Productivity change in the water industry in England and Wales ...

© 2011 Operational Research Society Ltd. All rights reserved. 0160-5682/11

Journal of the Operational Research Society (2011) 62, 2173–2188

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Productivity change in the water industry in England and Wales: application of the meta-Malmquist index 1

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MCAS Portela , E Thanassoulis , A Horncastle and T Maugg 1

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Portuguese Catholic University, Porto, Portugal; Aston Business School, Aston University, UK; and Oxera, UK

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This paper uses a meta-Malmquist index for measuring productivity change of the water industry in England and Wales and compares this to the traditional Malmquist index. The meta-Malmquist index computes productivity change with reference to a meta-frontier, it is computationally simpler and it is circular. The analysis covers all 22 UK water companies in existence in 2007, using data over the period 1993–2007. We focus on operating expenditure in line with assessments in this field, which treat operating and capital expenditure as lacking substitutability. We find important improvements in productivity between 1993 and 2005, most of which were due to frontier shifts rather than catch up to the frontier by companies. After 2005, the productivity shows a declining trend. We further use the metaMalmquist index to compare the productivities of companies at the same and at different points in time. This shows some interesting results relating to the productivity of each company relative to that of other companies over time, and also how the performance of each company relative to itself over 1993–2007 has evolved. The paper is grounded in the broad theory of methods for measuring productivity change, and more specifically on the use of circular Malmquist indices for that purpose. In this context, the contribution of the paper is methodological and applied. From the methodology perspective, the paper demonstrates the use of circular meta-Malmquist indices in a comparative context not only across companies but also within company across time. This type of within-company assessment using Malmquist indices has not been applied extensively and to the authors’ knowledge not to the UK water industry. From the application perspective, the paper throws light on the performance of UK water companies and assesses the potential impact of regulation on their performance. In this context, it updates the relevant literature using more recent data. Journal of the Operational Research Society (2011) 62, 2173–2188. doi:10.1057/jors.2011.17 Published online 30 March 2011 Keywords: productivity; Malmquist index; DEA; water companies

1. Introduction The water industry in England and Wales was privatised in 1989. It consists of water and sewerage companies (WaSCs) and a number of water-only companies (WoCs). In 2007, there were 10 WaSCs. WoCs have over time reduced in number due to mergers and acquisitions. As of 2006 there were 12 WoCs, but in 2007 this number reduced to 11 due to the merger between South East Water and Mid Kent Water. The water sector is England and Wales is regulated by the Office of Water Services (OFWAT). The regulator conducts price reviews (PR) periodically based on a RPIX framework. (Strictly speaking, the revenues of the water industry are regulated by a price cap that actually

Correspondence: MCAS Portela, Universidade Cato´lica portuguesa, Rua Diogo Botelho, 1327, Porto 4169-005, Portugal. E-mail: [email protected]

takes the form RPI þ K, where RPI is the retail price index (reflecting inflation), K is composed of X (efficiency factor reflecting the scope of each company to reduce costs) and Q (reflecting the need for higher costs for meeting the quality standards of drinking water and river quality). However, RPI–X is the generic terminology used for this form of regulation.) The first PR after privatisation was in 1994 and there has been a PR every 5 years ever since (in 1999, 2004, and 2009). When establishing price limits the regulator assesses separately the efficiency of clean water and of sewerage services, and for each of these services operating costs and capital costs are analysed separately. Further, in the case of operating costs of clean water services OFWAT assesses efficiency separately in four distinct functions: resources and treatment, power, distribution, and business activities (see, eg, OFWAT, 2007). In contrast to OFWAT’s

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approach, most existing studies assess water and sewerage functions jointly (focusing on WaSCs), and include operating costs and capital costs in a single model of efficiency so that trade-offs between these costs are accounted for. Examples of such studies are Saal and Parker (2000, 2001), Saal et al (2007), and Erbetta and Cave (2006). In this paper, we focus on the operating cost efficiency and productivity change of the clean water service. However, unlike OFWAT, we do not assess operating costs of clean water services at function level, taking instead the operating cost for the entire clean water service. We assess changes in productivity over the period 1993–2007 from two perspectives. One is the traditional one of the change of the productivity of a company over time and thereby of the industry itself. The second is from the perspective of a company looking at its own performance over time relative to its self-best. For both perspectives, we use a meta-Malmquist index based on Pastor and Lovell (2005), and further extended in Portela and Thanassoulis (2008). The meta-Malmquist approach results in simpler models and circular indices, since the meta-Malmquist index is defined in relation to a unique meta-frontier—that envelops all observations over the meta-period, normally covering many time periods, in our case some 15 years. The meta-Malmquist index, thus calculated, reflects operating cost productivity change, which can be decomposed into efficiency change and boundary shift, in the same manner as the traditional Malmquist index. Further, the meta-Malmquist approach can also be used to compare company productivities at different points in time, which can also be decomposed into between-period and betweencompany components of productivity change, each of which further decomposes into other efficiency change and frontier shift components. The efficiency measures used for computing the meta-Malmquist index are estimated through data envelopment analysis (DEA). The contribution of the paper is to methodology and to application of circular Malmquist indices. At the methodology level, the paper demonstrates the use of the circular Malmquist index for productivity change in two settings. One concerns the traditional setting of looking at a company within a cross-section of companies analysed over a number of time periods. The second is looking at a given company over time, within its own manifestations over that time span. This permits the derivation of information about the variability of the company’s performance relative to its self-best. This second type of analysis has not to our knowledge been carried out extensively, and certainly not within the UK water sector. Finally, the paper discusses the potential impact of privatisation and regulation on the performance of UK water companies over time. In this context, the paper uses more recent data than previous studies in this area, and unlike most previous studies in this area, it considers both WoCs and WaSCs.

The paper unfolds as follows. In Section 2, we review some previous assessments of the productivity of English and Welsh water companies. In Section 3, the metaMalmquist index is presented in brief. In Section 4, the index is applied to the water service of English and Welsh companies and the results are compared with those from the traditional Malmquist index (Fa¨re et al, 1994). In Section 5, the use of the meta-Malmquist index is illustrated from the company perspective relative to its self-best performance. Section 6 concludes.

2. Previous studies applied to the English and Welsh water companies The studies that have assessed productivity change of the water companies in England and Wales, in general also analyse regulatory issues that cannot be divorced from a longitudinal analysis of efficiency, since it is expected that efficiency and productivity changes are directly or indirectly affected by regulatory interventions. In this paper, we also address regulatory issues but the main focus of the paper is to analyse the evolution of operating cost productivity gains in the English and Welsh water companies. There are two main regulatory issues that have been addressed in the literature. The first is the impact of privatisation in 1989 on the efficiency and productivity of UK water companies, and the second is the impact of different price caps in the PR of 1994 and 1999. The PR of 2004 has not yet been fully addressed in the literature at the time of writing, and this paper gives an indication as to its potential initial impact on water company productivity. After privatisation, the average K factor was þ 5% per annum (ie companies were permitted to raise prices by 5 percentage points above inflation), and was set to ensure the success of privatisation (Saal and Reid, 2004). In the PR of 1994, the K factor was substantially reduced to þ 1.4% for the 5-year-period, representing a considerable tightening of prices, which continued in the PR of 1999 with an average K factor of 2.1% per annum (see OFWAT, 1999). In the PR of 2004, the K factor increased again to an average of 4.2% per annum (see OFWAT, 2004) and in 2009 the mean K factor was 0.5. (See Table 5 of the Final Determinations (p 23): http://www.ofwat .gov.uk/pricereview/pr09phase3/det_pr09_finalfull.pdf.) Studies that have analysed the impact of privatisation on the productivity of water companies are those of Ashton (2000) and Saal and Parker (2000, 2001, 2004). These authors looked at the 10 WaSCs. In Saal and Parker (2000), a multiple output translog cost function was used to analyse the effects of privatisation on efficiency. This study led to the rejection of the hypothesis that privatisation led to increased efficiency, but the hypothesis that the regulation tightening of the price cap after the PR in

MCAS Portela et al—Productivity change in the water industry in England and Wales

1994 led to efficiency gains was accepted. This led to the general conclusion, that it is not privatisation but regulation that can lead to efficiency gains. Saal and Parker (2001) extended the 2000 study to measure total factor productivity (TFP) changes. In this study, the authors used a Tornqvist-based index to measure profitability change and decomposed it into TFP and total price performance (TPP) changes. Conclusions point again to the rejection of the hypothesis that privatisation led to significant increases in productivity, but in this study the authors conclude that ‘the productivity results are not consistent with the hypothesis that the regulatory system became more effective in generating efficiency gains after the price review’ in 1994 (p 88). Note that in this study the authors analysed separately labour productivity and TFP (where capital costs were also considered). Labour productivity showed a significant improvement in its growth rate after privatisation even though TFP did not increase significantly. This suggests that the exclusion of CAPEX (capital expenditure) from a productivity analysis may lead to overestimated productivity gains. In Saal and Parker (2004), the investigation of the effects of privatisation on the WaSCs in England and Wales was continued and results from the non-parametric analysis of TFP (discussed in Saal and Parker, 2001) and the parametric analysis of a cost function (discussed in Saal and Parker, 2000) are compared. The studies that analysed water companies after privatisation, and were mainly interested in measuring the impacts of regulation on productivity, are those of Saal and Reid (2004) and Erbetta and Cave (2006). Saal and Reid (2004) analysed OPEX productivity growth of WaSCs in England and Wales from 1993 to 2003 being concerned not only with assessing the efficacy of the OFWAT regulatory regime but also the impact of significant levels of investment to improve drinking water quality on OPEX productivity growth. Conclusions from this study, where a quasi-fixed capital translog model was used, point for a statistically significant improvement in average OPEX productivity growth after the regulatory tightening in the 1994 PR, but subsequent tightening in the 1999 PR did not result in further OPEX productivity gains. This finding is not confirmed in the study of Erbetta and Cave (2006), who concluded that there was a significant effect on efficiency of water and sewerage firms of the PR in 1999, whereas this effect was not observed in the PR in 1994. These authors also analysed the 10 WaSCs in England and Wales, but used a different methodology to that of Saal and Reid (2004). They used DEA to compute overall cost efficiency and to decompose it into allocative and technical efficiency. They also carried out a secondstage parametric analysis to investigate the drivers of efficiency. Productivity change over time was not computed through a Malmquit index framework as in our paper, but rather time was a variable in the second-stage stochastic frontier model to capture frontier shifts.

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More recently, Saal et al (2007) used parametric Malmquist indices to measure productivity change of WaSCs in England and Wales. They analysed TFP change from 1985 to 2000 and could analyse the impact of privatisation (in 1989) and regulation. Results suggest that the imposition of regulation in 1994 was not very successful in maintaining efficiency growth in the longer term. In addition, the authors conclude that there was an impact of privatisation and/or regulation on companies’ performance but this impact has been mainly felt in terms of technological improvement rather than efficiency improvements. There were, therefore, substantial differences between findings in this paper and in the previous study of Saal and Parker (2001), which are attributed by the authors to a greater sophistication of the methodology employed in Saal et al (2007). The above studies analysed the 10 WaSCs in England and Wales (Ashton, 2000; Saal and Parker, 2000, 2001, 2004; Saal and Reid, 2004; Erbetta and Cave, 2006; Saal et al, 2007). Very few studies include the WoCs in the analysis. The exceptions are Bottasso and Conti (2003) and Saal and Parker (2005) who have assessed the water supply service of both WoCs and WaSCs, and Bottasso and Conti (2009) who have assessed the WoCs from 1995 to 2005. Thus, this paper updates the related literature by considering a more extended time period covering more recent data, while at the same time also using all 22 WaSCs and WoCs providing clean water services in England and Wales. Note that the consideration of WoCs and WaSCs together is consistent with OFWAT’s modelling, where implicitly it is assumed that the water and sewerage operations of a WaSC are fully separable. Note, however, that Saal and Parker (2005) assessed the clean water functions of WoCs and WaSCs and concluded that it is inappropriate to consider that they share the same production function as the WaSCs enjoy economies of scope. Our study strengthens this conclusion, since significant differences in productivity were found between WoCs and WaSCs as will be seen later. Studies of regulation impacts in other countries also seem to support the view that regulation policies do make a difference. For example, Aubert and Reynaud (2005) analysed water companies in Wisconsin and concluded that the cost efficiency of water utilities can be explained by their regulatory framework (in this study the regulatory frameworks being analysed were price cap regime, rate of return regime or a mixture of both). In Renzetti and Dupont (2004), the UK, France, and the US experience on water utilities was analysed, with particular emphasis on the impact of ownership on performance. The authors reviewed the literature for these three countries concluding that there is no strong evidence for the superiority of private firms over public firms. Given this finding, the authors tried to identify other explanatory factors among which the regulatory environment. Conclusions point to

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a strong influence of the regulatory environment on firms’ performance.

In the traditional Malmquist index of Caves et al (1982) distance functions are used as a means to aggregate multiple inputs and outputs obviating the need to use, for example, factor prices to aggregate input and output quantities (see also Fa¨re et al, 1994). More specifically, the traditional Malmquist productivity index is the ratio between two efficiency measures, the inverse of distance functions as originally used by Fa¨re et al, 1994). The efficiencies are calculated for the same unit observed at two different points in time in relation to a given technological frontier. Thus, if ytjt is the efficiency measure of unit j observed at time t (subscript) relative to the technology boundary of time period t (superscript) then a Malmquist index of the change of its productivity between period t and t þ 1 is defined as: yjtt þ 1/yjtt, where the t frontier is here taken as the reference frontier. According to Fa¨re et al (1994) the choice of the reference frontier can be either that of time period t or of t þ 1. In view of this, the traditional Malmquist index is computed relative to the t and t þ 1 frontier in turn, and then the geometric mean of two resulting indices is taken as in (1): MIj ¼

yjttþ1 yjtt

yjtþ1 tþ1 yjtþ1 t

!1=2 ¼

t yjtþ1 tþ1 yj tþ1

yjtt

yjtþ1 tþ1

yjtt yjtþ1 t

!1=2 ð1Þ

This index can be decomposed into a technological 1 change or boundary shift component (yjtt þ 1/yjtt þ þ1 1 t yjtt/yjtt þ 1)1/2 and an efficiency change components yjtt þ þ 1/yjt.

3.1. A meta-Malmquist index to compute productivity change over time The use of meta-production functions (defined as the envelope of group-specific production functions) was introduced in 1969 with the work of Hayami (see Battese and Rao, 2002; O’Donnell et al, 2008) for the estimation of stochastic meta-frontiers, and used by Pastor and Lovell (2005) for computing a global Malmquist index. It should be noted that Tulkens and Vanden Eeckaut (1995) also proposed the notion of inter-temporal technology for time series which corresponds to what we call in this paper meta-technology. The meta-Malmquist index of Pastor and Lovell (2005) was further explored and extended in Portela and Thanassoulis (2008) to the case where not only period-specific frontiers were being compared, but also (production) unit-specific frontiers were compared. In this paper, we use the approach as extended in Portela and Thanassoulis (2008) and deployed in Portela and Thanassoulis (2010) to the particular case of assessing

7 Output2/ input

3. A circular Malmquist-type index

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year 3

year 2

year 1

A2

Y

W

6

A3

5

C' D1

4

B2

D3

A1 C2

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Z

C3

D2

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C1

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5 3 4 Output1/ input

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Figure 1 Illustration of the meta-frontier approach to measuring productivity change.

productivity change when some data are negative. To briefly summarise the meta-Malmquist index used in this paper, let us consider the simple case depicted in Figure 1, where we have four production units (A, B, C, and D) observed during three periods of time (1, 2, and 3) and producing two outputs using one input (from Portela and Thanassoulis, 2008). Unit C observed in year 1 (point C1) has an efficiency of OC1/OA1 when it is assessed in relation to the year 1 frontier, and unit C in year 2 (C2) has an efficiency of OC 2/OC 0 , when it is assessed in relation to the year 2 frontier. Since we can also compute the efficiency of C1 and C2 in relation to the convex meta-frontier (Y A2 D3 B3 X), then the meta-efficiency (efficiency relative to the meta-frontier) of C1 is OC1/OW and the metaefficiency of C2 is OC2/OZ. This meta-efficiency can be decomposed into two components: the within-period efficiency and a technological gap. For C1, for example, this decomposition means that OC1/OW ¼ OC1/OA1 OA1/OW, where the within-period efficiency (OC1/OA1) is the traditional DEA efficiency and it measures how distant C1 is from the frontier of period 1, and the technological gap (OA1/OW) measures the distance between the period 1 frontier and the meta-frontier, at the input/output mix of unit C1. For the general case, and letting ym jt be the metaefficiency of unit j as observed in period t, we have: yjtm ¼ yjtt TGjt

ð2Þ

where yjtt is the within-period t efficiency of unit j, while TGjt is the technological gap between the period t frontier and the meta-frontier at the input–output mix of unit j. This component can be retrieved residually as TGjt ¼ yjtm/yjtt. Under the meta-Malmquist approach, a Malmquist index of productivity change is defined simply as the ratio between two meta-efficiency scores: Productivity change of


unit j between period t and t þ 1, MMIjttþ1 ¼

m yjtþ1 yjtm

ð3Þ 2

For unit C in Figure 1, we would have: MMIC1 ¼ Note that when MMIjtt þ 1 is greater than 1, the productivity of unit j has increased from period t to t þ 1 (since its meta-efficiency in t þ 1 is higher than that in t). Productivity decline has occurred in the converse situation. Clearly, the use of the decomposition in (2) within expression (3) results in a decomposition of the meta-Malmquist index as in (4).

m m yC2 /yC1 ¼ OC 2/OZ/OC1/OW.

MMIjttþ1 ¼

m yjtþ1 ytþ1 TGjtþ1 jtþ1 ¼ t ym TGjt y jt jt

ð4Þ

1 t The term ¼ yjtt þ þ 1/yjt in (4) captures the efficiency change from year t to year t þ 1 as in the traditional Malmquist index of productivity change. The term TGjt þ 1/TGjt captures frontier shift between period t and t þ 1. Its numerator reflects the distance from the period t þ 1 frontier to the meta-frontier measured at the input/output mix of unit j observed in period t þ 1. Similarly the denominator captures the distance from the frontier t to the meta-frontier, measured at the input/output mix of unit j observed in period t. As the meta-frontier is stationary, this ratio of distances reflects the distance between the period t and t þ 1 frontiers, normally referred to as boundary shift. For details on the differences between this term and the traditional frontier shift term of the Fa¨re et al (1994), see Pastor and Lovell (2005). As noted in Portela and Thanassoulis (2008), the metaMalmquist index has several advantages: it is simpler to compute than existing alternatives, since it does not require geometric means and requires the solution of a reduced number of DEA models. It satisfies the circularity property, and it is the most appropriate option when one wishes to compute technological change for variable returns to scale frontiers following the Ray and Desli (1997) approach. Note, however, that the circularity of the index is obtained at the price of making the index dependent on the fixed technology used. This has been empirically noted, for example, by Berg et al (1992) who developed a base period index, which is in all respects similar to the meta-Malmquist index, except that the fixed technology in their case is a chosen period of analysis, whereas in the meta-Malmquist approach it is the metatechnology constructed from the full panel of data used. Note that for base (or referent) period independence (and in fact also for circularity) to occur it is necessary that technological change involves only shifts in the frontier ‘inwards or outwards, but not in curvature’ (see Althin, 2001). This is the same as saying that the technology be Hicks neutral (see also Pastor and Lovell, 2007; Førsund, 2002). In the current context, our preference for

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the meta-Malmquist index is due to its transitivity that allows easy computation of productivity change between any sub-set of periods within the panel and also due to the fact that meta-efficiencies are comparable across time. The latter allows one to readily gauge the movement of units and of period-specific boundaries relative to the fixed meta-frontier. It should be noted that though in principle the addition of a new period to the data panel could alter the metafrontier and hence the efficiencies and productivities previously computed, in practice adding a new period can only change substantially the results if the period added to the panel brings in observations substantially different in location (ie mix and/or levels of inputs relative to outputs) to those within the panel. This rarely happens in practice over the short term. Thus, in general the metafrontier evolves gradually in practice making metaMalmquist indices robust when the meta-period involves significantly more than two periods of time, and it relates to a relatively mature industry such as water industry in this case.

3.2. Meta-Malmquist indices for measuring productivity differences between units The idea underlying the meta-Malmquist index of productivity change over time can be extended to an analysis of productivity differences between units rather than productivity change between time periods. The computation of productivity differences between companies observed at the same or at different time periods may help to understand if besides time effects (reflected in the existence of technological progress or regress) there are also company effects that are due to intrinsic heterogeneity between companies. This computation can be achieved by means of the meta-Malmquist index where, in addition to the meta-frontier, and to the period-specific frontiers, unit-specific frontiers (enveloping all the instances of a production unit within the meta-period) are also drawn. The resulting company-specific boundary and its position relative to the meta-frontier offer additional information on the performance of that company in relation to other companies. To illustrate the information that can be gleaned by company-specific boundaries consider the four companies depicted in Figure 2. The meta-period covers 3 years. The company-specific boundaries can be seen on the graph. Following Portela and Thanassoulis (2008), we can compute two efficiency scores for each company jt (ie company j as observed in year t). One efficiency will be relative to the meta-frontier as before (for unit C1, in Figure 2, it is OC1/OW) and denoted as yjtm, while the second will be relative to the company-specific boundary as defined above (for unit C1, in Figure 2, it is OC1/OV ) U and denoted as yjt j , where the index Uj relates to the

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8 7 Output2/ input

Unit A

A2

6

Unit B

Unit C

Unit D

A3 W

B2

5 D1

4

D3

A1 V C2

3 2

C3

D2

B3

C1 B1

1 0 O 0

1

2

4 5 3 Output1/ input

6

7

8

Figure 2 Illustration of meta-frontier and company-specific boundaries.

company-specific boundary of unit j. Then, we have U

yjtm ¼ yjt j UGjt

ð5Þ

where UGjt is retrieved residually and it measures the distance from the company-specific frontier to the metafrontier (for unit C1, in Figure 2, it is OV/OW). UGjt is referred as the Unit-Frontier Gap for company j, measured at the company’s input–output mix in time period t. U The within-unit efficiency, yjt j , reflects how far was the performance of company j in year t from its self-best performance over the meta-period. Its average value at the company level yields information regarding the stability of efficiency of the company over time. The meta-efficiencies of two companies at the same period in time can be used to reflect their relative productivities. For companies j and k at their instances in period t, a measure of their relative productivities is given m . by the ratio of their meta-efficiencies, MMIkjt ¼ yjtm/ykt Using the expression in (5), Portela and Thanassoulis (2008) decompose the index of comparative company productivities MMIkit of companies j and k, as observed in period t as follows: U

MMIkjt ¼ where

U

yjt j

.

k yU kt

yjtm yjt j UGjt ¼ k ; yktm yU UG kt kt

ð6Þ

is referred to as efficiency difference

between companies and it captures the component of the relative productivities MMItkj of companies j and k accounted for by the distance of company j in period t from its unit-specific boundary (Uj) compared to the corresponding distance of company k in period t from its own company-specific boundary (Uk). The term UGjt/UGkt, is referred as frontier shift between companies and it captures the component of the relative productivities MMItkj of companies j and k accounted for by the distance of the company-specific boundary for company j from the meta-frontier, taken at the input–output mix of company j at time t, compared to the corresponding distance of the

company-specific boundary of company k taken at its input–output mix in period t. That is the term UGjt/UGkt corresponds to the frontier shift component in (4) but the shift is not between periods but between companies. Generalizing the above concept for comparing two companies at two different points in time Portela and Thanassoulis (2008) propose the index in (7) to measure the relative productivity of units j and k observed in t and s, respectively. MMIkjts ¼

yjsm yktm

ð7Þ

If MMIkjts exceeds 1, the productivity of company j in period s is higher than that of company k in period t. Clearly, the converse is the case if MMIkjtso1. For details on the interpretation of the above index, including all its possible decompositions see Portela and Thanassoulis (2008). We present here in (8) the decomposition we shall use later in the empirical part of the paper. We have MMIkjts ¼

yjsm yjsm yjtm ¼ yktm yjtm yktm

ð8Þ

The decomposition in (8) shows that MMIkjts decomposes into two indexes: productivity change between periods (the first term that compares the same unit ( j ) at two different periods, t and s) and productivity difference between units (the second term that compares two different units ( j and k) at the same point in time t).

4. Assessing productivity of water companies in England and Wales using the meta-Malmquist index 4.1. Inputs and outputs used We have used data for the water services of the full population of water companies in England and Wales from 1993 to 2007. Since there were a number of mergers during this period, we used an unbalanced panel of companies. The DEA model used to assess operating cost productivity change of water companies considers one input and five outputs as specified in Table 1. Our model specification has a single input, operating expenditure (OPEX) measured in thousands of pounds at constant prices, that includes, power costs, distribution costs incurred in conveying water from treatment to clients, resources and treatment costs incurred in extracting and treating as necessary the water, and business activities costs relating to headquarter activities. In all cases labour costs are included in the OPEX figure. A single deflation index based on the RPI is used across aggregate OPEX to adjust for inflation. This could bias to an extent our productivity change results, if the deflation index in fact is not equally reflective of the actual inflation over time of each OPEX component (For example, electricity prices in certain years rose much faster than


Table 1 Inputs and outputs Inputs (£000’s)

Outputs

OPEX (opex)

Number of billed properties (btotal) (000’s) Adjusted distribution input surface water (adDIS) (Joules/day-scaled) Adjusted distribution input non-surface water (adDINS) (Joules/day-scaled) Number of sources (sources) Number of billed properties adjusted (adbtotal)

These variables are scaled measures of the energy needed to lift the volumes of water concerned over the height represented by the pumping head.

other components within OPEX. Thus, productivity change relative to electricity expenditure would tend to be underestimated by the model as opposed to the relative units of electricity used.) Bad debts and environmental charges were also excluded from the modelled OPEX. (The environmental charges relate to water abstraction licenses and they, along with bad debt, are deemed by OFWAT uncontrollable by companies.) The input–output set was created drawing on the models OFWAT uses for assessing by function the operating cost efficiencies of companies in relation to clean water services. However, we have avoided using ratios that OFWAT uses in some cases in combination with scale variables. The mixing of these two types of variable is not compatible with constant returns to scale in the DEA framework and may distort the DEA results (see, eg, Dyson et al, 2001). (Note that productivity change models as used here are based on constant returns to scale DEA models to capture productivity changes due to scale changes.) Five outputs were considered in the assessment to reflect the main activities of water companies and also to control for contextual factors that may impact the operating costs of water companies. The first output variable, billed properties (including household and non-household properties), was chosen to account for the number of clients each water company serves. In some models, OFWAT has used winter population as a scale variable. In our model, winter population is reflected by raw billed properties as the two are highly correlated. The water distributed (distribution input) reflects the quantity of water treated and put into the distribution network. This water is divided within our model into the water sourced from surface resources and that sourced from non-surface resources (boreholes). This distinction is intended to reflect the fact that the source of water is a driver of costs with surface water being in general cheaper to extract but more expensive to treat, whereas water from boreholes is cheaper to treat but more expensive to extract. Since the distribution costs are also driven by the average pumping head, the distribution input was adjusted by multiplying average pumping head by distribution input from surface and non-surface sources. The pumping head

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reflects the terrain over which the water is conveyed, as it reflects the average height over which water needs to be pumped. The number of sources was also included to account for the fact that more sources generally imply larger costs. This is because the more the sources for a given volume of water distributed the smaller scale of operations per source and therefore they may imply more costs through higher set up costs. Finally, we wanted to reflect in the analysis connection density (a proxy for urbanization), since OFWAT has established that water distribution expenditure per connected property is lower the lower the connection density. (See the model for water distribution page 19 in http://www.ofwat.gov.uk/publications/pricereviewletters/ ltr_pr0939_appendix2.pdf.) Thus, an output measure we could consider in line with OFWAT’s finding in this respect would be the number of connected properties per km of main. However, this is a ratio variable, and therefore ideally should not be used together with volume measures in our DEA assessment. Therefore, we ran a regression of billed properties on the length of main. The deviation from the regression line for each company provides an estimate of how much above or below the expected level of billed properties the company is, given its length of main (note that the R2 for this regression line is about 90% meaning that the length of main in fact explains most of the variation found in the number of billed properties). Therefore, a company with a positive residual has more billed properties than expected for its length of main and therefore this company is likely to have higher water distribution costs (ceteris paribus) than a company with a lower or even negative residual. Following this reasoning the residuals were used to adjust billed properties as follows: adjusted billed properties ¼ billed properties ðstandardized regressionresidual þ constantÞ: The standardized regression residual is the raw residual divided by the estimated standard error of the regression. (In most cases it varies from 2 to þ 2.) The addition of a positive constant in the above adjustment is required so that all companies have a positive adjustment factor. CRS models are not translation invariant, and therefore the results are likely to change for different constants added. The positive constant used should ideally be as close to the absolute value of the minimum standardized residual as possible to minimize the impact of the arbitrary constant used on the adjusted billed properties relative to impact of the standardized regression residual that we wish to capture. The effect of this variable on the efficiencies (when computed with and without the variable adbtotal in relation to the meta-frontier) is in the event negligible for all except one highly urbanized company. Its efficiency

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score rises by an average of 19 percentage points over its 15 instances over time. For the rest of the companies, the average efficiency change is about 1 percentage point between using and not using this output variable. Finally, it should be noted that we have imposed the weight restriction that the weight on water from surface sources should be higher than the weight on water from nonsurface sources because surface water is more costly than non-surface water to treat and distribute. (See OFWAT’s model for water resources and treatment page 19 in http://www.ofwat.gov.uk/publications/pricereviewletters/ltr_ pr0939_appendix2.pdf.) Note that since our model uses a cost measure on the input side rather than a quantity measure, the efficiency measures thus obtained are related to cost efficiency measures. Therefore, the productivity change values we obtain from the solution of DEA models using the inputs and outputs in Table 1 are cost productivity measures. As noted earlier, to the extent that price changes over time can vary for different components of OPEX (eg labour versus electricity), our findings on productivity change are likely to differ from those that would be derived on the basis of physical measures of inputs. Descriptive statistics of our data are shown in Table 2, where we also show the number of companies that were assessed in each year. OPEX data is deflated to 2007 prices. The descriptive statistics show large standard deviations. For most variables the standard deviation is higher than the mean, reflecting the fact that water companies differ much in scale size, especially so between those companies offering only clean water and those offering in addition sewerage services.

4.2. Comparison of the meta-Malmquist and traditional Malmquist index results Results on cost productivity change and its components were produced using both the meta-Malmquist approach detailed in Section 3 and the traditional Malmquist of Fa¨re et al (1994). As noted earlier, we have used an unbalanced panel of companies as some companies were merged with, or acquired by, other companies during the time period covered by our study. Therefore, Malmquist indices have only been computed for those companies and time periods t and t þ 1 where the company existed in an unmerged or pre-acquisition form in both periods. That said, all companies in existence in a given year t were used to establish the industry boundary in that year, even if some of the companies may then have disappeared in year t þ 1, making it impossible to compute a change of productivity specifically for them between years t and t þ 1. This approach ensured that no observed input–output correspondence was discarded in arriving at the efficient

boundary for each time period, even if some of the observations were later subsumed within others. Detailed results are shown in Table 3 (where the indexes were aggregated for each period using the geometric average). The results from both approaches are remarkably similar in this application. The correlation coefficient between the values (per company) of the two indexes of productivity change is 0.987, and that between the two measures of boundary shift is 0.983. The similarity between the results can be better seen in Figures 3 and 4, where we plot the average Malmquist index and its frontier shift (or technological change) component (since efficiency change is the same for both). Note that we used chain indices rather than a base period index given the fact that companies are changing throughout the period and the use of a base period index would imply the loss of information regarding the assessment of some companies (for those that were created after 1993—if the base period was this year—we would not be able to compute a base Malmquist index). Therefore, in this particular case, one reaches virtually the same conclusions on average cost productivity change and average frontier shift irrespective of the approach used. Note that agreement on results at individual unit level was also high between the two approaches. We computed the differences between the productivity change indices yielded by the two approaches at company level. The resulting differences between the traditional Malmquist and the circular meta-Malmquist values ranged from 0.068 to 0.064 (the average absolute difference was 0.008). Similarly, the differences in boundary shift values yielded by the two approaches ranged from 0.065 to 0.059 (with an average absolute difference of 0.008). Therefore, for individual units there was little difference between the circular and the traditional Malmquist index. This cannot, of course, be generalized to other data sets. As noted in Pastor and Lovell (2005, 2007), the necessary condition for the global Malmquist index (here called meta-Malmquist index) to be equal to the traditional Malmquist index is Hicks neutrality of technological change (or technologies being homothetic). Hence, our conclusion regarding this particular data set is that technological change is approximately Hicks neutral, meaning that the shape of the frontier is approximately the same over time (see Chambers and Fa¨re, 1994). The meta-Malmquist index suggests that operational cost productivity change has been showing an erratic behaviour from 1993 to 2007, with 2001 being the year where there was the biggest improvement in cost productivity in relation to the previous year, and 2006 as the year where there was the biggest decline in cost productivity in relation to the previous year. The main factor driving productivity change in the English and Welsh Water industry appears to be the component of frontier shift or technological change. Efficiency change or catch-up seems


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Table 2 Descriptive statistics of the data Opextot (£000’s)

Btotal (000’s)

adDIS

adDINS

sources

adbtotal

N

1993 Average SD

52.30 61.66

707.79 896.58

38 191.62 56 418.79

20 029.30 24 899.55

76.03 91.07

2 046.32 3 966.85

30

1994 Average SD

52.99 62.14

712.44 901.55

39 401.65 55 806.66

21 212.10 26 104.55

71.80 77.10

2 026.45 3 907.08

30

1995 Average Sdev

52.26 61.26

714.30 899.78

41 743.97 63 763.75

22 503.68 28 625.80

71.43 76.06

2 005.98 3 748.70

30

1996 Average SD

51.90 61.27

720.14 908.14

44 917.84 66 233.73

23 169.18 28 861.53

71.07 75.41

2 033.31 3 839.71

30

1997 Average SD

53.74 61.61

777.48 937.45

49 187.34 69 282.90

24 807.82 29 180.34

74.07 75.46

2 208.05 4 020.95

28

1998 Average Sdev

55.97 60.83

842.97 954.42

53 693.19 71 205.87

25 067.62 28 084.09

79.96 75.71

2 387.68 4 136.66

26

1999 Average SD

53.57 57.80

848.93 960.13

47 566.37 59 444.39

23 919.57 27 808.16

79.88 80.91

2 382.20 4 181.14

26

2000 Average SD

52.07 56.49

856.87 971.25

48 220.11 59 930.41

24 298.46 28 880.93

79.81 80.71

2 435.51 4 339.26

26

2001 Average SD

56.72 56.53

1 017.48 1 035.12

57 706.50 66 932.76

28 140.82 29 054.76

94.45 83.22

2 873.95 4 614.39

22

2002 Average SD

55.75 55.81

1 026.24 1 043.99

60 657.94 70 522.38

29 034.67 29 875.19

101.73 91.75

2 932.17 4 760.68

22

2003 Average SD

55.77 56.25

1 035.89 1 054.18

61 537.96 73 349.83

29 068.81 29 812.33

89.73 77.48

2 935.44 4 819.12

22

2004 Average SD

57.45 58.19

1 041.43 1 060.62

63 007.91 72 784.97

30 330.96 30 395.83

93.18 81.96

2 985.21 4 910.71

22

2005 Average SD

55.93 56.21

1 049.04 1 065.74

60 782.69 70 443.93

28 771.11 29 550.89

90.18 78.55

3 025.30 4 955.79

22

2006 Average SD

60.71 67.85

1 054.96 1 068.87

61 135.15 72 004.90

29 185.56 31 534.98

86.73 73.50

3 049.14 4 982.31

22

2007 Average SD

62.66 71.60

1 057.75 1 068.64

59 903.26 68 963.22

28 179.86 31 092.36

84.55 68.44

3 028.41 4 988.78

22

however important for productivity change in three periods: from 1993 to 1994 and from 1998 to 1999, contributing positively to an improvement in productivity change (given that technological change was ‘negative’), and from 2005 to 2006 where the high growth in efficiency

change (6.8%) reduced the impact of the highly negative technological change (12.2%) on productivity change. In order to better understand the drivers of productivity change we plot both the within-period efficiencies and the meta-efficiencies of water companies over time in Figure 5.

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Table 3 Results from two approaches Traditional approach

Year

1993/1994 1994/1995 1995/1996 1996/1997 1997/1998 1998/1999 1999/2000 2000/2001 2001/2002 2002/2003 2003/2004 2004/2005 2005/2006 2006/2007

Meta-Malmquist approach

Malmquist index

Efficiency change

Technological change

Malmquist index

Efficiency change

Technological change

0.997 1.042 1.041 1.037 1.056 1.018 1.043 1.082 1.028 0.990 0.992 1.021 0.941 0.979

1.045 1.015 1.026 0.971 0.997 1.046 0.979 1.003 0.994 0.975 0.986 1.002 1.068 0.996

0.954 1.026 1.014 1.068 1.060 0.973 1.065 1.078 1.034 1.015 1.007 1.019 0.882 0.983

1.002 1.041 1.033 1.036 1.056 1.010 1.042 1.084 1.025 0.991 0.988 1.019 0.949 0.982

1.045 1.015 1.026 0.971 0.997 1.046 0.979 1.003 0.994 0.975 0.986 1.002 1.068 0.996

0.958 1.025 1.006 1.067 1.059 0.966 1.065 1.080 1.031 1.016 1.002 1.017 0.888 0.986

Source: Fa¨re et al (1994).

1.100

100.00% 90.00%

1.050

80.00% 1.000

70.00% 60.00%

0.950

within period efficiency Meta-efficiency

50.00% 0.900 Traditional Malmquist

Meta-Malmquist

40.00% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

0.850 0.800

Figure 5 Evolution of average within period and metaefficiencies. 93/94 94/95 95/96 96/97 97/98 98/99 99/00 00/01 01/02 02/03 03/04 04/05 05/06 06/07

Figure 3 Productivity change.

1.100 1.050 1.000 0.950 0.900 0.850 0.800

Traditional frontier shift

Meta-frontier shift

0.750 0.700 93/94 94/95 95/96 96/97 97/98 98/99 99/00 00/01 01/02 02/03 03/04 04/05 05/06 06/07

Figure 4 Boundary shift.

In Figure 5, we observe no specific trend in the withinperiod efficiencies because each year’s frontier is generally different and, in fact, within-period efficiencies are not

comparable across years. In contrast, we observe a clear trend in the average meta-efficiencies computed against the stationary meta-frontier, showing that over time companies are moving closer to the meta-frontier, especially until 2002. After 2002, there was some stability on the metaefficiencies that remained almost stable between 2002 and 2005, to start decreasing in 2006 and 2007 (this is consistent with the productivity decline in the years 2005/2006 and 2006/2007 observed in Table 3). This improvement corroborates OFWAT’s statement in 2004 that ‘The improvement in relative efficiency since 1999 is striking. We now see companies clustering around the industry frontier for operating costs and capital expenditure, with several companies showing at or near best in class performance in both operating and capital maintenance efficiencies’ (OFWAT, 2004, p 152). This movement of water companies towards the frontier up to 2005 is indeed evident in Figure 5, since we see the gap between the meta-efficiencies and within-period efficiencies closing up to this year, meaning that the year-specific frontiers are moving closer to the meta-frontier. This speaks to the fact that the main driver of productivity change is indeed technological change. Indeed, the period between 2002 and


2005 is the period where the within-period frontiers are closer to the meta-frontier—meaning that most of the instances of companies defining the meta-frontier are instances observed in those years. These are, therefore, the years of highest accumulated productivity change and technological progress. Note that using the traditional Malmquist index approach would lead us to basically the same conclusions as those drawn from Figures 3 and 4, but those drawn from Figure 5 are only possible when meta-efficiencies are computed as in the approach presented in this paper. More generally for non-homothetic technologies the traditional and meta-Malmquist index would be expected to lead to results differing more than has been the case in this application. In choosing between the results from the two indices, where they differ, one may need to resort to a comparison of the raw input–output data of the unit concerned, for example, by using a ratio of the geometric means of output to input ratios as detailed in Portela and Thanassoulis (2006). More generally in choosing between the two indices it should be noted that each index has its advantages and disadvantages. The meta-Malmquist approach computes efficiencies in relation to a stationary frontier and therefore can provide a clear picture of how efficiencies are evolving over time. In addition, the metaMalmquist index is circular. The traditional Malmquist index on the other hand has the advantage that its results need not change with the introduction of new periods into the meta-period, something that can happen with the meta-Malmquist index. It is interesting to relate observed productivity changes with the regulatory cycle. It is clear from Figure 5 that the introduction of new price limits in 1995 (after PR94) and in 2000 (after PR99) appeared to spur the improvements of operating cost efficiency of water companies. In contrast, the introduction of new price limits in 2005 (after PR04) could partially be responsible for the reversal in the increasing trend in meta-efficiencies. To see this more clearly, we have sub-divided the entire time span covered by our data into four periods, in line with the periodic PR that have occurred within that time span. Thus, the periods we have created are: K K K K

Period Period Period Period

1: 2: 3: 4:

1993–1994; 1995–1999, 2000–2004, and 2005–2007.

Each period above commences in the year after a PR. For example, Period 2 reflects the price regime established as a result of PR94 and so on. Figure 6 shows the average meta-efficiencies, and Figure 7 shows the average technological gaps in the four periods created above. The results are shown separately for WoCs and WaSCs.

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Figure 6 Distribution of meta-efficiencies over the four periods.

Figure 7 Distribution of technological gaps over the four periods.

Looking at Figure 6 it is clear that meta-efficiencies are increasing from one regulatory period to the next, except for the very last, fourth period. The rise in meta-efficiencies reflects rising productivity for the average firm and this is true of both WaSCs and WoCs, the former generally having higher productivity than the WoCs. The metaefficiencies for WoCs and WaSCs are statistically significantly different (Mann–Whitney test). Figure 7 shows that the technology gap too is rising from one regulatory period to the next, except for the very last period, PR04. It is re-called that the higher the technology gap the closer are the within period and the meta-frontier. Thus, the rising technology gap over successive regulatory periods suggests the frontier companies of each regulatory cycle are improving in productivity just like the average

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company noted above. In fact, Figures 6 and 7 are very similar suggesting that there is improvement in productivity over successive periods for frontier and other firms, the exception being the very last period, PR04. Note that in terms of technological gap we cannot observe as big differences between the WoCs and the WaSCs as in the meta-efficiencies. That is, the best firms within the WoCs match better the best WaSCs in terms of productivity than is the case across the full population of WoCs and WaSCs. We conclude this discussion of the way productivity of water companies appears to have responded to the regulator’s price determinations with two caveats. First, there are factors beyond regulation, which could have impacted the productivity changes we have observed and so the productivity gains cannot necessarily be attributed solely to regulation. For example, clean water directives and spill over technological improvements in the broader economy have undoubtedly contributed to changes in productivity of English and Welsh water companies over our study horizon. Second, our approach may to an extent be underestimating productivity gains in the later years of that horizon, post-2004 for two reasons. One is the electricity prices had risen by 2005/2006 by more than the single deflation index used to deflate OPEX. Water companies consume substantial amounts of electricity for water treatment. The second reason is that companies implementing leakage control may in some cases have classified at least part of the related expenditure as OPEX rather than CAPEX. This would tend over time to increase OPEX while at the same time decreasing distribution input featuring as an output, leading to apparent loss of cost productivity as measured in our model.

5. Comparing company productivities In order to compare companies on productivity over time both within themselves over time and in relation to each other over time, we have used the decomposition in (5). Table 4 shows the mean meta-efficiencies and its components for each company, where companies are ordered according to the mean company frontier gap. Note that the larger the value of the company frontier gap, the closer is the company-specific frontier to the meta-frontier, and therefore the more productive the company is in relation to the others. The companies that no longer exist in 2007 have an asterisk next to their label in Table 4. We would expect these companies to cluster on the lower values of company frontier gap given that their performances have been observed only in the early years of the meta-period. Therefore, we would expect that their company-specific frontiers are likely to be further from the meta-frontier compared to those of companies still in existence in later years of the meta-period. This indeed happens by and large. The mean meta-efficiency of all companies including

those no longer in existence in 2007 is 72.8% and it is considerably lower than the mean within-company efficiency which is 92.63% and the mean company frontier gap which is 78.81%. This is interesting, suggesting that on average over the meta-period, efficiency was about 73% of what could have been attained using the technology revealed in the course of the meta-period. This gap is accounted for more by each company being short of the industry best (revealed by the company frontier gap) than by each company being short of its own best attained productivity over time during the meta-period (revealed by the within-company efficiency). The last column to the right in Table 4 identifies the company type. The mean meta-efficiency for WoCs is 71.08% and for WaSCs 79.46% (the mean company gaps are 77.26% and 87.30%, respectively). From Table 4, it is also apparent that some clustering of WoCs in the lowest average values of company frontier gaps and of WaSCs in the highest average values of this gap. Performing non-parametric tests (Mann–Whitney and Kolmogorov– Smirnov) on the distribution of the meta-efficiencies and company frontier gaps for these two types of companies shows that the two distributions are statistically significantly different. This means that WaSCs seem to outperform WoCs in their meta-efficiency performance, that is on average WaSCs are closer to the meta-frontier than WoCs. In Figures 8 and 9, we plot the distribution of metaefficiencies and company frontier gaps for these two groups of companies, where only existing companies in 2007 were taken into account. Note that when only existing companies are considered the differences between average meta-efficiency and company-frontier gaps are higher (WoC companies have an average meta-efficiency of 73.63% in relation to 83.72% for WaSC, and the average company frontier gap is 80.6% for WoC companies and 92.19% for WaSC). These findings further attest to the superior performance in general of water and sewerage compared to WoCs. (Note that similar findings are reported in Bottasso and Conti (2003) and Saal and Parker (2005)). It is, however, possible that WaSCs may classify some water-related expenses as sewerage expenses, thus appearing apparently more cost efficient than WoCs. The within-company efficiency score should be of special interest internally to management. It is a measure of how the water company in a specific year compares with itself in other years. Interestingly, most water companies show an increasing trend of within-company efficiencies over the meta-period suggesting that their efficiency has in fact been improving. Since the company is being compared with itself, we expect high average within-company efficiencies if its performance has been consistent over time. In contrast, low within-company efficiencies show variable performance over time. To see this consider the profile of two companies (C38 and C17) plotted in Figure 10.


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Table 4 Mean values of within-company efficiency and company frontier gaps Company C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36 C37 C38

Average metaefficiency (%)

Average withincompany efficiency (%)

Average companyfrontier gap (%)

N

Type

49.25 51.79 53.97 55.96 59.13 59.25 61.65 67.69 65.56 67.59 69.81 63.61 69.52 73.25 72.28 72.75 73.12 72.08 72.99 73.79 68.42 78.33 70.66 71.75 75.71 79.71 72.84 82.03 87.27 86.35 82.80 86.07 93.31 76.85 81.84 85.50 94.58 86.93

98.67 92.96 94.83 94.10 93.12 92.90 96.34 99.31 95.91 96.95 96.97 87.72 93.61 97.81 96.44 95.91 94.99 92.96 90.97 91.93 84.60 95.99 85.61 86.54 91.55 95.58 85.98 93.75 97.76 94.17 88.02 91.22 98.25 80.71 84.59 87.85 95.96 87.38

49.92 55.61 56.92 59.27 63.68 63.72 63.98 68.15 68.38 69.69 71.96 72.88 74.29 74.90 74.91 75.86 77.07 77.50 80.18 80.34 80.69 81.58 82.16 82.29 82.47 83.06 84.57 87.45 89.28 91.74 94.18 94.24 94.95 94.96 96.54 97.29 98.53 99.49

4 5 5 4 15 4 4 8 5 8 8 8 11 15 15 7 15 8 10 15 8 10 5 15 8 4 15 15 7 15 15 15 7 15 15 15 7 15

WoC WoC WoC WaSC WoC WoC WaSC WoC WoC WoC WaSC WaSC WoC WoC WoC WoC WoC WaSC WoC WaSC WaSC WoC WoC WoC WaSC WaSC WoC WaSC WaSC WaSC WaSC WaSC WaSC WaSC WoC WoC WaSC WaSC

Companies no longer in existence in 2007.

Figure 10 shows the meta-efficiencies and withincompany efficiencies for companies C38 and C17. Company C38 has virtually identical within-company and meta-efficiency values. This suggests C38’s self-best performance matches the best in the industry over the meta-period. In contrast, C17 has high within-company efficiencies of about 100% suggesting its performance has varied little over the meta-period after 1995. However, its meta-efficiency is low and declining sharply after 2002 suggesting its self-best is far from the industry best performance and indeed getting worse after 2002. This type of information is valuable to both the regulator for comparing companies over time, but also to management at company level who may, for example, wish to identify factors that cause variations in performance over time both relative to industry and relative to the company itself.

We can glean additional information of the comparative performance of two companies using the decompositions in (6) and (8). We illustrate this with reference to companies C38 and C17. C38 is a good performer and therefore we use it as reference for analysing the evolution of the productivity of C17 in relation to this ‘benchmark’ company. m m c17 c38 Computing for each year t: yc17t /yc38t ¼ yc17t /yc38t UGc17t/UGc38t, we find that on average the productivity of C17 is 0.854 lower than the productivity of C38 (measured by the distance of each unit from the metafrontier), and this value is mostly explained by the fact that the C17 company-specific frontier is well below the C38 company-specific frontier (frontier shift between companies is 0.774). The average within-company efficiency of C17 is higher than the average within-company efficiency of C38 (the ratio between the two, that is the company efficiency change, is 1.101).

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100.00% 95.00% 90.00% 85.00% 80.00% 75.00% 70.00% 65.00%

Meta-efficiency C38 Within-company efficiency C38 Meta-efficiency C17 Within-company efficiency C17

60.00% 55.00%

19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07

50.00%

Figure 10 Meta-efficiency and within-company efficiency scores for two companies.

Figure 8 Differences in meta-efficiency distributions.

Productivity change of C17 observed in 07 in relation to unit C38 observed in 01 0.614

Productivity change between periods (unit C17 from 01 to 07) 0.669

Efficiency change between periods (unit C17 from 01 to 07) 0.769

Frontier shift between periods (from 01 to 07) 0.870

Productivity difference between companies (for 2001, unit C17 to C38) 0.918

Efficiency difference between companies (unit C17 to C38 in 2001) 1.039

Frontier shift between companies (unit C17 to C38) 0.833

Figure 11 Decomposition of productivity change between C17 and C38.

Figure 9 Differences in company frontier gaps distributions.

Comparing further C17 as of 2007 and C38 as of 2001 using the decomposition in (8) we have: 0107 MIC38C17 ¼

¼

m yC1707 ym ym ¼ C1707 C1701 m m m yC3801 yC1701 yC3801

y07 TGC1707 yC17 CGC1707 C1707 C1701 : 01 C38 TG yC1701 yC3801 CGC3801 C1701

0107 MIC38C17 is the meta-Malmquist index for company C17 observed in 2007 in relation to company C38 observed in 2001. Applying the foregoing decomposition results in the values shown in Figure 11. Company C17 in 2007 has productivity, which is 61.4% of the company C38 in 2001 (see 0.614 in Figure 11). This is explained more by company C17 not keeping up with productivity changes registered by

C38 between 2001 and 2007. Specifically in 2001, C17 had 91.8% of the productivity of C38 (see 0.918 in Figure 11), but the productivity of C17 declined from 2001 to 2007 so that it was only 66.9% in 2007 compared to 2001. This decline was by a combination of the 2007 frontier being less productive compared to that of 2001 (0.87 frontier shift) and C17 itself falling behind the declining frontier between 2001 and 2007 (efficiency change 0.769). When in 2001 C17 had closer performance compared to C38, it was because it was closer to its own company-specific frontier by 3.9 percentage points than was the case for C38 (see 1.039 in Figure 11), but unfortunately C17’s company-specific frontier was some 17 percentage points less productive than that of C38 (see 0.833 in Figure 11). The decompositions of the type depicted in Figure 11 give valuable information to management about the comparative performance of companies over time and identify where discrepancies in performance lie.

6. Conclusion This paper is grounded on the theory of productivity change over time, focusing specifically on a circular


Malmquist index for measuring such change. The paper demonstrates the use of the circular Malmquist index for measuring productivity change not only in the traditional way, looking at each production unit over time within the comparative set of units existing at that time, but also in a context where a unit’s own manifestations over time constitute the comparative set. The paper enhances these approaches to productivity change elaborating on decompositions of the indices that would enable a regulator or a manager of a company to identify the sources of productivity change across and/or within company, depending on setting. Such information is clearly of value in managing the performance of production units. The foregoing uses and decompositions of the circular Malmquist index are deployed on data over the period 1993–2007 from the companies offering clean water services in England and Wales. Analysing the data first in unbalanced panel format, we find that their operating cost productivity has been increasing cumulatively from 1993 until 2005. However, it started decreasing from 2006 and it continued this decreasing trend in 2007. It would be interesting to pursue this analysis in the future to see whether this trend persists and also to investigate more fully the possible reasons for this. One reason may be the specifics of the price cap imposed by the regulator in PR04, and also the rise in electricity and fuel prices that moved up operational costs up. The regulatory regime is only one, albeit major, factor affecting water company productivity. The paper has also used the circular meta-Malmquist index to compare companies on productivity over time using within-company frontiers nested within the overall meta-frontier. The productivity differences between companies, observed at the same time period, was decomposed into components of ‘efficiency change’ and ‘frontier shift’ but these relate to within-company frontier shifts rather than the traditional frontier shift between one period and the next. The idea was taken a step further to compare productivities of two companies at two different points in time and this index decomposes into productivity change between periods and productivity change between companies. The within-company frontiers and measures of productivity change based on them and the distances of within company from meta-frontier are especially useful for managers of companies. For example, where policy or operating practice changes have been initiated at certain points in time their impact on productivity can be assessed as within-company assessments control in effect for all exogenous factors affecting the company, making it easier to attribute changes in productivity to within-company interventions.

References Althin R (2001). Measurement of productivity changes: Two Malmquist index approaches. J Prod Anal 16: 107–128.

2187

Ashton JK (2000). Total factor productivity growth and technical change in the water and sewerage industry. Serv Ind J 20(4): 121–130. Aubert C and Reynaud A (2005). The impact of regulation on cost efficiency: An empirical analysis of Wisconsin water utilities. J Prod Anal 23(3): 383–409. Battese GE and Rao DSP (2002). Technology gap, efficiency and a stochastic metafrontier function. Int J Bus Econ 1(2): 87–93. Berg SA, Forsund FR and Jansen ES (1992). Malmquist Indices of Productivity growth during the deregulation of Norwegian banking, 1980–89. Scand J Econ 94(Supplement): 211–228. Bottasso A and Conti M (2003). Cost inefficiency in the English and Welsh water industry: An heteroskedastic stochastic cost frontier approach. DIEM Universita` di Genova, mimeo. Bottasso A and Conti M (2009). Scale economies, technology and technical change in the water industry: Evidence from the English water only sector. Reg Sci Urban Econ 39: 138–147. Caves DW, Christensen LR and Diewert WE (1982). The economic theory of index numbers and the measurement of input, output and productivity. Econometrica 50: 1393–1414. Chambers RG and Fa¨re R (1994). Hicks’ neutrality and trade biased growth: A taxonomy. J Econ Theory 64: 554–567. Dyson RG, Allen R, Camanho AS, Podinovski VV, Sarrico CS and Shale EA (2001). Pitfalls and protocols in DEA. Eur J Opl Res 132(2): 245–259. Erbetta F and Cave M (2006). Regulation and efficiency incentives: Evidence from the England and Wales water and sewerage industry. HERMES Working Paper 8. Fa¨re R, Grosskopf S, Norris M and Zhang Z (1994). Productivity growth, technical progress and efficiency changes in industrialised countries. Am Econ Rev 84: 66–83. Førsund FR (2002). On the circularity of the Malmquist productivity index. Working paper, Department of economics, University of Oslo. O’Donnell CJ, Rao DSP and Battese GE (2008). Metafrontier frameworks for the study of firm level efficiencies and technology ratios. Empirical Econ 37(2): 231–255. OFWAT (1999). Final determinations: Future water and sewerage charges 2000–05. November, http://www.ofwat.gov.uk/legacy/ aptrix/ofwat/publish.nsf/Content/finaldeterminations.html. OFWAT (2004). Future water and sewerage charges 2005–10: Final determinations. December, http://www.ofwat.gov.uk/legacy/aptrix/ ofwat/publish.nsf/Content/pr04fd.html. OFWAT (2007). RD 21/0 relative efficiency assessment 2006–07. http://www.ofwat.gov.uk/legacy/aptrix/ofwat/publish.nsf/Content/ rd2107.html. Pastor JT and Lovell CAK (2005). A global Malmquist productivity index. Econ Lett 88: 266–271. Pastor JT and Lovell CAK (2007). Circularity of the Malmquist productivity index. Economic Theor 33: 591–599. Portela MCAS and Thanassoulis E (2006). Malmquist indexes using a geometric distance function (GDF): Application to a sample of Portuguese bank branches. J Prod Anal 25(1/2): 25–42. Portela MCAS and Thanassoulis E (2008). A circular Malmquisttype index for measuring productivity. Aston Working Paper RP08-02, Aston University Birmingham, UK. Portela MCAS and Thanassoulis E (2010). Malmquist-type indices in the presence of negative data: An application to bank branches. J Bank Financ. doi: 10.1016/j.jbankfin.2010.01.004. Ray SC and Desli E (1997). Productivity growth, technical progress and efficiency changes in industrialised countries: comment. Am Econ Rev 87(5): 1033–1039. Renzetti S and Dupont D (2004). The performance of municipal water utilities: Evidence on the role of ownership. J Tox Env Health Part A 67: 1861–1878.

2188


Saal D and Parker D (2000). The impact of privatization and regulation on the water and sewerage industry in England and Wales: A translog cost function model. Manage Decis Econ 21: 253–268. Saal D and Parker D (2001). Productivity and price performance in the privatized water and sewerage companies of England and Wales. J Regul Econ 20(1): 61–90. Saal D and Parker D (2004). The comparative impact of privatization and regulation on productivity growth in the English and Welsh water and sewerage industry 1985–99. Int J Regul Gov 4(2): 139–170. Saal D and Parker D (2005). Assessing the performance of water operations in the English and Welsh water industry: A panel input distance function approach. RP0502 Aston Business School Research Papers.

Saal D and Reid S (2004). Estimating OPEX productivity growth in English and Welsh water and sewerage companies: 199–2003. RP0434 Aston Business School Research Papers. Saal D, Parker D and Weyman-Jones T (2007). Determining the contribution of technical change, efficiency change and scale change to productivity growth in the privatized English and Welsh water and sewerage industry: 1985–2000. J prod Anal 28: 127–139. Tulkens H and Vanden Eeckaut P (1995). Non-parametric efficiency, progress and regress measures for panel data: Methodological aspects. Eur J opl Re 80: 474–499.

Received February 2010; accepted January 2011 after one revision