Environmental factors in DEA analysis

Besides the conventional inputs and outputs, there are other factors that could impact the technical efficiency of transit systems. The term environment is used to describe factors that could influence the efficiency of a firm (DMU), where such factors are not traditional inputs (or outputs) and are assumed not under the control of the manager. Environmental factors may be measured directly or through the use of surrogate measures. Environmental variables include

1. ownership differences, such as public/private or corporate/non-corporate;

2. location characteristics, such as schools influenced by socioeconomic status of children and city/country location, or electric power distribution networks influenced by population density and average customer size;

3. labour union power; and 4. government regulations, etc.

There are a number of ways in which environmental variables can be accommodated in a DEA study (see Coelli et al, 1998, for details).

More recently, another so called three-stage methodology is developed by Fried et al.

(2002). They propose a new technique for incorporating environmental effects and statistical noise into a producer performance evaluation based on DEA. The technique involves a three-stage analysis. In the first stage, DEA is applied to outputs and inputs only,

to obtain initial measures of producer performance. In the second stage, SFA is used to regress first stage performance measures against a set of environmental variables. This provides, for each input or output (depending on the orientation of the first stage DEA model), a three-way decomposition of the variation in performance into a part attributable to environmental effects, a part attributable to managerial inefficiency, and a part attributable to statistical noise. In the third stage, either inputs or outputs (again depending on the orientation of the first stage DEA model) are adjusted to account for the impact of the environmental effects and the statistical noise uncovered in the second stage, and DEA is used to re-evaluate producer performance. Throughout the analysis emphasis is placed on slacks, rather than on radial efficiency scores, as appropriate measures of producer performance.

CHAPTER 5 The Case Study 1

─ The Effects of Privatization on Return to the Dollar:

A Case Study on Technical Efficiency and Price Distortions of Taiwan’s Intercity Bus Services

5.1 Introduction

In the preceding input-oriented and output-oriented models, discussed in Section 4.4, the input oriented measure of technical efficiency seeks to identify a scalar by which one can equiproportionately scale down (contract) the inputs with output levels held constant, while the output oriented measure of technical efficiency searches for a scalar by which one can scale up (expand) the outputs with input levels held fixed. In order to allow for simultaneous scaling of inputs and outputs, or desirable and undesirable outputs, Fare et al.

(1985, 1994) introduced the hyperbolic approach to efficiency measurement. This approach allows for a simultaneous and equiproportionate expansion of outputs and contraction of inputs (or undesirable outputs), and thus, performs simultaneously what the above input-oriented and output-oriented measures do.

However, as mentioned before, it appears that most of previous measurements in relation to performance focus on technical efficiency (TE), where either an input-oriented technical efficiency measure or output-oriented technical efficiency measure, or both were applied, while ignoring any measure of allocative efficiency (AE). Further, there have been relatively few attempts to apply the hyperbolic approach to efficiency measurement and to look further at allocative efficiency to measure price distortions in the bus transportation market.

Based on production frontier methodologies, the production efficiency of a firm is often measured by fitting an upper-envelope profit function or a lower-envelope cost function to a firm’s price and production data. The assumption of profit maximization implies that “best-practice” production plans are, in the ideal, technically efficient; that is to say, they are located on the boundary of the set of inputs required to produce any given set of outputs. In addition, profit maximization requires that “best-practice” plans be allocatively efficient, which is to say that out of all technically efficient plans, the allocatively efficient plans maximize profit at their given prices (Hughes, 1999). A variety of parametric and non-parametric techniques are available for computing the best practice frontier. Recall that Farrel (1957) proposes that the efficiency of a firm consists of two components: technical efficiency, which reflects the ability of a firm to obtain maximal output from a given set of inputs, and allocative efficiency, which reflects the ability of a firm to use the inputs in optimal proportions, given their respective prices and the production technology. These two measures are then combined to provide a measure of overall (total) economic efficiency.

In this framework for measuring efficiency, the role of input and output prices is to aggregate production plans into a money metric that permits their ranking by relative efficiency or, equivalently, by their respective distances from the best-practice frontier. On the other hand, when information on each input price and output price are not available, allocative efficiency cannot be estimated. This paper argues that these cases that lead to information on prices being unavailable pose a serious problem for the standard techniques of efficiency measurement, and their alternative pricing strategies influence a firm’s profit margin through their effect both on expected profits and on the discount rate applied to those profits’effects that are not taken into account by the standard techniques of efficiency measurement. To solve these two problems, this paper turns to an alternative technique of efficiency measurement which was proposed by Färe et al. (2002), based on a model of

production developed by Chambers et al. (1998). This alternative gauges efficiency relative to frontiers that are not conditioned on prices and hence account for the efficiency of different pricing strategies. These techniques are described in some detail to analyze how their measures of efficiency differ and how they are related to the profit margins of firms.

To illustrate the importance of accounting for price distortion in measuring efficiency, this alternative model is employed to study how differences in pricing strategies affect the profit margin of the firms before and after privatization.

Färe et al. (2002) establish the relations between a hyperbolic graph measure of technical efficiency and the radial measures of technical efficiency and show that the dual cost and revenue interpretation of the hyperbolic efficiency measure are related to Georgescu-Roegen’s (1951) notion of “Return to the dollar”. Once this relation is established, it leads to a derivation of an allocative efficiency index, which measures price distortions using data on observed costs and revenues without requiring explicit information on prices.

Using station-level data composed of 15 stations for the years 2000 and 2002, the goal of this study is to analyze the impact of the privatization on “return to the dollar” change by investigating both the technical efficiency and price distortion changes of the TMTC and KKTC operations.

The impact of privatization has resulted in an improved financial performance by KKTC. Prior to privatization, TMTC’s 15 subsidiaries (stations) had returned losses in aggregate for each year between 1996 and 2000. The 2000 accounts show a loss for TMTC of $5.5 million on a turnover of $90 million.

There is little useful data available from which one can infer the financial performance of KKTC’s transit activities. Its annual accounts of 2002 show a gross revenue of $81.7 million for the entire network, but give no details about patronage other than saying it continues to grow. On the other hand, KKTC created new labor terms and conditions and

then with the help of government bought out the old terms and conditions so as to create a cost structure which was capable of competing properly against the other low-cost independent operators in the transportation market. This resulted in a decline of real wage rates, up to 60% that of TMTC on average.

Prior to privatization there had been single, day return and period return fares with a 10% reduction for passengers. Discriminatory pricing by day was immediately established following privatization, in response to competition from other incumbent operators and the railway. This more heavily-discounted rate, set at around 70% of two single fares at the pre-privatization level, was only available for passengers making both legs of their journey on a Monday (after midday), Wednesday, Thursday, and Friday (before midday), i.e. the times of the greatest spare capacity. This change in price structure was based on the concept of elastic demand where fare reductions increase traffic sufficiently to increase revenue.

Aside from describing the operating changes of SOE and the POE response to privatization which ultimately resulted in a profit increase in the POE, this study seeks to identify:

1. whether or not technical efficiency improved following privatization; and 2. to what extent price distortions were created under each ownership type.

5.2 Model formulation

5.2.1 The hyperbolic graph measure

As indicated by Fielding (1987), cost effectiveness measures the relationship between input and consumed service such as passenger-kilometer or passenger trips. It is concerned with demand-side relationships. Assume that one is interested in cost effectiveness, this requires that one simultaneously adjusts input and output quantities, since one wishes to increase output quantities and decrease input quantities concurrently. A technology with a

hyperbolic graph efficiency approach which seeks the maximum simultaneous equiproportionate expansion for the output and contraction for the inputs is modeled here.

In contrast to radial contractions or expansions of observed data, the model introduced here is a hyperbolic path to the frontier of technology.

To measure technical efficiency, one can follow Fare et al’s (1985, 1994) hyperbolic Farrell measure. Let y∈R^M+ and x∈R^N+ denote respectively vectors of outputs produced and inputs employed by an individual station which represents a decision making unit (DMU) in this study. The graph reference set, T

( ) ( )

x,y =

{

x,y :x can producey

}

, satisfies constant returns to scale (CRS) and the strong disposability of inputs and outputs.

The hyperbolic graph measure of technical efficiency is defined as:

( )

x y

{ (

x y

)

T

}

F_g , =min λ: λ , λ ∈ . (5.1) The term graph is indicated by the subscript g . If F_g

( )

x,y =1, then the firm operates on the frontier of T ,

( )

x y , while F_g

( )

x,y <1 indicates that the firm operates inside

( )

x y

T , . Following Fare et al. (1985, 1994) the input-oriented Farrell measure is defined as

( )

x y

{ (

x y

)

T

}

F_i , =min λ: λ , ∈ , with the input measure F_i

( )

x,y equal to the square of the hyperbolic measure F_g

( )

x,y (see Fare et al. (2002) for more details in such a relationship).

The reciprocal of F_i

( )

x,y serves as the output-oriented Farrell measure F_o

( )

x,y if and only if technology exhibits CRS. Thus, CRS implies

(

^Fg

( )

^x,y

)

² = ^Fi

^{( )}

^{x,y ,} (5.2)

( ( ) ) _{( )}

y x y F

x F

o

g ,

, ² = 1 (5.3)

Those stations that are able to minimize the proportional or scaling factor λ, relative to other stations, are considered perfectly efficient and are thus found on the “best practice frontier” with a λ-value of “1”. Those firms which are less efficient are found at some distance from the frontier, with that distance being the basis for measuring their inefficiency;

the λ-value of these stations will be “less than 1”. Figure 5.1 illustrates the case with only one input and one output. Given observed

(

x ,j yj

)

, Fg

(

xj,yj

)

simultaneously expands

y and contracts j x at the same rate, following the hyperbolic path shown in the Figure _j

5.1. In contrast, the Fi

(

xj,yj

)

measure of input technical efficiency contracts x _j following the horizontal path to the graph. The Fo

(

xj,yj

)

measure of output technical

efficiency expands y to the graph, holding _j x fixed, i.e., following the vertical path to _j the graph.

Figure 5.1 Comparison of Hyperbolic, Input, and Output Measures of Technical Efficiency

5.2.2 “Return to the dollar” and the hyperbolic graph measure

If one knows the prices of the inputs w and the outputs _s p , then one can measure _s overall efficiency as follows:

(

x y w p

)

A

(

x y w p

) (

F x y w p

)

O_g , , , = _g , , , ⋅ _g , , ,

, (5.4) where A_g

( )

⋅ denotes the allocative efficiency. It is difficult to know all of the input and output prices of each station in detail, but it is easier to obtain the observed revenue and observed cost. Thus, the hyperbolic measure is related to “return to the dollar” which can be seen as the dual to the hyperbolic technical efficiency measure (Färe et al., 2002).

y x Fi(xj, j)⋅ j

)) , ( , ) , (

(Fg xj yj ⋅xj yj Fg xj y_j

y x y Fo( j, _j)⋅ _j

) , ( yx T

) , (xj yj

x y

Let w∈R^N++ represent the set of strictly positive input prices and p∈R^M++output prices. With this additional information, the maximum profit can be defined as follows:

(

p,w

)

=max

{

py−wx:

( )

x,y ∈T

}

π , (5.5) Thus, one can

(

p,w

)

≥ py−wx

π _{for all} (x,y)∈T , (5.6)

since

(

^xFg(^x,^y),^{y F}g(^x,^y)∈^T

)

, one has

(

p,w

)

≥ py F_g(x,y)−F_g(x,y)wx

π (5.7) However, the maximum feasible profit π^* is equal to zero.

Following Färe et al. (2002) the dual relationship between the hyperbolic graph measure and “return to the dollar” is defined as:

(

^F

( )

^{x, y}

)

²

wx py

≤ g (5.8) In order to derive a graph measure analog of the “return to the dollar”, one must introduce Georgeson-Roegen’s “return to the dollar” measure py wx , where py represents observed revenue and wx stands for observed cost. There is no need to know input or output prices in calculating the “return to the dollar”.

Following Farrell (1957) the allocative efficiency can be defined as a residual, i.e. the value of the allocative efficiency measure is

(

^F

( )

^x1,y

)

²

wx AE py

g

= (5.9)

thus

TE wx AE

py = ⋅ . (5.10)

The technical efficiency component TE equals

(

^Fg

( )

^{x, y}

)

², given an indication of how well resources are being managed, since it represents the gap between the DMU and the best

practice frontier. This takes values between zero and one. The allocative measure AE gives an indication of the appropriateness of the mix of inputs. On the other hand, AE can also be rearranged as

are technically efficient quantities of outputs and inputs, respectively. If prices pˆ and ^wˆ support yˆ and ^xˆ, then ^{AE= pˆyˆ wˆxˆ=1}, The term AE represents the short-run prices p deviating from their optimal long-run values pˆ with respect to the short-run prices w that deviate from their optimal long-run values wˆ. Since AE is computed in reference to the “return to the dollar” which may take a value bigger or smaller than one, AE may also take values smaller or bigger than one. If the value of AE is greater than one, then it implies the ability to distort output prices at higher rates than input prices (Fare et al. 2002).

Since this is an index based on discrete time, each station here will have an index for each year. This entails calculating the hyperbolic efficiency incorporating an environmental variable as well as using linear programming methods. In the interest of simplicity, however, neither the complete picture of the complexity inherent in the station efficiency problem being modeled and conveyed in Figure 5.1, nor the working of constraints expressing the existence of an environmental variable (non-discretionary input), are depicted in the graph.

Nonetheless, such constraints are used in this modeling effort in order to “control” for the service area population of the station effort faced by each station. Since contraction does not take place along these dimensions, comparisons of “like-to-like”, in the form of service area population, are facilitated by the model.

The hyperbolic measure of technical efficiency,F_g

( )

x,y , for each DMU is calculated by solving the following linear program:

k corresponding to the level of efficiency. One can assume that there are k =1 L, ,K stations with p=1 L, ,P environmental variables which use n=1 L, ,N inputs to produce m=1 L, ,M outputs. z is an intensity variable. _k

5.3 The data

Data on inputs and outputs were drawn from both TMTC’s and KKTC’s annual statistical reports and accounts and were supplemented by further data requested from both operators. Since both TMTC and KKTC were undoubtedly undergoing a degree of

“privatization turmoil,” characterized by a fundamental shake-up, business or working practices changing, and employees entering and leaving the firms, the data for the year of privatization (i.e., 2001) was excluded to avoid any possible bias. In addition, no significant reforms appear to have taken place after the year of structural change in the KKTC.

Therefore, the TMTC station-level data during the period of 2000 and the KKTC data for the period of 2002 can be used. Moreover, a desirable feature of the data is that except in a few cases, both public and private activities co-exist allowing for a comprehensive analysis of relative distortions created by each ownership type (Färe et al., 2002).

The wild variability in the use of inputs and outputs in transit technology specifications has been reviewed by De Borger et al. (2002). They indicate that this variability simply suggests that there is generally no accepted set of relevant variables in the bus industry. In this study, for each DMU (station) in the sample, therefore four traditional inputs for the assessment of efficiency can be used, which are measured in physical units: fleet size (x₁), which is taken to be the total number of vehicles operated at maximum service, number of employees (x₂), number of liters of fuel used (x ), and network length (₃ x₄). The quantity of passenger-kms ( y ) for the measurement of efficiency is taken as the single measure of output. A further series, differences in service area population (e) of each DMU, was added to these measures as an environmental (input) variable to reflect the differences in potential demand impacting on intercity service outputs, but outside of the control of the station management. The intention was to prevent DMUs in remote areas from being disadvantaged in an assessment of relative efficiency over time. All these input and output data constitute the terms x , _n y , and _m e of the previous section. _p

The whole sample therefore consists of the 15 stations (denoted by S1~S15) of both TMTC and KKTC, for which all the input and output data were available over the 2000-2002 period (excluding the data of 2001). All these related data are used to calculate the comparison of the before and after effects of privatization on efficiency. In the interest of analysis, however, these 15 stations can be divided into three groups based on the geographical characteristics of the area in which bus stations operate. Such information would probably help explain some of the differences found in the performance between stations of the different regions; that is, the northern (N) region including seven stations (S1~S7), the central (C) region including three stations (S8~S10), and the southern (S) region including five stations (S11~S15). Moreover, the measure of the profit rate is the ratio of operating revenues to the operating costs as measured by the total cost of all the

inputs including administrative, driver and mechanics wages, fuel expenses, and maintenance costs.

A preliminary examination of summary data before and after privatization reveals the operating changes that have been instituted at TMTC and KKTC, as well as the market response to their service offers (Table 5.1). In terms of resources, KKTC has cut the number of employees by 44%, the number of vehicles by 36%, the liters of fuel used by 24%, and the network length by 22% as compared to TMTC over the study period. On average regions had a population of 1,467,232 with a standard deviation of 1,232,266 in 2002.

Although the number of service area population has slightly increased by 1.1%, the amount of desired outputs of passenger-kilometers has decreased by 12%.

Table 5.1 Data Summary for TMTC and GGBC by Station Type

Station Employees Fleet Fuel Network length

Note: (1) The value in the parenthesis represents standard deviation.

(2) * With 2000 levels=100.

When these figures are viewed by station type, different patterns emerge. Employee reductions are deepest in the stations of the central (C) region (62%), with the stations of the southern (S) region sustaining about half the men, and followed by the stations of the northern (N) region with a 27% decrease following privatization. A similar pattern can be seen for fleet size and fuel use. Similarly, different station types experienced different market responses. The stations of the northern (N) region not only give the highest average passenger-kilometers, but also the only increase in passenger-kilometers over this time period (1.3%). This increase in service of the stations in the northern region, however, is marked by a substantial decrease in the amounts of the central (C) region (32%) and the southern (S) region (23%).

Given these changes in input resources and differential output production levels, the

Given these changes in input resources and differential output production levels, the

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