Geography and the local public transport
Marco Alderighi
Universita della Valle d’Aosta
Gianni Gorla
Università della Valle d’Aosta
This paper investigates how geography affects the performance of
local public transport firms in Italy. Using data on 110 firms involved in
urban and intercity transport in 2002, we provide different estimates of
stochastic cost frontiers. The analysis is then performed for two different
models: a long-run cost function and a short-run variable cost function.
These two procedures lead to similar results. It emerges that geographic
variables impact on the efficiency of firms. In particular, we find that
metropolitan transport and mountain transport account for a loss in
efficiency of 14%-20% and of 14%-16% respectively, whilst differences
between transport in the North and South part of Italy does not have a
significant impact.
INTRODUCTION
It becomes apparent that human settlements and
territorial
morphology affect the political choice on local public transport (LPT). In
established settlements, LPT is organized to satisfy the requests of
mobility of citizens and to reduce congestion. In recent settlements, LPT
can play an important role in determining the location of citizens and
firms and the growth of the settlement itself. In this paper we assume
political choices on LPT as given and we focus on the impact of
morphology and human settlements (i.e. geography) on the cost efficiency
of LPT.
The modern analysis of the firm’s performance dated to the pioneering
contributions of Aigner, Lovell and Schmidt (1977) and Meeusen and van
den Broeck (1977) who developed the stochastic frontier (SF) approach.
In literature, SF approach mainly applies to the estimation of production
and cost functions but it may be used to the estimation of profit and
revenue functions as well. For sake of clarity, we limit the discussion to
the analysis of a stochastic cost function, being it the subject of this
paper.1
1
For an overview on the topic, see for example: Kumbhakar and Lovell (2000) or
Coelli, Rao and Battese (1997).
2
The study of cost frontiers allows us to measure the level of
inefficiency of firms and to identify the main determinants. Cost
efficiency is usually defined as the ratio between the expenditure a firm
incurs in producing the output given the factor prices and the minimum
cost a firm incurs combining the resources in an efficient fashion. More
formally:
CE:= C(Y, P) / E(Y, P)
(1)
where E(Y, P) is the firms’ expenditure for producing output Y given
vector prices P and C(Y, P) is minimum cost. Hence, CE=1 only if a firm
is efficient, while is 0<CE<1 if a firm is inefficient. Cost inefficiency
captures two types of inefficiency: technical inefficiency and allocative
inefficiency. The latter comes from the fact that firms can fail to choose
the right input mix for given input prices whilst the former comes from
the fact that firms might not exploit the factors of production in the better
way.
The SF approach assumes that the cost fuction is not deterministic but
that it is affected by some random shocks that are not under the control of
the firm. To incorporate firm-specific random shocks into the model
requires the specification of a stochastic cost frontier. Hence, replacing
3
C(Y, P) with Cd(Y, P)*exp[v] in equation (1), after re-arranging the terms
we obtain:
E(Y, P) = Cd(Y, P) *exp[v] * exp[u]
(2)
where v is a random noise and exp[-u]=CE. Equation (2) shows that
the expenditure function is represented by a deterministic component plus
an error term, which is split into two components. The first one is the
usual random noise term, which captures the impact of some variables
omitted in the analysis. The second one is a positive term which captures
the cost inefficiency.
In this paper, we use the SF approach to study how geography affects
the performance of local public transport firms.
Using data on 110 firms involved in urban and intercity transport in
2002, we provide different estimates of stochastic cost frontiers. The
analysis is then performed for two different models: a long-run cost
function and a short-run variable cost function. The two analyses are
convergent in the results. It emerges that some geographic variables are
crucial for explaining technical and allocative inefficiency. Metropolitan
transport and mountain transport account for an efficiency loss ranging
from 14% and 20% and from 14% to 16% respectively, while transport in
the North part of Italy does not substantially affect the efficiency.
4
The paper is organized as follows. In Section 2 we present some
methodological issues, Section 3 is devoted to the description of the
dataset and main variables of the analysis. In Section 4, we summarize the
econometric models and in the following we show the main results of the
estimation and we discuss some critical aspects. Finally, Section 5
concludes the paper.
METHODOLOGICAL ISSUES
The analysis of the cost inefficiency of LPT firms requires four orders
of considerations.
First, traditional measures of output are passenger-kilometres and
output-kilometres. As the former often presents measurement problems,
we follow recent literature assuming that output is measured by the
number of vehicle-kilometres.
Second, LPT firms are usually operating for urban and intercity
connections. To increase the accuracy of estimation, it is often required to
consider both urban and intercity transport jointly in the analysis.
However, these transports are not homogeneous as urban transport
accounts a higher number of stops, more traffic density and congestion.
To solve this problem there are two main techniques: 1) the estimation of
5
a multi-output cost function and, 2) the identification of a weighting
factor which makes different outputs summable.2 The estimation of multioutput cost function requires a translog (Christensen, Jorgenson and Lau,
1971) specification as a Cobb-Douglas specification do not satisfy the
conditions on the curvature of the cost function (Diewert and Wales,
1987). However, translog specification (even if some restrictions on the
coefficients can be imposed) produces a loss in the number of degree of
freedom and the estimation of the first-order and especially of secondorder coefficients is often not accurate when the number of observations
is not large3. Alternatively, it is possible to apply a weighting factor to
specify urban and intercity transport in equivalent units. In this paper, we
choose this second way and we assume that a vehicle-kilometre of
intercity transport accounts for a percentage of vehicle-kilometre of urban
2
Other papers solve the problem differently. In some studies, where time series data
were available, it was possible to limit the number of firms to urban or intercity firms (for
example, see: Mizutani and Urakami, 2002). Other works introduce dummy variables or
other control variables (as the commercial velocity) to capture differences on local and
intercity transport (Fraquelli et al., 2002).
3
Moreover, Translog estimation provides a second-order approximation of the cost
function around the median of the data and results may be not accurate when the size of the
firms, as in our case, are very different (see: Perrone and Rutherford, 1996)
6
transport. The choice of the weighting factor is done by estimating an
auxiliary regression.4
Third, the treatment of capital is particularly tricky as the capital
purchases are strictly dependent from government grants-in-aid program
(See Fabbri, 1998, and Levaggi, 1994). Capital purchases (using grantsin-aid program) increase the total cost of a firm sustains but contextually
it also increases the revenue of the firm as it receives a subsidy.
Accounting procedures require that capital depreciation is included into
the total costs of the firms and that subsidies are registered as revenue.
This has an important consequence. Capital investment decision may be
affected by grants-in-aid program as the real capital price is smaller than
the market capital price. In fact, the accounting statistics register
depreciation cost of capital in the total cost function, while managers
usually evaluate the economic costs (the market depreciation net of
subsidies). Noting this, Fabbri (1998) and Levaggi (1994) guest that LPT
firms are not optimizing a long-run total cost function but on a short-run
variable cost function and they focus their analysis on the variable cost
function. More precisely, they focus on the operational costs of the firms
4
Since the weighting factor can affect the estimation of the main regression, we also
perform a sensitivity analysis. See: Friebes, Ivaldi and Vibes (2003) for the computation of
the weighting factor in a similar context.
7
in which depreciation costs and financial costs are excluded.
Unfortunately, we do not have information on the value of depreciation
from accounting data (as our source is from the ASSTRA database,
2002), so that in order to use a variable cost function, we need to estimate
the value of depreciation.
The estimation of the total cost function and the variable cost function
are quite similar in terms of the geography impact on the efficiency of the
firm.
However, the estimation of the variable costs presents some problems
with the sign of the coefficient of the capital. Thus, we will find that
operative costs are positively affected by the level of capital, which
contrasts with the prediction of the theory. In fact, being capital and
labour substitute, the higher the capital, the lower the variable costs. This
problem often appears in PTL literature and authors usually explain it as a
strong collinearity between capital and output variables (Filippini, 1996)
or as effect of generous government programs of subsiding investments
(Caves et al., 1985). To mitigate this problem we follow Levaggi (1994)
correcting capital by the average age although the positive sign of the
coefficient persists.
Fourth, the estimation of cost function needs information on the prices
of factors of production. However, ASSTRA database (2002) contains
data on the cost of labour but not on the cost of fuel and capital. This
8
implies that we need to integrate the original database with data collected
from secondary sources.5 This result may distort the estimation of the
coefficient of factor inputs even if it does not seem to affect the
coefficient of other variables.
DATA AND VARIABLES
Data come from ASSTRA database and refers to the year 2002
(mainly). The database constitutes of 110 observations at the firm level:
44 firms are specialized urban transport, 31 intercity and 35 mixed. The
original database counts more than 200, but we keep 110 records only as
we excluded firms which offer rail transport and those for which we have
not got enough information. The original dataset has been integrated with
5
We collect data on fuel prices, on capital deprecietion from the balance sheets of a
selected sample of firms (about 20 firms). Then, we estimate the fuel prices and capital
depreciation for the firms out of the sub-sample. As these recovered values could affect the
estimation of the cost function we have performed the analyses under different assumptions
and we find that results are quite robusts. We finally decided to make the cost of
depreciation depending on the number of vehicles a firm owns and to make the average
depreciation cost equivalent to the average value of the sub-sample we have collected. The
cost of fuel is computed assuming that large LPT firms pay lower prices per liter and that the
average cost of fuel be equivalent to the average value of the sub-sample.
9
data collected from secondary sources (as mentioned in previous
paragraph).
In order to select variables for the analysis we follow the recent
literature on LPT. Table 1 lists the variables.
[TABLE 1]
Descriptive statistics are depicted in Table 2 (values in logs, except
dummies):
[TABLE 2]
ESTIMATION
In Section 2, we define the output in terms of vehicles-kilometres and
we justify our choice of estimating the cost function through a CobbDouglas specification. As already mentioned, this choice is correct only
when we deal with a single output and hence there is a need to
homogenize the urban and intercity offer. In order to identify the
weighting factor, we perform an auxiliary regression using non-linear
10
ordinary least square estimator.6 Stemming on the results,7 hereafter we
adopt a weighting factor equal to 0.70.
Equation (3) describes a Cobb-Douglas cost function where variables
are in logs.
log Cd(Y, P)= a0 + a1 PL+ a2 PKM + a3 PF + a4 Y
(3)
Replacing it in equation (2) after taking logariths we have:
CT = a0 + a1 PL+ a2 PKM + a3 PF + a4 Y + v + u
(4)
where CT = log E(Y, P) and P = (PL , PKM , PF ).
6
See for example Friebes, Ivaldi and Vibes (2003) which applied this procedure to the
estimation of the weighting factor for a production function.
7
We find that the weighting factor ranges from 0.70 to 0.72 for total cost function, it
ranges from 0.68 to 0.70 for the operative cost function. Sensitivity analysis shows that all
coefficients of the estimates are quite similar for the range analyzed (0.66 to 0.74) and hence
the estimates of the cost functions are quite robust to a limited modification of the weighting
factor.
11
Homogeneity of degree one in prices of the cost function implies that
a1 + a2 + a3 = 1. This restriction allows us to re-write equation (4)
normalizing for the price of the fuel. It yields to equation (5):
CT - PF = a0 + a1 (PL - PF )+ a2 (PKM - PF ) + a4 Y + v + u
(5)
The econometric specification of this model requires the inclusion of
some controls, which in our analysis concerns the geographic variables
and some assumptions on the noise term. As practiced, we assume that v
is normally distributed and that u ≥ 0. We test the model with the most
popular distribution, i.e. exponential distribution and half-normal
distribution. The final version of stochastic frontier total cost function is
hence:
CT - PF = a0 + a1 (PL - PF )+ a2 (PKM - PF ) + a4 Y +
+ b1 AM +b2 M +b3 N + v + u
(6)
We also estimate a short-term variable cost function (i.e. operative
cost function), where we assume that capital plays the role of fixed input.
Equation (7) describes the specification of the operative cost function:
12
CO - PF = a0 + a1 (PL - PF )+ a2 (PM - PF ) + a4 Y + a5 K +
+ b1 AM +b2 M +b3 N + v + u
(7)
Table 3 reports the estimation of the total cost function coming from
equation (6). We propose three different estimates. The OLS estimation
that produces unbiased estimate of parameters apart from the contrant
term. The SFE that is the maximum likelihood estimator when assuming u
esponentially distributed and SFH estimator that is the maximum
likelihood estimator assuming that u is half-normal distributed. As noted
the OLS estimator and SFE produces similar results. However, SFH
presents higher values for a1. From an economic point of view notice that
being the variables in logs, the coefficients measure the elasticity of the
total cost to a variation of the variable. In particular, notice that a4 is close
to 1 meaning that the LPT present constant economies of scale.
Coefficients a1 and a2 capture the contribution of labour and capital
respectively to total cost. Notice that the three models understimate the
contribution of capital and materials (that is about 30%) and consequently
overstimate the contribution of fuel. Altough this values are in the range
of the interval estimation and hence it can be acceptable in statistical
terms, we think that this distortion can be also explained by the fact that
13
some explaining variables may be subject to measurement issues (see
footnote 5).
Coming to the geographical variables, we notice that firms operating
in the metropolitan areas have on average an increase in cost of 14-20%
and those operating in mountain regions of 15-16%. Finally, the location
of firms in the North part of Italy does not substantially affect the
efficiency (less than 2% and not significant).8
[TABLE 3, 4]
Table 4 presents the estimation results when we consider the variable
costs. Results are quite similar to previous case. Geographical variables
indicates that firms opeating in the metropolitan areas have on average an
increase in cost of 16-19% and those operating in mountain regions of 1416%. Again, the location of firms in the North part of Italy scarcely
affects the efficiency (about 5% and not significant).
8
We have also performed an estimation of the total cost function assuming two inputs
of production (labour and capital including fuel) to avoid measurement problem in the
pricing variable. In this estimates we observe that the coefficients concerning the
geographical variables as well as the output do not present any substantial change. This fact
suggests that the estimation of geographical variables do not seem to be affected by possible
measurement problems on the price of fuel and capital depreciation.
14
Note that the short-run economies of scale SRES= 1/a4 = 1.18 and the
long-run economies of scale LRES=(1- a5)/a4 = 0.98, which confirm that
there are long-run constant economies of scale. 9 These results are quite
different from those of Fazioli, Filippini and Prioni (1993), Fabbri (1998),
Fraquelli et al. (2001), Fazioli, Filippini and Kunze (2002) and Karlaftis
and McCarthy (2002) who find increasing return to scale for LPT.
Contrary, Windle (1988) analysing LPT in US can not reject the
hypothesis of constant return to scale and Filippini and Prioni (2003)
found that there are important economies of density but weak economies
of scale.
Before concluding, it is useful to calculate the mean cost efficiency
(MCE) for different sets of explanatory variables (controls) and models in
order to measure the contribution of some variables in the explanation of
the cost efficiency. Following Battese and Coelli, MCE can be obtaining
by averaging cost efficiency of different firms (Battese and Coelli, 1988).
We have computed the MCE for equations (7) and (8) both including and
excluding geographical controls.
[TABLE 5]
9
See: Caves et al. (1981) for an interpretation.
15
If the contribution of geography is minimal, then the MCE estimation
of the unrestricted (i.e. including geographical variables) and restricted
(i.e. excluding geographical variables) models must be similar. On the
contrary, if the contribution of geography is important, we expect that
MCE reduces when we use the unrestricted model.
We note that the assumptions on the distribution of the inefficiency
component is very important. (Results are summarized in Table 5).
Assuming
esponential distribution of the inefficiency term, the cost
inefficiency after controlling for geographic variable is about 5% while in
the restricted model, it is about 14%. This result shows that geographical
variables explains about two-thirds of the firms inefficiency and hence the
geography appears to be one of the main determinants of firms
performance. However this result is not confirmed by assuming halfnormal distribution of the inefficiency term. In that case geographical
variables account only for a one-fifth of total inefficiency.
CONCLUSIONS
The study of cost efficiency is one of the main issues in the transport
literature. Although transport is mainly dependent from the human
settlements and territory, most of the focus on the study of efficiency has
16
devoted to the management capabilities or institutional settings (see, for
example: Cebenoyan et al., 1993, Altunbas et al., 2001). In this paper, we
have showed that geography matters and its impact is rather relevant. In
particular, we have showed that, in the exponential model, mean cost
inefficiency reduces from 14% to 5% when we include some territorial
morphology attributes. We showed that there are same characteristics
springing from the morphology of the territory and the human settlements
that strongly affect the performance of the firm. Being in a metropolitan
area increases the costs of about 15%, as well as being in a mountain area,
whilst the location in the North part of Italy is weakly related to an
increase in firms performance.
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19
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20
TABLES AND FIGURES
Table 1 – List of variables
vehicle-kilometres for urban transport
plus vehicle-kilometres for intercity
Output
Y
transport weighted by a coefficient of
0.70.
the number of vehicles in the rolling stock
weighted by the relative average fleet age,
Capital
K
(i.e. the number of vehicles times the
firm’s average fleet age over the average
fleet age of the sample)
Labour
L
total labour
Fuel
F
total fuel
Total costs
CT
sum of the salary, fuel, material, spare and
repairs expense and capital depreciation
sum of the salary, fuel, material, spare and
Operational costs
CO
repairs expense (excluding capital
21
depreciation)
Price of labour
PL
total salary expenses / labour
estimated price for fuel. (average price of
Price of fuel
PF
the fuel discounted by a factor of 15% and
corrected by the size of the firm)
expenses for material, spare, repairs and
Price of material
PKM
and capital
capital depreciationa / vehicles-km.
expenses for material, spare, repairsb /
Price of material
PM
vehicles-km.
Dummy for
MA
firms operating in a metropolitan area
metropolitan area
firms operating in mountain. It assumes
three value: 1 when the firm only
Dummy for
M
operates in mountain; 0.5 whether the
mountain
firm operate in mountain and in height; 0
otherwise.
Dummy for North N
firms operating in North Italy.
a=computed as difference between total cost and cost of labour and estimated cost of fuel.
b= computed as difference between total cost, cost of labour, estimated cost of fuel and
capital.
22
Table 2 - Variables (in log)
Mean
Max
Min
Y
14.977
17.829
11.765
1.231
K
4.603
7.374
1.609
1.182
L
5.156
8.122
1.386
1.298
F
14.210
17.245
10.833
1.292
CT
16.221
19.416
12.582
1.295
CO
16.122
19.355
12.393
1.312
PL
10.513
11.032
10.037
0.171
PF
-0.303
-0.266
-0.427
0.035
PKM
10.413
11.636
9.664
0.357
PM
10.014
11.544
8.656
0.528
MA
0.090
1.000
0.000
0.287
M
0.048
1.000
0.000
0.198
N
0.468
1.000
0.000
0.501
23
StDev
Table 3 - Total cost function estimation
OLS
(R2=0.9820)
SFE
SFH
(LL= 34.306)
(LL=34.791)
a0
-6.9007**
-6.9703**
-7.7819**
a1
0.5662**
0.5681**
0.6254**
a2
0.2138**
0.2126**
0.2058**
a4
1.0001**
1.0018**
1.0096**
b1
0.2021**
0.1982**
0.1401+
b2
0.1638*
0.1610+
0.1567*
b3
-0.0209
-0.0195
-0.0025
v
0.1738
0.1079
u
0.0487
0.2390
2
0.0314
0.0688
λ
0.2861
2.2146
**= significant at 1%, *=significant at 5%, +=significant at 10%
24
Table 4 - Variable cost function estimation
OLS
(R2=0.9820)
SFE
SFH
(LL=32.859)
(LL=33.101)
a0
-4.8424**
-4.9318**
-5.4611**
a1
0.5366**
0.5393**
0.5676**
a2
0.1976**
0.1964**
0.1937**
a4
0.8474**
0.8490**
0.8603**
a5
0.1714**
0.1706**
0.1631 **
b1
0.1921**
0.1890**
0.1632+
b2
0.1604+
0.1551+
0.1432+
b3
-0.0599
-0.0578
-0.0442
v
0.1720
0.1318
u
0.0516
0.2045
2
0.0322
0.0592
λ
0.3000
1.5507
**= significant at 1%, *=significant at 5%, +=significant at 10%
25
Table 5 – Mean cost efficiency
SFE
SFH
Total cost function, unrestricted
0.9512
0.8167
Total cost function, restricted
0.8579
0.7955
Operative cost function, unrestricted
0.9484
0.8423
Operative cost function, restricted
0.8619
0.7901
26