger demand for the metro while also providing additional capacity which could either mitigate uncomfortable congestion or provide room for extra demand growth in the future. Increasing service speeds, however, appears to have little effect on levels of passenger demand. Policy makers and metro managers should also note the large differences between short and long run elasticities with respect to both price and service supply. This reflects the fact that passengers take time to adjust their travel patterns and behaviour due to imperfect knowledge and habit formation; and in the longer term, car ownership decisions and changes in the origins and destinations of trips. Demand ‘ramp-up’ due to service improvements, for example, can affect the financial viability of investment projects which require an early demand response. Finally, our results show that income elasticities are positive and significant, which suggests that metros are perceived as normal goods and will thus tend to experience increases in patronage as standards of living rise. References Acutt, M.Z., Dodgson, J.S., 1996. Cross-elasticities of demand for travel. Transport Policy 2, 271–277. Arellano, M., Bond, S.R., 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297. Arellano, M., Bover, O., 1995. Another look at the instrumental variable estimation of error component models. Journal of Econometrics 68, 29–51. Baltagi, B.H., 2005, third ed. Econometric Analysis of Panel Data Wiley, Chichester. Blundell, R., Bond, S.R., 1998. Initial conditions of moment restrictions in dynamic panel data models. Journal of Econometrics 87 (1), 115–143. Blundell, R.W., Bond, S.R., 2000. GMM estimation with persistent panel data: an application to production functions. Econometric Reviews 19, 321–340. Blundell, R., Bond, S., Windmeijer, F., 2000. Estimation in dynamic panel data models: improving on the performance of the standard GMM estimator. In: Baltagi, B. (Ed.), Advances in Econometrics Vol. 15 Nonstationary Cointegration & and Dynamic Panels. JAI Elsevier, Amsterdam. Bowsher, C.G., 2002. On testing overidentifying restrictions in dynamic panel data models. Economic Letters 77 (2), 211–220. Dargay, J., Hanly, M., 2002. The demand for local bus services in England. Journal of Transport Economics and Policy 36, 79–91. Goodwin, P., 1992. A review of new demand elasticities with special reference to short and long run effects of price changes. Journal of Transport Economics and Policy 26, 155–164. Imbens, G.W., Spad, R.H., Johnson, P., 1998. Information theoretic approaches to inference in moment condition models. Econometrica 66, 333–357. Litman, T., 2004. Transit price elasticities and cross-elasticities. Journal of Public Transportation 7, 37–58. Litman, T., 2007. Valuing transit service quality improvements. Journal of Public Transportation 11, 43–64. Luk, J.Y.K., Hepburn, S., 1993. New Review of Australian Travel Demand Elasticities, Australian Road Research Board Ltd., Research Report ARR No. 249 ARRB, Vermont South. McCollom, B.E., Pratt, R., 2004. Transit Pricing and Fares. Chapter 12, TCRP Report 95, Transit Cooperative Research Program, Transportation Research Board, Federal Transit Administration. Nickell, S., 1981. Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426. Oum, T., Waters, w., Yong, J., 1992. Concepts of price elasticities of transport demand and recent empirical estimates: an interpretative survey. Journal of Transport Economics and Policy 26, 139–154. Paulley, N., Balcombe, R., Mackett, H., Titheridge, J., Preston, M., Wardman, J., Shires, White, P., 2006. The demand for public transport: the effects of fares, quality of service, income and car ownership. Transport Policy 13, 295–306. Pham, L., Linsalata, J. 1991. Effects of Fare Changes on Bus Ridership. American Public Transit Association, Washington, DC. Romilly, P., 2001. Subsidy and local bus service deregulation in Britain. A Re-Evaluation. Journal of Transport Economics and Policy 35, 161–194. Roodman, D., 2008. A note on the theme of too many instruments, Centre for Global Development, Working Paper No. 125. TRACE, 1999. Elasticity Handbook: Elasticities for Prototypical Contexts, European Commission, Directorate-General for Transport. TRL, 2004. The Demand for Public Transit: A Practical Guide, Transportation Research Laboratory, Report TRL 593.
Contents lists available at ScienceDirect
Transportation Research Part E journal homepage: www.elsevier.com/locate/tre
A dynamic panel analysis of urban metro demand Daniel J. Graham *, Amado Crotte, Richard J. Anderson Imperial College London, Railway and Transport Strategy Centre, Centre for Transport Studies, Department of Civil and Environmental Engineering, London SW7 2AZ, UK
a r t i c l e
i n f o
Article history: Received 23 July 2008 Received in revised form 23 January 2009 Accepted 24 January 2009
Keywords: Urban metro Demand Dynamic panel GMM
a b s t r a c t A dynamic panel model is used to estimate the effect that fares, income and quality of service have on demand for a sample of 22 urban metros. The estimated price elasticity is 0.05 in the short run and 0.33 in the long run. The estimated long run income elasticity is small but positive (0.18), indicating that metros are perceived as normal goods. The quality of service elasticities are positive and substantially higher than the absolute value of fare elasticities. The implication is that quality of service improvements, rather than fare reductions, may be more effective in increasing metro patronage. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Public transport performance benchmarking offers operators a means to gauge their own performance, relative to that of other providers, when there are few similar operators in their own immediate environment. Such inter-system comparative analyses can be particularly valuable for urban metros because there typically tends to be only one metro system operating in any city, and therefore, limited opportunities to obtain performance comparisons at the local level. Benchmarking analyses cover a diverse range of different activities, from ‘qualitative’ comparisons of best practice to quantitative analyses of different performance based measures. From the quantitative analyses, operators seek to get some idea of how the performance of their metro compares to that of others, typically by constructing rankings or by using deviations from some measure of central tendency derived from a sample of firms. In this paper, we use data on urban metros collected for the CoMET and Nova benchmarking groups, which are facilitated by the Railway and Transport Strategy Centre (RTSC) at Imperial College London, to analyse the demand for metro services. We derive a set of elasticities that describe the effect that fares, income and quality of service have on metro demand, and we then show how passenger demand for each metro within the sample compares to this evidence generated across the range of different systems. In estimating urban metro demand we are faced with a number of difficult empirical issues. The use of cross-sectional data, which tend to be readily available, is problematic due to the potential for omitted variable bias or confounding, the need to find a vast array of variables that can adequately characterise demand, and because many of the variables that should be included in the demand function are potentially endogenous but obvious external instruments may not be available. Of course, cross-sectional models also suffer from the disadvantage that they do not allow for any period of adjustment in the demand relationships. The use of time series data, taken one system at time, provides a potential solution to problems of
* Corresponding author. Tel.: +44 0 20 7594 6088; fax: +44 0 20 7594 6102. E-mail address: [email protected] (D.J. Graham). 1366-5545/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2009.01.001
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endogeneity and dynamics, but still cannot tell us much about the effect of individual heterogeneity on demand and also tend to be plagued with multicollinearity which can prevent proper identification of the demand function. Estimation of demand using panel data offers a number of advantages. It tends to provide more variance than contained in time series alone, it allows for individual system specific heterogeneity and thus a potential solution to the problem of omitted variables bias, and it can reduce the potential for multicollinearity and aid identification. Furthermore, dynamic panel data techniques allow us to study the temporal adjustment of demand and can accommodate endogenous regressors. But crucially, for the purposes of this paper, a key benefit of panel data is that it allows us to derive some intuition about the key drivers of demand from across a range of systems while also allowing us to model system specific effects. We can then use this intuition to make some comparisons of actual metro performance compared to average sample performance. In this paper, we use dynamic panel data techniques to estimate the effect that fares, income and quality of service have on the demand for medium sized and large urban metros from around the world. Our statistical approach allows for system specific heterogeneity, dynamic adjustment of the demand function, and can also accommodate endogenous regressors; an important concern when modelling quality of service. The paper is divided into five sections. Section 2 reviews previous literature on public transport demand. Section 3 describes the data available for estimation and outlines the Generalised Method of Moments (GMM) estimator for dynamic panel data. The Section 4 presents our results, and conclusions are then drawn in the final section of the paper. 2. Previous research There are a number of excellent surveys of the empirical literature on public transport demand (see in particular Pham and Linsalata, 1991; Oum et al., 1992; Goodwin, 1992; Luk and Hepburn, 1993; TRACE, 1999; TRL, 2004; McCollom and Pratt, 2004; Paulley et al., 2006). There is, therefore, no contribution to be made by providing an extensive literature survey here. However, it is worth reviewing some of the main findings from previous research to provide a context for the empirical work of this paper. The major survey articles cited above review results on the responsiveness of demand to changes in fares, income, quality of service, the price of competitive modes, and other factors. They show that there is a great deal of variation across studies in the magnitude of the relevant public transport demand elasticity estimates. This is mainly due to six key study characteristics: (1) type of data used (aggregate or disaggregate), (2) time frame analysed (month, quarter, year), (3) model structure (static and dynamic), (4) econometric technique used, (5) specification of the dependent variable (travel volume, modal choice or route choice), and (6) demand specification. The influence of these characteristics limits our ability to make direct comparisons of results from one particular study to those of another. In fact, the survey articles show that elasticity estimates can still vary substantially between studies even when the six key elements are consistent. This is due to the influence of certain country-specific characteristics such as natural circumstances, travel distances, and cultural differences that determine the level of competitiveness between transport modes. Thus, to some extent one of the key messages from the literature surveys is that the evidence on the magnitude of demand elasticities can be divergent and consequently direct comparisons may not be useful. That said, the reviews also point towards some basic generalisations about the responsiveness of demand to changes in price, income, service quality and price of competing modes. These are as follows. With regards to fare elasticities, the difference between estimates can be largely explained by four factors. First, rural areas in general have greater fares elasticities than urban areas, reflecting greater feasibility of using a car as an alternative mode due to less congestion and cheaper parking. Second, public transport choice or discretionary users that can choose to make a trip by car tend to be more responsive to fare changes than captive users who do not have the alternative of the car. Third, non-commute trips such as shopping and leisure are more elastic than work trips while off-peak trips have larger fare elasticities than peak-time values, mainly because peak-hour trips are work related. Finally, public transport fare elasticities depend on the type of transit analysed. In general, metros seem to have less sensitivity to fare changes than buses, possibly due to higher speeds and lower travel time particularly for longer journeys. Regarding income elasticities, some studies estimate negative coefficients perhaps indicating that public transport is an inferior good (e.g. Dargay and Hanly, 2002), while some studies show that the relationship is positive (e.g. Romilly, 2001) suggesting that as incomes grow and wealth increases people engage in activities that require more transportation services since transport is a derived demand. The literature shows that in general, income elasticities are found to be positive when vehicle ownership is included in the model, however, when it is excluded income picks up the negative effect that vehicle stock has on public transport demand. In fact, not many studies have included both variables in the same model due to problems of multicollinearity. Some authors believe that the inclusion of a time trend can improve estimation, arguing that if the trend coefficient is negative it accounts for vehicle ownership, while if it is positive it accounts for other unobservable or difficult to measure factors, such as traffic, car journey times and other car costs. In general, the literature surveys caution great care in interpreting the income elasticities since they depend on the variables selected for inclusion in the model. Some generalisations are also possible with regards to quality of service elasticities. Quality of service is a difficult characteristic to measure and while there is no consensus within the literature on a single appropriate proxy variable, we can define three approaches that are most commonly used: (1) number of vehicles/trains in operation and train kilometres operated (as these figures increase per passenger or per route length, service frequency also increases and there is less crowding),
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(2) some measure of time or money (for instance in vehicle time or waiting time through a value of time factor), and (3) other quality factors that are not directly measurable in terms of time or money (such as service reliability, infrastructure quality, and ventilation). As with fare elasticities, the main factors that give rise to variance in service quality elasticity values include city size, type of trip, type of user and type of mode. For instance, larger cities tend to have higher service elasticities than price elasticities, while smaller cities have comparable values. Rural areas have higher service elasticities because improvements to a poorer service have a greater impact. Another important point about the service quality variables is that they may be simultaneously determined with demand, but their potentially endogenous nature is often not addressed in empirical work. With regards to cross elasticities no general guidelines can be drawn. Oum et al. (1992) argue that the specification of the demand for public transport should include prices and service quality factors of competing modes to truly capture the effect of public transport markets. However, such cross elasticities are not directly transferable across time and space because they depend on the relative size of the two markets represented (Acutt and Dodgson, 1996). Oum et al. (1992) show that the estimated cross-elasticity of transit with respect to fuel prices ranges between studies from as little as 0.01 up to 1.32. In this section we have briefly summarised some of the key influences, both theorised and estimated, that affect the demand for public transport, as reported in the literature. The results reviewed in this literature have been derived for different modes in a variety of different empirical contexts. In this paper, we focus on the demand for urban metro services using a dynamic panel data approach which provides elasticities net of system or city specific characteristics. In this way we hope to be able to provide some general guidance about the characteristics of demand for this mode. 3. Data and model estimation The data we have available for estimation are for an unbalanced panel of 22 urban metros over a 13 year period. These data are collected by the Railway and Transport Strategy Centre (RTSC) at Imperial College London and used for their two urban metro benchmarking exercises CoMET and NOVA.1 We also have data on the Helsinki metro for the sample period. The panel data include the annual number of passengers per metro normalised by population, and a proxy for metro fares is estimated for each metro system with annual revenue from fares divided by annual number of passengers. We also have information on inflation and currency factors that allows us to transform the data into real comparable figures in US dollars. National GDP per capita is used as a proxy for local income and was obtained from the World Bank website as was annual national population. All financial quantities are converted into real US Dollars using Purchasing Power Parities, again published by the World Bank. The data available allow for five different specifications to measure quality of service. The data include rail car kilometres travelled and rail car operating hours. Both variables capture the effect of changes in metro supply as a result of line extensions, changes in frequency, and changes in hours of operation of the service. Ceteris paribus, changes in any of these three elements imply changes in both rail car kilometres travelled and rail car operating hours. Both variables can be normalised by metro passengers, to capture crowding and comfort, or by metro network length, to capture the same effect net of line extensions. The fifth specification includes rail car kilometres normalised by rail car operating hours, which would capture changes in speed. As mentioned in Section 2 above quality of service is a difficult attribute to quantify. With the data we have available we are only really able to represent those characteristics of quality of service which are related to supply, for instance, frequency, hours of service, and speeds. We do not include other potentially important aspects of service quality such as station and vehicle cleanliness, crowding, security, temperature control, and the availability of station facilities (see Litman 2007). Estimation with panel data does allow for the inclusion of individual effects which provide a means of capturing differences between metros in quality of service as well as other characteristics. Nonetheless, it is worth emphasising that we look explicitly at only a subset of quality of service variables and consequently the results do not have relevance over the broader definition discussed by Litman (2007). Given the dimensions of the panel, particularly the small number of annual observations relative to cross-sectional units, dynamic panel estimation should proceed with GMM rather than panel cointegration2. The main issue to be addressed in the context of dynamic panel estimation is correlation between the lagged endogenous terms and the unobserved cross-section individual effects. For instance, consider the autoregressive distributed lag (ADL) dynamic panel model
yit ¼ ayit1 þ bxit þ ðgi þ eit Þ
ð1Þ
1 The CoMET (Community of Metros) data include a consortium of twelve of the world’s largest metropolitan metros: Berlin BVG, Hong Kong MTR, London Underground Ltd, Metro de Madrid, Mexico City STC, Moscow MoM, Paris Metro (RATP), Paris RER, New York City Transit, Metro de Santiago, São Paulo MSP and Shanghai SMOC. The Nova group is a consortium of fifteen small to medium sized metros: Bangkok BMCL, Barcelona TMB, Buenos Aires Metrovías, Delhi DMRC, Glasgow SPT, Metropolitano de Lisboa, Milan ATM, Montréal STM, MetroNapoli, Newcastle Nexus, Metro Rio, Singapore SMRT, Taipei TRTC, Toronto TTC and Sydney CityRail, We have not been able to include data on the Delhi, Hong Kong (KCW), Lisbon, Milan, Taipei and Toronto metros in the model due to the small number of annual observations currently available. 2 Although the literature does not explicitly suggest the minimum number of annual observations needed for estimation of elasticities with a panel cointegration approach, most studies use at least from 20 to 25 annual observations.
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where y is the dependent variable, xit can be a vector of current and lagged values of the independent variables, the term gi is an unobserved time-invariant individual specific effect, and eit IID(0, r2) is a serially uncorrelated error term. Clearly there is a correlation between yit1 and gi. Furthermore, this correlation cannot be purged through the within transformation of the fixed effects estimator, that would effectively remove the individual effect gi, but would still result in correlation between the transformed regressors and the transformed errors with the consistency of the estimator dependent on having a large T dimension (e.g. Nickell, 1981). A similar problem prevents application of the quasi-demeaned GLS random effects estimator which still gives biased and inconsistent estimates for dynamic panel data models. When the assumption of zero conditional mean of the error term given the regressors is not satisfied, the GMM estimator provides a potential solution. The principle underpinning GMM is that, given a set of exogenous instrumental variables which are correlated with the regressors but orthogonal to the errors, we can define and solve a set of moment conditions which will be satisfied at the true value of the parameters to be estimated. In the context of dynamic panel data models the time series nature of the data is used to derive these instruments and establish the moment conditions (e.g. Arellano and Bond, 1991; Arellano and Bover, 1995; Blundell and Bond, 1998). For instance, given 1 the GMM estimator proceeds by taking first differences to eliminate the individual effects
yit yit1 ¼ ayit1 yit2 þ bxit bxit1 þ ðeit eit1 Þ:
ð2Þ
The correlation between yit1 and eit1 in 2 implies that OLS estimation will be inconsistent. Drawing on the panel nature of the data, however, we can derive a set of instruments which are both correlated with Dyit1 and orthogonal to Deit1. For instance, in the absence of serial autocorrelation, the lagged level yit2 will be correlated with Dyit1 but uncorrelated with Deit1. Following this line of reasoning, if T P 3 we also have yit3 available as an instrument, and so on, such that with each additional time period we can add an extra valid instrument. Similarly, this can be done for any other endogenous explanatory variables in the model giving rise to an instrument matrix denoted Zi = (yi, xi). The moment conditions are
E Z 0i Dei ¼ 0
ð3Þ
where Dei = (De3, De4,. . ., DeT)’, and the GMM estimator based on these moment conditions minimizes
qN ¼
n
1
n X
!
0 i Zi
De
1
WN n
n X
i¼1
!
Z 0i D i
e ;
ð4Þ
i¼1
where WN is the weight matrix
" W N ¼ n1
n X
Z 0i Dei De0i Z
#1 :
ð5Þ
i¼1
The GMM estimator can be derived in two steps by substituting the differences residuals from an initial estimation for Dei in (5). This so called difference GMM estimator (e.g. Arellano and Bond, 1991), therefore, has two attractive properties. First, it permits unobserved heterogeneity in the means of the yit series across individuals; and second, it accommodates the use of endogenous or stochastic regressors. In practice however the difference GMM estimator has been shown to perform poorly on data with persistent series. The main reason for this is that under these circumstances, the lagged levels of variables will sometimes tend to have only weak correlations with the first-difference equations. In particular, it has been shown that when the series have near unit roots the lag variable instruments tend to contain little information about the endogenous variables in first differences. The proposed solution to this problem gave rise to the development of the so called system GMM estimator, which uses lagged first differences as instruments for equations in levels as well as the lag variable instruments for first-difference equations (e.g. Arellano and Bover, 1995; Blundell and Bond, 1998; Blundell and Bond, 2000; Blundell et al., 2000). The validity of the extended system GMM estimator in the ADL context rests on the assumption that the (yit, xit) series each satisfy a mean stationarity assumption, yielding the additional moment conditions
E½DZ it1 ðgi þ eit Þ ¼ 0:
ð6Þ
Using both sets of moment conditions together, 3 and 6, gives rise to a system GMM estimator with first-differenced and levels equations. This estimator has been shown to offer much increased efficiency and less finite sample bias compared to the difference GMM estimator3. The consistency of the GMM estimator relies on the assumptions that there is no first-order serial autocorrelation in the errors of the level equation 1, and that the instrument matrix is truly exogenous and therefore valid to define the moment conditions. The Arellano and Bond test for serial autocorrelation (Arellano and Bond, 1991) tests the hypothesis that there is no second-order serial correlation in the first differenced residuals, which in turn implies that the errors from the levels equations are serially uncorrelated. The standard test for validity of the instrument matrix is the Sargan/Hansen test of
3
A good summary of this literature is given in Baltagi, 2005.
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overidentifying restrictions. The assumption of exogeneity of the instruments implies that we have a set of moment conditions which will be satisfied at the true value of our parameter estimates. If the model is overidentified (i.e. if there are more moment conditions than there are parameters to be estimated) the GMM framework allows us to test the validity of the additional moment conditions (overidentifying restrictions) in terms of whether they are set close enough to zero at the optimal GMM parameter estimates. Essentially, this is akin to testing for correlation between the model residuals and a subset of the instruments used. The Difference Sargan test is used to compare the results from difference and system GMM. The drawback of the Sargan test is that apart from detecting serial correlation, it can reject the restrictions if the model is miss-specified. Imbens et al. (1998) show that the Sargan test has poor size properties and propose alternative Tilting Parameter tests of overidentifying restrictions, however, Bowsher (2002) finds that the Tilting Parameter is only preferred to the Sargan test when few moment conditions are tested, which applies with panels with small T, or when few variables are treated as predetermined or strictly exogenous. The results from the Sargan test should therefore be interpreted with care. GMM estimation in the context of dynamic panel data models offers a means of obtaining consistent parameter estimates when regressors are potentially endogenous and where measurement error may be present. It also allows for unobserved individual heterogeneity and a period of adjustment in the demand relationships. For all of these reasons, it is highly suited to the estimation of metro demand functions given the available data. The dynamic demand model we estimate has the following form:
ln M it ¼ ci þ a ln Mi;t1 þ b0 ln P it þ b1 ln Y it þ b0 ln QoSit þ eit
ð7Þ
for i = 1,. . .,22 and t = 1,. . .,T (Ti is the number of annual observation for metro i), where Mit, Pit, Yit and QoSit denote metro patronage per capita, real fares in US dollars, real income per capita in US dollars, and quality of service, respectively, all expressed in logarithmic form. ci denotes the unobserved system specific effects that capture a whole range of individual characteristics such as city size, metro network coverage, and the supply and price of other modes and eit IID(0, r2) is the disturbance term. For comparative purposes, we also present estimates obtained by applying pooled OLS and fixed effects estimators to a dynamic demand model. 4. Results The demand model was first tested using each of the five possible quality of service variables and also with various combinations of these variables. The coefficient on the proxy for metro speed (rail car kilometres divided by rail car operating hours) was consistently found to be statistically insignificant and this variable was therefore excluded from the analysis. For the remaining variables, the results of diagnostic tests showed a significant improvement in fit when the quality of service variable was normalised by route length rather than by number of passengers. In fact, we found that normalisation by the number of passengers produced high correlation with the lagged dependent variable. The results also showed that the inclusion of more than one quality of service variable gives multicollinearity. We therefore found that the viable options for quality of service proxies include either rail car kilometres or rail car operating hours, both normalised by route length. The four columns of Table 1 report the results using OLS levels, Within Groups, difference GMM, and system GMM, respectively, for the model that uses rail car kilometres travelled normalised by network length as a proxy for quality of service. For the GMM estimators, several specifications were tested with regards to the endogeneity of the variables. The choice of model was based on the significance of the estimates, as well as the Arellano-Bond tests for AR(1) and AR(2) in first differences, the Sargan and Hansen tests of overidentifying restrictions, and the Difference-in-Hansen tests of exogeneity of instrument subsets. The most appropriate difference GMM model treats quality of service as endogenous, prices as predetermined but not strictly exogenous, and income as strictly exogenous. The results from both difference and system GMM pass the instrument validity tests, however, the estimate of the autoregressive term in the system GMM model is larger than that of OLS levels, which suggests the estimates are biased. System GMM also produces insignificant estimates with counterintuitive signs. The difference Sargan test statistic for system GMM appears unusually large, which may indicate failure of the model to satisfy the necessary condition for system GMM that the lagged differences are uncorrelated with the individual effects (Blundell and Bond 1998). A key problem here is that when the number of moment conditions is large relative to the number of cross-sectional units, the system GMM estimator increases potential for finite sample bias while at the same time weakening the ability of the Sargan tests to detect an invalid specification. It is well known that problems can arise with system GMM estimation in samples with a small number of cross-sectional relative to temporal units, as is the case with our data (N = 22, T 6 13). When the instruments used in the difference GMM estimator are not weak, the additional instruments employed in system GMM can overfit the endogenous variables and are themselves potentially endogenous unless some rather strict conditions are satisfied (see Roodman 2008). For these reasons, we believe the difference GMM specification is probably more appropriate for our data. Table 2 presents the results of the model with rail car operating hours normalised by route length as a proxy for quality of service, which also measures frequency of service and metro operating hours net of the effect of line extensions or construction of new lines4. Again, both difference and system GMM models pass the instrument validity tests, however, the estimate of
4 The number of observations for the regressions in Table 2 is less than in Table 1 because some of our metros did not report rail car hours operated for certain years.
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Table 1 Results of the dynamic panel model with quality of service measured as rail car kilometres per route kilometre. Dependent variable: metro patronage per capita (lnM). Variable
OLS levels
Within groups
Diff GMM
Sys GMM
lnP
0.010 (0.006) 0.007 (0.006) 0.010 (0.010) 0.999* (0.003) – – – – – 0.99 192
0.088* (0.016) 0.074* (0.018) 0.015 (0.040) 0.816* (0.038) – – – – – 0.99 192
0.047* (0.011) 0.026* (0.008) 0.072* (0.005) 0.858* (0.045) 0.001 0.445 0.242 0.246 34 – 170
0.043 (0.046) 0.067 (0.087) 0.187 (0.100) 1.003* (0.031) 0.008 0.533 0.124 1.000 50 – 192
lnY lnQoS (rail car kms/route km) lnMt1 AB AR (1) AB AR (2) Sargan Dif Sargan no. Instruments Adj. R2 No. observations
All variables are expressed in logarithmic form. Real Income (lnY) is in per capita terms, quality of service (lnQoS) is measured as rail car kilometres normalised by route kilometres, fares (lnP) and income (lnY) were converted into real terms and are expressed in 2006 US dollars. * denotes significance at the 1% level. The estimated coefficients without a* are not statistically significant at a level lower than 10%. Standard errors in parenthesis.
Table 2 Results of the dynamic panel model with quality of service measured as rail car hours per route kilometre. Dependent variable: metro patronage per capita (lnM). Variable
OLS levels
Within groups
Diff GMM
Sys GMM
lnP
0.009 (0.006) 0.007 (0.006) 0.015 (0.011) 0.998* (0.003) – – – – – 0.99 182
0.096* (0.017) 0.082* (0.018) 0.044* (0.035) 0.850* (0.043) – – – – – 0.99 182
0.048* (0.024) 0.024* (0.009) 0.053* (0.021) 0.852* (0.050) 0.015 0.944 0.557 0.339 35 – 160
0.047 (0.031) 0.063 (0.033) 0.203* (0.079) 0.999* (0.039) 0.019 0.957 0.243 0.970 39 – 182
lnY lnQoS (rail car hrs/route km) lnMt1 AB AR(1) AB AR(2) Sargan Dif Sargan no. Instruments Adj. R2 No. Observations
All variables are expressed in logarithmic form. Real Income (lnY) is in per capita terms, quality of service (lnQoS) is measured as rail car operating hours normalised by route kilometres, fares (lnP) and income (lnY) were converted into real terms and are expressed in 2006 US dollars. denotes significance at the 1% level. The estimated coefficients without a * are not statistically significant at a level lower than 10%. Standard errors in parenthesis. *
the autoregressive term,a, appears too close to that of Within Groups in the difference GMM specification, and does not lie between the corresponding OLS levels and Within Groups estimates in the system GMM specification. This suggests that for the panel of metros analysed the instruments may be weak and the coefficients may be downward biased. Comparing the results shown in Tables 1 and 2, we can see that although both difference GMM specifications produce almost identical price and income coefficients, the quality of service coefficient is much smaller in the second model. This is not surprising as rail car operating hours can increase even if hours of operation or frequency do not change, for instance if trains spend more time at platforms to allow passengers to get on and off, or due to signalling problems. The interesting result, however, is that in both models the coefficient of the quality of service proxy is larger in absolute value than the price elasticity, which suggests that quality of service improvements, rather than fares reductions, may offer a more effective way of attracting metro passengers. Table 3 shows the short and long run price, income and service elasticities derived using difference GMM and the two different definitions of quality of service. These results indicate a price elasticity of 0.05 in the short run and 0.33 in the long run. Income elasticities are positive, which suggests metros are perceived as normal goods, with a short run elasticity of 0.03 and a long run elasticity of 0.18. The results also show that service elasticities, either measured by rail car kilometres travelled per route kilometre or rail car operating hours normalised by route length, are positive and higher than the absolute value or fare elasticities, which suggests that quality of service improvements, rather than fares reductions, may be more
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D.J. Graham et al. / Transportation Research Part E 45 (2009) 787–794 Table 3 Summary of elasticity estimates from difference GMM models. Variable
P Y KM
Quality of service (rail car kms per route km)
Quality of service (rail car hrs per route km)
Short run
Long run
Short run
Long run
0.047 0.026 0.072
0.331 0.183 0.507
0.048 0.024 0.053
0.325 0.162 0.358
30% 20% 10% 0% -10% -20%
Asia 5 Europe 8 Europe 3 Europe 10 Europe 7 Europe 5 Europe 1 Europe 2 Europe 9 Europe 4 Europe 6
-40%
Americas 5 Americas 7 Americas 2 Americas 1 Americas 6 Americas 3 Americas 4 Asia 3 Asia 4 Asia 2 Asia 1
-30%
Fig. 1. Forecast error for the most recent year of data.
effective in attracting additional metro passengers. The results indicate a supply or ‘quality of service’ elasticity of 0.07 in the short run and 0.50 in the long run. The estimated elasticities provide intuition about the key drivers of demand from across a range of systems, and we can think of these estimates as representing the weighted average responsiveness across the sample. How does the demand experience of the individual metro systems compare to these sample average parameters? Fig. 1 shows the forecast error of the first model specification for each of the metros included in the analysis. The forecast error is computed as the percentage difference between the actual level of patronage and the forecasted value for the most recent year of data. Given differences between metros and cities such as network coverage, mode share, interaction between modes, and size of the markets analysed, such forecast errors are inevitable5. However, it is interesting to note that the error is less than 20% in 18 of the 22 metros analysed. This indicates that the parameters from the demand model are reasonably effective in explaining variation in the demand for metro services and that these elasticities could therefore serve as useful parameters in metro benchmarking. As our dynamic panel model allows for different levels of heterogeneity among metros, the individual metro characteristics shift each metro regression line up or down. Therefore, the difference in forecast errors between metros also shows that, for some metros, those individual characteristics play a more important role in determining patronage levels. For instance, the fact that four of the five Asian metros have similar forecast errors, but most European metros present various levels of forecasting error, perhaps shows that individual city and metro characteristics tend to be more homogeneous in Asian than in European metro systems. 5. Conclusions This paper uses panel data on metros from around the world to estimate the responsiveness of demand to changes in fares, incomes and quality of service. The data allow for dynamic panel estimation which accommodates individual system specific heterogeneity, endogenous regressors, and measurement error. The results distinguish between short and long run demand responses. Litman (2004) suggests that in general short run fare elasticities of demand for public transport are between 0.2 and 0.5, while long run elasticities are between 0.6 and 0.9. Compared to these results our price estimates for urban metros are quite low, particularly in the short run. There are two important characteristics of metros that could explain this difference. First, metros in large or dense cities often have a degree of monopoly power in the market for mass transit, particularly 5
Due to the need to respect confidentiality it is not possible to reveal the name of the metro system.
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when there is traffic congestion or some other restrictions that adversely affect the speed or generalised cost of road transport. Second, historically metro fares have been set well below their revenue maximising fare for social, political and economic reasons. At any rate, the magnitude of the elasticities we estimate are consistent with the rule-of-thumb frequently used in the past that (in the long run) a 10% increase in fares will reduce patronage by around 3%. Thus, if the aim is to improve the finances of the metro systems, fare increases (at least at the margin) will lead to higher revenue without substantial negative effects on patronage in the short run. We also find that the effect of a 10 per cent increase in service quality tends to be more effective in attracting additional metro passengers than a 10 per cent fare reduction. It seems, therefore, that changes in frequency of service where viable could have a greater impact on demand than changes in fares. The long-term elasticity of demand with respect to service quality (measured as rail car kilometres per route kilometre) is 0.51. Thus, by increasing service frequencies we can expect to generate additional passenger demand for the metro while also providing additional capacity which could either mitigate uncomfortable congestion or provide room for extra demand growth in the future. Increasing service speeds, however, appears to have little effect on levels of passenger demand. Policy makers and metro managers should also note the large differences between short and long run elasticities with respect to both price and service supply. This reflects the fact that passengers take time to adjust their travel patterns and behaviour due to imperfect knowledge and habit formation; and in the longer term, car ownership decisions and changes in the origins and destinations of trips. Demand ‘ramp-up’ due to service improvements, for example, can affect the financial viability of investment projects which require an early demand response. Finally, our results show that income elasticities are positive and significant, which suggests that metros are perceived as normal goods and will thus tend to experience increases in patronage as standards of living rise. References Acutt, M.Z., Dodgson, J.S., 1996. Cross-elasticities of demand for travel. Transport Policy 2, 271–277. Arellano, M., Bond, S.R., 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297. Arellano, M., Bover, O., 1995. Another look at the instrumental variable estimation of error component models. Journal of Econometrics 68, 29–51. Baltagi, B.H., 2005, third ed. Econometric Analysis of Panel Data Wiley, Chichester. Blundell, R., Bond, S.R., 1998. 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