PROFIT, PRODUCTIVITY, PRICE AND QUALITY PERFORMANCE CHANGES IN THE ENGLISH AND WELSH WATER AND SEWERAGE COMPANIES

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3 OFIT ODUTIVIT IE AND UALIT EFOMANE HANGE IN THE ENGLIH AND ELH ATE AND EEAGE OMANIE Alexandros MAZIOTI Fondazione Eni Enrico Maei (FEEM) and Euro-Mediarranean enre on limae hange (M) Island of an Giorgio Venice Ialy David. AAL Ason Universiy Emmnauel THANAOULI Ason Universiy Absrac The purpose of his paper is he evaluaion of various profi drivers such as price changes produciviy changes and qualiy levels on he financial performance of he aer and ewerage ompanies (as) over ime in he case when he number of observaions is limied. e hereby follow Maziois aal and Thanassoulis (202) approach and exend i by measuring he impac of exogenous facors such as drinking waer and sewerage reamen qualiy on profiabiliy produciviy and price performance measures. The resuls sugges ha while qualiy improvemens have significanly conribued o he produciviy performance of he as hey have also conribued negaively o heir price performance. Overall afer 2000 seady reducion in average price performance gains in produciviy and sable economic profiabiliy were apparen. This rend indicaes Ofwa s policy on passing produciviy benefis o consumers and susaining sable profiabiliy han i was in earlier regulaory periods. This echnique is of grea ineres for boh regulaors and regulaed companies o beer idenify he sources of profi variaion and aid hem in evaluaing boh he effeciveness of a regulaory price cap scheme and he performance of he regulaed companies when he sample size is exremely limied. Keywords: rofi Decomposiion roduciviy rice erformance ualiy hange anel Index Numbers egulaion aer and ewerage Indusry

4 . Inroducion The waer and sewerage indusry in England and ales was privaized in 989 and before privaizaion here were 0 egional aer Auhoriies responsible for he waer and sewerage supply in England and ales and 29 auory aer companies which were already privaized companies ha were only responsible for he supply of waer. Afer 989 he 0 egional aer Auhoriies were privaized and formed he aer and ewerage ompanies (as) and he 29 auory aer ompanies became aer Only ompanies (os). Today here are 0 as whose duies include he supply of waer in areas ha are no supplied by he os and he collecion reamen and disposal of sewerage in all areas. However here are now only os afer mergers and akeovers. The as supply drinking waer o 80% of he populaion in England and ales wih os supplying he res. There are hree regulaory bodies in he waer and sewerage indusry. The Office of aer ervices (Ofwa) which is he economic regulaor and ses he price limis for each company every five years he Environmen Agency (EA) which is responsible for polluion conrol licensing and regulaion of waer absracion and he Drinking aer Inspecorae (DI) which is responsible for conrolling and monioring drinking waer qualiy. There were pleny of sudies in he pas ha used ochasic Fronier Analysis (FA) or Daa Envelopmen Analysis (DEA) echniques o measure he produciviy performance of he UK waer and sewerage indusry before and afer privaizaion and evaluae he impac of he regulaory price cap scheme on heir financial performance (see Maziois (202) for a comprehensive lieraure review). However few sudies exis ha use index number echniques o measure he overall performance (profis produciviy and price performance) of he UK waer and sewerage secor. The imporance of index numbers lies on he fac ha hey allow he measuremen of he performance of companies when he number of observaions is exremely limied. A significan advanage compared o oher esimaion echniques such as FA and DEA which require a relaively large number of observaions o specify an efficien fronier The auhors would like o express his graiude for he suppor of he Economic and ocial cience esearch ouncil as well as he Office of aer ervices (Ofwa) and noe ha he usual disclaimer applies. 2

5 The firs profi decomposiion analysis using index numbers o assess performance measuremen in he UK waer and sewerage indusry was developed by aal and arker (200) originally inroduced by aers & Treheway (999) for he Ausralian elecommunicaion indusry. aal and arker (200) employed a emporal (over ime) Tornqvis index approach o measure he impac of privaizaion and regulaion on produciviy (TF) price performance (T) and profiabiliy for as for he years The auhors concluded ha indicaed ha privaizaion did no lead o a significan improvemen in he overall produciviy growh of as whereas he ighened 994/95 price review reduced firm-specific economic profiabiliy bu here were no any significan improvemens in produciviy. Moreover aal and arker s (200) approach was hen developed by Maziois aal and Thanassoulis (2009) and (202). The former used a cross secional (spaial) index number echnique o allow for he cross-secional (spaial) measuremen of TF regulaory price performance (T) and profiabiliy and showed he subsequen comparison of how hese cross secional measures have changed over ime. hanges in TF T and profiabiliy were measured afer aking ino accoun he impac of exogenous characerisics such as drinking waer and sewerage reamen qualiy. Maziois aal and Thanassoulis (202) developed a panel index approach across as over ime o decompose uni-specific (emporal) index number based profiabiliy growh as a funcion of he profiabiliy produciviy and price performance growh achieved by benchmark firms and he cach-up o he benchmark firm achieved by less producive firms. However he auhors did no ake ino accoun he impac of qualiy in he produciviy and price performance measures. Therefore he purpose of his paper is o follow Maziois aal and Thanassoulis (202) approach and exend i by measuring he impac of exogenous facors on profiabiliy produciviy and price performance measures. As adjusmens for qualiy affec he produciviy and price performance measures leaving he measured economic profiabiliy unchanged he uni-specific profiabiliy growh can be expressed as a funcion of he uni-specific qualiy adjused produciviy and qualiy-adjused price performance change. This can be furher decomposed as a funcion of he qualiy adjused cach-up in produciviy and he qualiy adjused produciviy growh of he benchmark firm and he qualiy adjused cach-up in price performance and he qualiy adjused price performance growh of he benchmark firm. The inclusion of qualiy in our analysis allows us o finally decompose uni- 3

6 specific economic profiabiliy change as a funcion of he qualiy unadjused cach-up in produciviy he cach-up in qualiy regarding produciviy and he qualiyunadjused produciviy and qualiy performance over ime of he benchmark firm and he qualiy unadjused cach-up in price performance he cach-up in qualiy regarding price performance and he price performance and qualiy growh of he benchmark firm. e illusrae our analyical decomposiion of profi change wih an empirical applicaion o he regulaed English and elsh waer and sewerage indusry during he period This paper unfolds as follows. ecions 2 and 3 consider he mehodology necessary o apply his approach in a bilaeral and mulilaeral conex. The following secion provides a discussion of daa employed and he nex secion deails he empirical resuls. ecion 6 evenually concludes. 2. Mehodology 2.. Uni specific rofiabiliy roduciviy and rice erformance Indices Following he approach of aers & Treheway (999) aal & arker (200) and Maziois aal and Thanassoulis (202) we firs measure profis produciviy and price performance beween wo ime periods year and he base year for firm i. Economic profis of firm i a he base year Π are defined as a raio of oal revenues and oal coss in year. Toal revenues of a firm i a period are defined as i where and respecively represen he oupu price index and he aggregae oupu index a period. imilarly.e can hus define and decompose a uni-specific (emporal) index of economic profiabiliy for firm i a period relaive o he base period follows: U as U Π Π TFi T TF T U U U U TF U T U () Thus he uni-specific economic profiabiliy index U can be expressed as a funcion of an index of uni-specific oal facor produciviy in period relaive o he 4

7 base year TF and an index of uni-specific oal price performance beween U i period and T U i. As TF U U U i and T U U U i hese indices U can be furher decomposed as funcions of he uni-specific oupu ( i ) U U inpu ( ) oupu price ( i i ) and inpu price ) indices. This decomposiion highlighs ha observed changes in U ( uni-specific profiabiliy over ime can be explained by changes in produciviy changes in price performance or changes in boh paial rofiabiliy roduciviy and rice erformance Indices e nex consider he relaionship beween profis produciviy and price performance for firm i relaive o a base firm b a ime which we call a spaial index hereby adoping he erminology employed in he price index lieraure (Hill 2004). As a resul of is definiion hese indices only direcly measure differences in performance in he spaial dimension (beween firms) a any given ime. Economic profis of he base firm b a ime b and oal coss Π b are defined as a raio of is oal revenues b a ime. Thus he oal revenues of he base firm b a period are defined as b b b where b and b presen he oupu price index and he aggregae oupu index respecively of he base firm b a period. Is oal coss a year b are defined as b b b where b and denoes he inpu price index and he aggregae inpu index respecively of he base firm a year. imilarly we can define economic profis of any firm i a period b Π as a raio of is oal revenues i and is oal coss i. e can hus define and decompose a spaial economic profiabiliy index for any firm i relaive o he base firm b a period b as follows: Π Π b b b b b b b TF TF b T T b b b b b TF T (2) 5

8 Thus a ime a spaial economic profiabiliy index can be expressed as a funcion of an index of spaial oal facor produciviy for firm i relaive o he base firm b TF and a spaial index of oal price performance beween firm i and he i base firm b T. As i TF i and T i hese indices can be furher decomposed as funcions of he spaial oupu ( ( i b i b ) inpu ) oupu price ( i b ) and inpu price ( b ) indices. This decomposiion of spaial profiabiliy highlighs ha a any given ime observed differences in profiabiliy beween firms can be explained by differences in produciviy differences in price performance or differences in boh. By definiion spaial indices esimae firm i's performance relaive o any poenial base firm b and can herefore be employed o measure cach up in relaive performance. Thus if we have access o daa for he base year and any oher year we can define and decompose an index of economic profiabiliy cach up for any firm i a ime and relaive o he base firm b a period as follows: TF TF T TF TF T (3) Thus for firm i a ime an index of economic profiabiliy cach up can be expressed as a funcion of an index of oal facor produciviy cach up for firm i relaive o he base firm b TF and an index of oal price performance cach up i relaive o firm b T. As i TF and i i T hese indices can i i be furher decomposed as funcions of cach up indices for oupus ( inpus ( ( i i i i ) oupu prices ( i i i i i i ) ) and inpu prices ). This decomposiion of profiabiliy cach up highlighs ha a firm s cach up in profiabiliy can be explained no only by improving is produciviy performance relaive o he base firm bu also by improving is price performance relaive o he base firm. 6

9 2.3. elaive rofiabiliy roduciviy and rice erformance Indices e finally define he relaionship beween profis produciviy and price performance for any firm i a any ime relaive o a base firm b a he base ime. As by consrucion hese indices are measured relaive o a consan base for all and all i hey herefore capure differences in boh he spaial and he emporal dimensions for any given firm a any given ime. As above we define he economic profis of he base firm b a year Π b as a raio of is oal revenues b and oal coss b a year. Thus he oal revenues of he base firm b a period are defined as b b b where b and b presen he oupu price index and he aggregae oupu index respecively a period. Is oal coss a year b are defined as b b b where b and b denoes he inpu price index and he aggregae inpu index respecively of he base firm a year. e can hus define and decompose a relaive index of economic profiabiliy change a ime for firm i relaive o he base firm b a ime as follows: Π Π b b b b b b b TF TF b T T b b b b b TF T (4) Thus for firm i a ime he relaive economic profiabiliy index can be expressed as a funcion of an index of relaive oal facor produciviy for firm i a ime relaive o he base firm b a ime TF and an index of oal price i performance for firm i a ime relaive o he base firm b a ime T. As i TF and i i T hese indices can be furher decomposed as i i funcions of he relaive oupu ( i b ) inpu ( b ) oupu price ) and inpu price ( b ) indices. ( b Given he binary definiion of and is componens ( TF i T i i i and ) hese relaive performance esimaes are heoreically equivalen o i i 7

10 he separae binary performance esimaes provided by he uni-specific and spaial performance measures. Thus as U TF TF TF U T T T U U i i i U i U i i i and U i U i is sraighforward o demonsrae ha can be esimaed and fully decomposed as a funcion of relaive performance measure esimaes. U TFi Ti TF T (5) imilarly as i b TF TF TF b T T T b i b i b i i b and i b : b b b TFb Tb b b TF T (6) Esimaes of can hen be consruced wih he underlying relaive profiabiliy indices and can in fac be consruced as he raio of eiher uni specific or spaial indices as defined in (5) and (6). This also clearly demonsraes ha he cach up index is a is core simply a raio of uni specific profiabiliy growh raes. i i U i b i i i U i i b b b b (7) Moreover by rearranging (7) and decomposing he profiabiliy index we can wrie: U U b U U ( TF TF ) ( T T ) (8) b Thus given he availabiliy of relaive performance indices he emporal economic b profiabiliy of a firm i over ime U can be decomposed as a funcion of he U profiabiliy growh of he base firm b b and he profiabiliy cach-up of he firm 8

11 i relaive o he base firm beween year and e.g. profi performance of any firm can be decomposed ino a measure capuring he profi change of a reference firm and he given firm s performance change relaive o ha reference firm. Equaion (8) herefore highlighs he srong poenial o apply his index based approach o regulaory seings where i is desirable o no only measure firm performance bu also o judge ha performance relaive o a base firm normally defined as a bes pracice or benchmark firm. Equaion (8) previously developed by Maziois aal and Thanassoulis (202) lacks he impac of exogenous facors like qualiy in a profi decomposiion analysis. Therefore as is well documened in pas sudies (see aal & arker aal arker and eyman-jones 2007 Maziois aal and Thanassoulis 2009) he English and elsh waer and sewerage companies have been obliged o carry subsanial capial invesmen projecs in order o improve waer and sewerage qualiy and environmenal sandards. aal and arker (200) and Maziois aal and Thanassoulis (2009) demonsraed ha qualiy improvemens do significanly impac emporal and spaial produciviy and price performance esimaes. Thus we feel i is imporan o measure he impac of qualiy in our uni-specific spaial and relaive profiabiliy produciviy and price performance measures hereby allowing for he cross secional and ineremporal variaion in he sewage and drinking waer qualiy. e herefore calculae qualiy-adjused measures of oupu as he produc of oupu and a qualiy index following he approach of aal and arker (2000) and (200) one & ebser onsulans (2004) aal e al (2007) Maziois aal and Thanassoulis (2009). As a resul qualiy is included in a profi decomposiion approach as an exogenous facor and is inended o conrol for changes over he assesmen period in waer qualiy environmenal sandards and characerisics ha reflec differences beween firms in erms of heir operaing environmen (one & ebser onsulans 2004). Once he qualiy adjused waer and sewerage oupus are consruced qualiy adjused indices are sraighforward o produce by firs producing spaially consisen qualiy adjused oupu indices ( i ). A spaial aggregae qualiy-adjused aggregaed oupu price index is hen consruced as. e can also 9

12 derive a spaial implici qualiy index ( i ) which measures he implied difference in qualiy relaive o he base firm as. Therefore qualiy adjused spaial oupus and oupu prices can also be respecively expressed as i i and i i which illusrae ha he impac on spaial oupu quaniies will be perfecly balanced by changes in spaial oupu prices. This also implies ha measured spaial economic profiabiliy ( ) is no influenced by qualiy adjusmen. In conras he impac of qualiy adjusmen implies ha qualiy adjused spaial TF can be expressed as TF TFi and similarly qualiy adjused spaial price performance can be expressed as T Ti / and spaial economic profiabiliy can be decomposed as TF T. In an analogous manner we can derive measures of relaive qualiy adjused oupu indices over ime i and relaive implici qualiy index over ime ( i ) which measures he implied difference in qualiy over ime relaive o he base firm a he base period as / i. Therefore measures of qualiy adjused relaive oupus and oupu prices can also be expressed as i and i i. Thus qualiy adjused relaive TF and T over ime can be expressed as TF TF and i i T Ti / whereas he relaive economic profiabiliy over ime as TF T. This also implies ha measured relaive economic profiabiliy ( ) is no influenced by qualiy adjusmen. Also we can produce measures of uni-specific qualiy adjused oupu indices over ime U i and implici qualiy index over ime ( U i ) which measures he implied difference in uni-specific qualiy over ime as U U U i / i. Therefore esimaes of emporal qualiy adjused oupus and oupu prices can also be expressed as U U U i and U U U i i. Thus he qualiy adjused uni-specific TF U U U and T over ime can be expressed as TF TF and U U U T Ti / while he uni-specific economic profiabiliy over ime U U U as TF T. i i i 0

13 As saed above our adjusmen of oupu prices and quaniies for qualiy implies ha any changes in he qualiy adjused T index over ime are balanced by an equivalen proporional change in he qualiy adjused TF index over ime hereby keeping he measuremen of economic profiabiliy unaffeced by qualiy adjusmen. e wish o emphasize ha his is a reasonable assumpion. Firsly aking accoun of qualiy should no effec our underlying definiion of economic profiabiliy as urnover divided by economic coss. econdly i reflecs he mahemaical necessiy ha if urnover is consan allowing for increases in oupu resuling from qualiy improvemens mus resul in a perfecly proporional reducion in oupu prices. Therefore by adjusing TF and T measures for qualiy keeping economic profiabiliy unchanged we are able o offer an alernaive decomposiion of uni-specific profiabiliy growh which will more properly aribue qualiy improvemens o produciviy improvemen raher han o over esimaed improvemens in price performance ha would resul from a qualiy-unadjused measure. Moreover as we will illusrae his allows a furher decomposiion of equaion (8) ino he cach-up in qualiy regarding produciviy and price performance achieved by less produciviy firms and he qualiy growh in produciviy and price performance of he base firm in a mulilaeral conex. Given he derivaion of he spaial implici oupu qualiy index ( i ) which measures he implied difference in qualiy relaive o he base firm we are able o consruc measures of he cach-up in qualiy as a raio of he spaial implici i qualiy index for any firm i o he base firm beween year and. Moreover given he availabiliy of i and U i he cach up in qualiy can be i expressed in a similar manner o wha was demonsraed in equaion (7): i i U i b i i i U i i b b b b (9)

14 earranging (9) we can express he uni-specific qualiy index of any firm i over ime as a funcion of he cach-up in qualiy o he base firm and he qualiy improvemen of he base firm U U i b. Given our discussion of our approach o qualiy adjusmen he decomposiion of firm specific economic profiabiliy change deailed in (8) can now be exended in he mulilaeral conex as follows: U U U U b ( TFi TFb )( Ti Tb ) ( U )( U ) ( U TF T TF TF )( T T U ) b b (8 ) T T U U U ( )( ) b TF i TFb b U i b Thus as in (8) in he firs line of (8 ) uni-specific economic profiabiliy change U can be decomposed as a funcion of he qualiy unadjused cach-up in produciviy TF and he produciviy growh of he benchmark firm i TF and U b he qualiy unadjused cach-up in price performance T and he price i performance growh of he benchmark firm T By including qualiy in TF and U b T measures in he second line of equaion (8 ) he uni-specific economic profiabiliy over ime can be expressed as a funcion of he uni-specific qualiy adjused produciviy U TF and qualiy-adjused price performance change U T. This can be furher decomposed as a funcion of he qualiy adjused cachup in produciviy TF and he qualiy adjused produciviy growh of he benchmark firm U TF b and he qualiy adjused cach-up in price performance T and he qualiy adjused price performance growh of he benchmark firm U T b. Finally he hird line of (8 ) demonsraes he impac of qualiy in TF and T measures over ime. Thus uni-specific economic profiabiliy change U can be decomposed as a funcion of he qualiy unadjused cach-up in produciviy TF i he cach-up in qualiy regarding produciviy and he qualiy-unadjused i 2

15 produciviy and qualiy performance over ime of he benchmark firm TF U b and and he qualiy unadjused cach-up in price performance U b T he cach-up in i qualiy regarding price performance / and he price performance and qualiy i growh of he benchmark firm T U b U and /. If TF or T hen firm b > > i improved is produciviy or price performance relaive o he base firm from year o whereas a value lower han indicaes ha produciviy or price performance of firm i has declined relaive o ha of he base firm. If or / < hen he > firm i improved is qualiy regarding produciviy or price performance relaive o he base firm from year o year whereas a value lower han indicaes ha relaive qualiy regarding produciviy or price performance of firm i has declined relaive o ha of he base firm. Finally he decomposiion of he uni specific economic profiabiliy over ime in equaion (8 ) can be visualized in Figure. As adjusmens for qualiy affec he produciviy and price performance measures leaving he measured economic profiabiliy unchanged he uni-specific profiabiliy growh can be expressed as a funcion of he uni-specific qualiy adjused produciviy and qualiy-adjused price performance change. This can be furher decomposed as a funcion of he qualiy adjused cach-up in produciviy and he qualiy adjused produciviy growh of he benchmark firm and he qualiy adjused cach-up in price performance and he qualiy adjused price performance growh of he benchmark firm. The inclusion of qualiy in our analysis allows us o finally decompose uni-specific economic profiabiliy change as a funcion of he qualiy unadjused cach-up in produciviy he cach-up in qualiy regarding produciviy and he qualiy-unadjused produciviy and qualiy performance over ime of he benchmark firm and he qualiy unadjused cach-up in price performance he cach-up in qualiy regarding price performance and he price performance and qualiy growh of he benchmark firm. i 3

16 ualiy Unadjused roduciviy ualiy Adjused roduciviy ualiy ach-up Uni pecific Economic rofiabiliy hange ualiy Adjused roduciviy hange ualiy Adjused rice erformance hange ualiy Adjused Benchmark roduciviy ualiy Adjused rice erformance ach-up ualiy Adjused Benchmark rice erformance hange ualiy Unadjused Benchmark roduciviy ualiy Benchmark hange ualiy Unadjused rice erformance /ualiy ach-up ualiy Unadjused Benchmark rice erformance /ualiy Benchmark hange Figure Decomposiion of Uni pecific Economic rofiabiliy hange afer Adjusmens for ualiy 4

17 2.3. Mulilaeral roduciviy rice erformance and rofiabiliy ompuaions In racice hained Uni-specific roduciviy rice erformance and rofiabiliy Over Time In his secion we define chained uni-specific profiabiliy produciviy and price performance growh. Temporal Fisher oupu and inpu indexes beween wo ime periods and where is he base period in he case of m oupus and n inpus for a firm i are respecively i and i : M M N N m m m m n n n n m m 2 n n 2 [ ] M M [ ] N N m m m m n n n n m m n n (0) where and denoe he quaniies for he mh oupu for periods and m m respecively whereas and presen he quaniies for he nh inpus for n n periods and respecively. Moreover and are he prices for mh oupu m m while and denoe he inpu prices. The Fisher oupu and inpu indexes of a n n firm i beween wo ime periods and can also be expressed as he geomeric means of Laspeyers and aasche oupu and inpu indexes. A emporal Fisher produciviy index TF i is consruced as a raio of Fisher oupu index relaive o Fisher inpu index which akes he value in he year (base period): i TFi () A emporal Fisher produciviy index can be used in he unchained form denoed above or in a chained form where weighs are more closely mached o pair-wise comparisons of observaions (Diewer & Lawrence 2006). The uni-specific oupu and inpu indices are hus chained indices which are given by: H i and beween observaions and H i H H i (2) 5

18 The uni-specific produciviy of a firm i over ime can be similarly calculaed as a chained index alhough i can be equivalenly calculaed as a raio of he chained uni-specific oupu and inpu indices over ime H i and : H i H TFi (3) H H Given hese chained uni-specific indexes we can proceed o derive relaed T and rofiabiliy indices as in aal and arker (200). To derive T index we firsly express uni-specific urnover a period relaive o he base year as U H /. The chained uni-specific aggregae oupu price index ( ) is hen H U H calculaed as. imilarly we express uni-specific nominal economic U coss a period relaive o he base year as /. The chained uni- H specific aggregae inpu price index ( ) H U H is hen calculaed as. H Finally a chained uni-specific T index for any firm i over ime ( ) obained as: i i i T can be T U (4) H H U H H H Therefore a chained uni-specific economic profiabiliy index a period relaive o H he base year is calculaed as he produc of a chained index of uni-specific oal facor produciviy over ime TF and a chained uni-specific index of oal H i price performance over ime T. H i paial roduciviy rice erformance and rofiabiliy In he previous secion we used a chained Fisher index o measure profiabiliy produciviy and price performance of any firm beween period and period. In his secion we derive a mulilaeral Fisher index o measure profiabiliy produciviy and price performance across companies a any given year (mulilaeral spaial comparisons). hen he price and quaniies across differen companies are 6

19 compared i is imporan ha such comparisons are underaken for every pair of companies being considered (mulilaeral comparisons). However in order o achieve consisency beween all he pairs of comparisons we need o derive mulilaeral indexes ha fulfill he propery of ransiiviy. Inernal consisency (ransiiviy) implies ha a direc comparison beween wo firms gives he same resul when comparing indirecly hese wo firms hrough a hird firm. Therefore binary Fisher oupu and inpu indices beween wo firms i and j i j and i j can be convered ino mulilaeral consisen ransiive indices by applying he EK mehod developed by Eleo-Koves (964) and zulc (964) o derive ransiive Fisher indices (see aves hrisensen and Diewer (982a) Diewer and Lawrence (2006) and Ball e al (200) for a discussion on mulilaeral ransiive indices). e herefore derive ransiive Fisher oupu and inpu indices using he EK mehod which is equivalen o aking he geomeric mean of he I possible direc and indirec (hrough any possible 3 rd firm k) binary Fisher comparisons of firms i and j. The resuling Fisher oupu and inpu indices ransiiviy propery: ij and ij herefore fulfill he ij I [ ik kj ] k I ij I [ ik kj ] k I (5) Adoping he erminology of he price index lieraure (Hill 2004) we refer o hese mulilaeral oupu and inpu indices as spaial indices as hey provide spaially consisen measures across all firms. The spaial oal facor produciviy Fisher index for a firm i relaive o firm j TF i j can hen be consruced as he raio of he spaial Fisher oupu index relaive o spaial Fisher inpu index: TF ij (6) ij ij hile we can generae he I I possible ransiive spaial oupu inpu and produciviy indexes beween all firms ransiiviy also implies ha all meaningful informaion wih regard o relaive produciviy is available in a subse of only I of 7

20 hese indices. Thus if we arbirarily choose one firm as a base firm and se j b hen each spaial measure is a measure of firm i relaive o he chosen base firm and we can also simplify noaion such ha TF. Therefore b TFi b i b i produciviy relaive o he base firm s produciviy can be expressed as: TF i (7) i i However his simplificaion comes a no loss of generaliy as anoher spaial produciviy measure beween any given firms can simply be calculaed as TF TF / TF. imilarly / and i j i j i j i j /. If spaial comparisons are available for each of T ime periods indexed by and we assume he same base firm in all years we can define he spaial produciviy of firm i relaive o firm b a ime as: i j i j TFi (8) e now urn our discussion o he consrucion of he spaial oal price performance T index ( ) i. Firsly we express urnover of a firm i relaive o he base firm as. The spaially consisen aggregae oupu price index ( ) is hen b calculaed as. imilarly we express nominal economic coss of a firm i relaive o he base firm as. The spaially consisen aggregae inpu price index ( ) i b is hen calculaed as. Finally a spaially consisen T index of any firm i relaive o he base firm a any given ime ( ) obained as: i T can be i T (9) 8

21 Therefore a spaial economic profiabiliy index a ime is calculaed as he produc of an index of spaial oal facor produciviy for firm i relaive o he base firm b TF and a spaial index of oal price performance beween firm i and he i base firm b T. i elaive roduciviy rice erformance and rofiabiliy hange Over Time In order o simulaneously measure and decompose he profiabiliy growh of any firm in he sample across ime and relaive o oher firms in pracice i is necessary o reconcile he spaial profiabiliy measures defined above wih he underlying uni-specific chained profiabiliy of each firm. This is because while secion 2 has heoreically demonsraed ha relaive produciviy measures can be expressed as a funcion of uni-specific and spaial produciviy measures his is no as sraighforward in a mulilaeral empirical applicaion. Thus as demonsraed by Hill (2004) we canno in pracice derive mulilaeral measures of he producive change of any firm i relaive o he base firm which can saisfy boh spaial and emporal consisency. 2 e have herefore chosen o pursue measures of relaive produciviy change over ime ha guaranee spaial consisency as his approach is mos consisen in he regulaory applicaion we demonsrae below. Thus regulaors in comparaive or yard sick regulaory regimes ypically employ cross secion echniques o measure differences in produciviy or efficiency across firms (relaive comparaive performance) and herefore use wha are in fac spaial performance measures o inform heir decision wih regard o appropriae regulaed prices. Thus as our applied relaive performance measures reain spaial consisency by consrucion he relaive performance indices will yield comparaive performance measures ha are consisen wih regulaory pracice in any given year. However because our relaive measures will also allow ineremporal analysis across firms hey have he advanage of allowing a more deailed analysis of firm performance change over ime which is no possible wih a spaial index alone.. 2 paially consisency implies ha each year s relaive produciviy measures do no depend on he oher years in he comparison and emporal consisency implies ha each firm s produciviy esimaes do no depend on he number of observaions in he ime series 9

22 Given hese argumens we follow Hill s approach (2004). Therefore firm i's relaive produciviy change over ime ( TF i ) is deermined as he geomeric average of he I alernaive poenial esimaes of relaive produciviy as derived by employing he chained ime rends and spaial produciviies of all he I firms in he sample: TF TF I H ( TFj TFj ) j TFj I (20) Thus when i j TF can be simply expressed as he produc of he firm s own i chained produciviy index and is spaial produciviy measure in year : TF TF TF. In conras for he alernaive I- esimaes when i j. i H TF i can also be expressed as a funcion of any oher firm j s relaive produciviy index calculaed as TF TF TF and he spaial produciviy of firm i relaive o j H j j firm j which given he definiion of our spaial produciviy measures can be expressed as TF TF j. Thus raher han relying on a single one of hese poenial esimaes he definiion of TF in (20) employs all available spaial and chained i produciviy esimaes o provide an arguably superior geomeric average esimae of TF i. e can similarly derive measures of he relaive oupu and inpu indices over ime and. i i Following our approach in (4) hese relaive measures are indices of any firm i measured relaive o he base firm in he base year. onsrucion of consisen price and T indices can herefore be accomplished by firsly expressing urnover of firm i relaive o he base firm a he base year as. The relaive aggregae oupu price index over ime ( ) i b is hen calculaed as. imilarly we express nominal economic coss of a firm i relaive o he base firm a he base year as. The relaive aggregae inpu price index over ime ( ) b is hen calculaed as. Finally a relaive T index of any firm i relaive o he base firm a he base year ( ) T can be obained as: i i 20

23 T (2) As a resul a relaive economic profiabiliy index can be calculaed as he produc of an index of relaive oal facor produciviy for firm i relaive o he base firm b a base year TF and a relaive index of oal price performance beween i firm i and he base firm b a he base year T. i In order o achieve our ulimae goal of decomposing uni specific profi growh in he mulilaeral conex as demonsraed in (8) in he bilaeral conex we mus finally derive uni specific indices which are consisen wih he relaive indices developed in (20) and (2). e herefore calculae a consisen measure of unispecific produciviy over ime which can be obained as TF U TF. imilarly TF consisen measures of uni-specific oupu and inpu growh are respecively U and U. In an analogous manner consisen measures of uni- specific T oupu price inpu price and economic profiabiliy indexes are respecively T U Ti T U U U U U and TFi Ti. Given our modeling decision o mainain spaial consisency a he cos of emporal consisency and he subsequen employmen of he geomeric average of he I alernaive poenial relaive indicaors as appropriae uni specific relaive produciviy oupu and inpu indices we mus noe ha he uni-specific chained emporal indexes will by consrucion no be perfecly consisen wih he uni specific emporal indexes consruced from he mulilaeral relaive indices. Neverheless i can be readily mahemaically demonsraed ha he geomeric average of he I chained uni specific emporal indices and hose derived from he relaive indices deailed in equaions (25) and (26) are equal. Thus for example if we ake he geomeric average across all firms I in he sample hen 2

24 I I I U ( ) ( ) I I I H I H U TF i TFi and ( T ) ( ) I i Ti i i i i. This implies ha while our approach o deriving he relaive indicaors necessary o decompose uni-specific rends in firm performance can resul in minor deviaions from he emporal rends implied by he uni-specific chained indices we can noneheless be fully confiden ha on average he uni specific esimaes are consisen wih he underlying chain-based esimaes of emporal change in firm performance. e herefore focus on hese average esimaes and heir decomposiion in our resuls below. This secion has specified a mehodology o allow he empirical applicaion of uni-specific spaial and relaive economic profiabiliy indices and heir decomposiion ino uni-specific spaial and relaive produciviy and price performance indices in a mulilaeral seing by reconciling ogeher emporal chained and spaial indices following Hill s approach (2004). Moreover we have demonsraed ha hese esimaes are no only spaially consisen bu are also on average consisen wih alernaive uni-specific chained indices of emporal performance change. Thus his secion has demonsraed an appropriae mehodology o allow for decomposiions of profiabiliy indices in a mulilaeral seing hereby exending he approach illusraed in equaions () (2) and (3) in he binary conex. onsequenly we are able o consisenly decompose uni specific profiabiliy change as a funcion of he profiabiliy growh of a base firm and profiabiliy cachup relaive o ha firm over ime which can be furher decomposed as a funcion of he produciviy and price performance of a base firm and produciviy and price performance cach-up relaive o ha firm over ime in a mulilaeral seing as illusraed in equaion (8) in he binary conex. Finally i can be easily proven ha by adjusing oupu wih qualiy we can also exend equaion (8 ) in a mulilaeral seing. 4. Daa Our model includes separae oupus for waer and sewerage services and he hree inpus capial labor and oher inpus. The daa covered are for he period for a balanced panel of 0 aer and ewerage companies (as). aer conneced properies and sewerage conneced properies are he proxies for waer and sewerage oupu and are drawn from he companies regulaory reurns o Ofwa 22

25 which are used o consruc he oupu indices. These binary oupu indices hen formed he basis of consrucing fully spaially consisen oupu indices wih he EK mehod. Finally spaially consisen aggregae oupu price indices were consruced as he raio of relaive aggregae urnover in nominal erms o his spaial aggregae oupu index as discussed above. Our physical capial sock measure is based on he inflaion adjused Modern Equivalen Asse (MEA) esimaes of he replacemen cos of physical asses conained in he companies regulaory accouns. However as periodic revaluaions of hese replacemen cos values could creae arbirary changes in our measure of physical capial we canno direcly employ hese accouning based measures. Insead we accep he year ending 2006 MEA valuaions as our base value and use ne invesmen in real erms o updae his series for earlier and laer years. eal ne invesmen is herefore aken as he sum of disposals addiions invesmens and depreciaion as deflaed by he onsrucion Oupu rice Index (OI). Following aal and arker s (200) approach we averaged he resuling year ending and year beginning esimaes o provide a more accurae esimae of he average physical capial sock available o he companies in a given year. e subsequenly employed a user-cos of capial approach o calculae oal capial coss as he sum of he opporuniy cos of invesed capial and capial depreciaion relaive o he MEA asse values and consruc he price of physical capial as he user cos of capial divided by he above MEA based measure of physical capial socks. The opporuniy cos of capial is defined as he produc of he weighed average cos of capial (A) before ax and he companies average egulaory apial Value (V). The V is he financial measure of capial sock acceped by Ofwa for regulaory purposes. The A calculaion is broadly consisen wih Ofwa s regulaory assumpions and is esimaed wih he risk free reurn assumed o be he average annual yields of medium-erm UK inflaion indexed gils. The risk premium for company equiy and corporae deb was assumed o be 2% following Ofwa s approach a pas price reviews. e also allowed for differences in company gearing raios and effecive corporae ax raes which were calculaed as he sum of aggregae curren and deferred ax divided by he aggregae curren cos profi before axaion. Finally following he approach in Ofwa s regulaory curren cos 23

26 accouns capial depreciaion was he sum of curren cos depreciaion and infrasrucure renewals charge. The average number of full-ime equivalen (FTE) employees is available from he companies sauory accouns. Firm specific labour prices were calculaed as he raio of oal labour coss o he average number of full-ime equivalen employees. Oher coss in nominal erms were defined as he difference beween operaing coss and oal labour coss. 3 Given he absence of daa allowing a more refined break ou of oher coss we employ he UK price index for maerials and fuel purchased in purificaion and disribuion of waer as he price index for oher coss and simply deflae nominal oher coss by his measure o obain a proxy for real usage of oher inpus. Given hese inpu quaniy and price measures we are able o calculae indices of uni-specific spaial and relaive inpu usage discussed above. As oal nominal economic coss are obained as he sum of oal capial coss labour coss and oher coss in nominal erms division of his sum by he uni-specific spaial and relaive inpu index allows he consrucion of uni-specific spaial and relaive inpu price indices. Finally economic profis are calculaed as he difference beween urnover and calculaed economic coss. Following aal and arker (200) he drinking waer qualiy index is calculaed as he raio of he average percenage of each a s waer supply zones ha are fully complian wih key waer qualiy parameers relaive o he average compliance percenage for England and ales in 99. aer supply zones are areas designaed by he waer companies by reference o a source of supply in which no more han people reside. The daa were drawn from he DI s annual repors for drinking waer qualiy for he calendar years ending The drinking waer qualiy can be defined eiher based on he sixeen waer qualiy parameers or nine waer qualiy parameers idenified as being imporan for aesheic healh 3 hile i would be paricularly desirable o disaggregae oher inpu usage daa furher and in paricular o allow for separae energy and chemical usage inpus he daa available a company level from Ofwa s regulaory reurn does no allow a furher meaningful decomposiion of oher inpu usage. 4 The DI provides qualiy daa based on calendar years while all oher informaion employed in his paper is based on fiscal years ending March 3 s. e noe his inconsisency in he daa bu emphasize ha he repored years overlap each oher for 9 monhs. Thus he year end o year end esimaes of qualiy change obained from he DI daa provide consisen esimaes of qualiy change by he waer companies a a fixed poin 9 monhs ino each fiscal year. 24

27 reasons and cos reasons or based on based on he six waer qualiy parameers idenified as being indicaive of how well reamen works and disribuion sysems are operaed and mainained. Due o changes in some of he drinking waer qualiy sandards and he new regulaions he DI repor for 2005 no longer included he wo qualiy indices ha compared companies compliance for he sixeen or nine waer qualiy parameers wih he average for England and ales. o we decided o repor resuls for he drinking waer qualiy based on he six waer qualiy parameers 5 ha Ofwa also employs in his assessmen and reflec how well reamen works and disribuion sysems are operaed and mainained (Ofwa 2006). The sewage reamen qualiy index is defined as a weighed index of he percenage of conneced populaion for which sewage receives primary reamen and he percenage of populaion for which sewage receives a leas secondary reamen. I also implicily includes he percenage of conneced populaion for which sewage is no reaed wih a zero weigh. This daa choice reflecs boh he availabiliy of consisen daa capuring qualiy rends for he enire period and does clearly capure subsanial increases in sewage reamen levels paricularly in he earlier par of he sample period. The sewage reamen daa were aken from aerfacs for he firs years o and he companies regulaory reurns for he fiscal years o Moreover we henceforward refer o daa based on he ending year of he fiscal years. I is clearly necessary o employ a weighed index of hese measures as boh he qualiy and coss of higher reamen levels exceed hose associaed wih non reamen or primary reamen alone. e herefore endeavoured o consruc a cos based weighing sysem alhough he necessary daa o accomplish his was relaively limied. However we were able o calculae relaive cos measures based on he raio of sewerage reamen coss o volumes of sewerage reamen using wo alernaive cos esimaes available from company regulaory reurns. One of hese alernaive esimaes was based on oal sewerage reamen funcional expendiure and direc coss for all reamen works while he oher was based on oal sewage reamen 5 The six waer qualiy parameers which form he Operaional erformance Index (OI) are iron manganese aluminium urbidiy faecal coliforms and rihalomehanes. The resuling drinking waer qualiy index suggess an increase in qualiy of 0.3 percen beween 99 and 2008 afer aggregaing he daa for all as. 25

28 coss for large reamen works only. These esimaes sugges ha higher levels of reamen are.68 o 2.40 imes more cosly han primary reamen only. Given his esimae range we chose o weigh he percenage of populaion receiving secondary reamen of sewage or more wice as much as he percenage receiving primary reamen only. hile admiedly somewha ad hoc we emphasize here is some empirical evidence o suppor hese weighs. e noe ha i is sraighforward o demonsrae ha he resuling weighed qualiy index is nesed beween an index based solely on he percenage of populaion receiving a leas primary sewage reamen which would underesimae gains in sewage reamen qualiy and one based solely on he percenage of populaion receiving a leas secondary sewage reamen which would overesimae gains in sewage reamen qualiy. 5. esuls from produciviy price performance and profiabiliy afer conrolling for qualiy The above spaial and relaive profiabiliy produciviy and price performance measures were defined relaive o he base firm in he sample. However if he base firm is defined as he firm wih he highes produciviy in he sample hen each firm s produciviy prices and profis will be relaive o his bes pracice or benchmark firm. 6 In his secion we firs repor geomeric average measures of unispecific profiabiliy produciviy and price performance. onsequenly we decompose heses changes ino an average cach-up componen and he performance of he benchmark firm as illusraed in equaion (8). Figure 2 illusraes he decomposiion of uni-specific economic profiabiliy change ino qualiy adjused uni-specific produciviy and price performance change over he period The resuls indicae ha beween 99 and 2008 average economic profiabiliy increased by 5.9% which was aribued o a significan improvemen in TF of 5.7% and a reducion in T of 30.2%. On average here 6 e have no idenified firms for confidenially reasons. The same firm is consisenly found o have he highes spaial produciviy esimaes in all years and is herefore modelled as he benchmark mos producive firm in each year of our sudy Moreover we noe ha his same firm was found o have he highes spaial produciviy esimaes in each year of he sudy regardless of wheher we applied he spaially consisen Fisher indices provided in he main ex similar spaially consisen Tornqvis indices or he mulilaeral ranslog index for as based on he Tornqvis index developed by aves e al (982a). Furhermore here is lile subsanive difference beween he resuls regardless of which mehod is employed. 26

29 was a sable and subsanial increase in TF over ime while T followed an upward rend unil 994 which was inerruped in 995 bu was again followed by a subsanial increase beween 999 and e noe ha during he years average economic profiabiliy increased due o increases in T which was subsanially greaer han TF growh. As documened in previous sudies Ofwa s ighening of price caps in he 994 price review decreased he growh in real oupu prices and herefore resuled in a downward rend for boh T and economic profiabiliy unil 998 while TF coninued o improve significanly. Afer 2000 reduced oupu prices caused T o dramaically decline and is value remained consisenly below afer This indicaes ha regulaory price changes implemened afer 2000 caused he price performance of firms o fall subsanially below is level in 99. Moreover average uni-specific T followed a downward rend excep for 2006 when oupu prices were allowed o momenarily rise in he firs year of he regulaory period. Unsurprisingly given he dramaic fall in price performance afer 2000 average economic profiabiliy also subsanially declined even if TF coninued o follow a seady upward rend which was only momenarily inerruped in Thus in he pos 2000 period rends in emporal economic profiabiliy followed he rend of T indicaing ha changes in price performance were a significan deerminan of changes in economic profiabiliy Economic rofiabiliy ualiy Adjused TF ualiy Adjused T Figure 2 Decomposiion of Average Uni pecific rofiabiliy ino Average ualiy Adjused Uni pecific TF and T 27

30 Moreover Figure 3 depics he decomposiion of qualiy adjused average TF change ino qualiy unadjused average TF change and qualiy change. High capial invesmen programs o improve qualiy condiions since privaizaion had a posiive impac on qualiy adjused oupu growh and consequenly qualiy adjused TF increased more han qualiy unadjused TF. Over he whole regulaory period average qualiy adjused TF improved by 5.7% whereas average qualiy unadjused TF improved by only 22.9% implying ha average esimaed qualiy change amouned o 23.4%. Much of he measured qualiy improvemen occurred during he years and qualiy showed is highes level of improvemen in he years 999 and Thus by 2002 average qualiy improved by 22% resuling in an increase in average qualiy adjused TF of 40.% and exceeded average qualiy unadjused TF which improved by only 4.8%. Afer 2003 on average here were small improvemens in qualiy and hus small changes in he qualiy adjused TF growh rae whereas in he las wo years of our sudy average qualiy followed a slighly decline rend. Neverheless produciviy sill coninued o improve in his laer period suggesing ha firms were able o achieve produciviy improvemens by reducing inpu usage ualiy Adjused TF ualiy Unadjused TF ualiy Figure 3 Decomposiion of Average Uni pecific ualiy Adjused TF hange ino Average Uni-pecific TF and ualiy hange Figure 4 displays he decomposiion of qualiy adjused average uni-specific T change ino qualiy unadjused average T change and qualiy change. ince 28