! ! M.SC.!APPLIED!ECONOMICS!&!FINANCE! MASTER’S!THESIS! ! ! ! ! ! ! ! ! ! ! Economic!Effects!from!Hospital!Mergers! Analysis(of(the(horizontal(merger(between(Bispebjerg(and(Frederiksberg(Hospitals( ! ! SUNE!FOLDEN!LINDHOLDT! ! ! ! ! ! ______! ! DECEMBER!18th,!2014! SUPERVISOR:!HERDIS!STEINGRIMSDOTTIR,!! DEPARTMENTS!OF!ECONOMICS! ! 137.874!CHARACTERS! 73!PAGES! ! ! ! ! ! ! COPENHAGEN!BUSINESS!SCHOOL!2014

1!! !

Executive)Summary) Introduction:" Healthcare! costs! in! OECD! countries! have! risen! significantly! since! the! 1990s! along!with!the!increasing!welfare.!Projections!show!that!public!healthcare!costs!will!continue! to!increase,!and!discussions!on!a!more!efficient!healthcare!system!are!increasingly!relevant.!In! Denmark,!the!Structural!Reform!in!2007!led!to!an!increasing!centralization!of!the!public!hosJ pitals!including!a!series!of!hospital!mergers.!Bispebjerg!and!Frederiksberg!Hospitals!merged! in!2012,!and!planned!to!fully!merge!in!2025,!when!New!Bispebjerg!Hospital!is!completed.! Methodology:!Data!Envelopment!Analysis!is!applied!to!estimate!the!optimal!efficiency!fronJ tier! for! Danish! public! hospitals,! and! their! efficiency! scores! under! variable! returns! to! scale! (VRS)! and! nonJdecreasing! returns! to! scale! (NDRS)! technologies.! Based! on! these! efficiency! scores,!we!estimate!total!economic!effects,!learning!effects,!harmony!effects!and!size!effects!of! the!merger.!Furthermore,!the!bootstrap!method!is!applied!to!biasJcorrect!the!data!samples,!to! provide!an!alternative!and!more!accurate!approach!to!the!merger!analysis.! Data:!We!utilize!adjusted!operational!costs!and!DRG!income!in!2011!to!compare!efficiencies! among! twentyJseven! Danish! public! hospitals.! The! data! sample! includes! somatic! hospitals! from! all! five! regions! in! Denmark.! Hospitals! only! handling! elective! treatments! are! excluded! from!this!study,!which!includes!all!private!hospitals.!An!alternative!data!sample!is!introduced! as!2012!DRGJtariffs!is!applied!to!2011!DRGJactivity.!! Results:"We!consistently!find!economic!gains!from!the!total!economic!effects!of!the!merger! between! Bispebjerg! and! Frederiksberg! Hospitals.! The! preJmerger! analyses! indicate! that! Bispebjerg! and! Frederiksberg! Hospitals! are! individually! inefficient! in! comparison! to! other! public!hospitals!in!the!data!sample.!Decomposing!the!total!economic!effects!of!the!merger,!we! find!that!the!main!potential!cost!reduction!is!learning!effects.!The!potential!savings!from!harJ mony!effects!and!size!effects!are!trivial,!and!the!pure!merger!effects!indicate!an!increase!in! costs.!Bispebjerg!and!Frederiksberg!Hospitals!will!realize!larger!reduction!in!costs!by!applyJ ing!best!practice!instead!of!a!merger.!! Conclusions:!We!find!that!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!will! generate!cost!reductions!from!the!total!economic!effects!of!the!merger.!A!postJmerger!analyJ sis!supports!this!conclusion.!!!

! 1! !

Table)of)Contents) 1)INTRODUCTION)...... )6! 1.1!PUBLIC!HEALTHCARE!EXPENDITURE!...... !7!

1.2!THE!DANISH!HEALTHCARE!SYSTEM!...... !8!

1.3!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!...... !9!

2)LITERATURE)REVIEW)...... )13! 2.1!HORIZONTAL!MERGERS!...... !13!

2.2!HOSPITAL!MERGERS!...... !14!

2.3!HYPOTHESIS!1:!TOTAL!ECONOMIC!EFFECTS!...... !17!

2.4!HYPOTHESIS!2:!LEARNING!EFFECTS!...... !18!

2.5!HYPOTHESIS!3:!HARMONY!EFFECTS!...... !19!

2.6!HYPOTHESIS!4:!SIZE!EFFECTS!...... !19!

2.7!SUMMARY!...... !20!

3)METHODOLOGY)...... )21! 3.1!DATA!ENVELOPMENT!ANALYSIS!...... !21! 3.1.1"Free"Disposability"...... "22! 3.1.2"Convexity"...... "23! 3.1.3"Scaling"...... "24! 3.1.4"Additivity"...... "26! 3.1.5"DEA"Models"...... "26! 3.1.6"Peer"Units"...... "29! 3.1.7"Scale"Efficiencies"...... "30! 3.1.8"Limitations"of"DEA"...... "30! 3.1.9"Bootstrapping"...... "31!

3.2!MERGER!EFFECTS!...... !32! 3.2.1"Total"Economic"Effects"...... "33! 3.2.2"Learning"Effects"...... "34! 3.2.3"Harmony"Effects"...... "35! 3.2.4"Size"Effects"...... "35! 3.2.5"Pure"Merger"Effects"...... "36!

3.3!SUMMARY!...... !36!

4)DATA)...... )37! 4.1!DATA!SAMPLES!...... !37! 4.1.1"Bispebjerg"and"Frederiksberg"Hospitals"...... "39!

! 2! !

4.1.2"Variables"...... "40! 4.1.3"2012"DRG"Tariffs"...... "43!

4.2!DATA!QUALITY!...... !43!

4.3!POSTJMERGER!DATA!SAMPLE!...... !44!

4.4!SUMMARY!...... !45!

5)ANALYSIS)...... )46! 5.1!PREJMERGER!ANALYSIS!...... !47! 5.1.1"Efficiency"scores"...... "47! 5.1.2"Scale"Efficiencies"...... "50! 5.1.3"Peer"Units"...... "50!

5.2!BIASJCORRECTED!PREJMERGER!ANALYSIS!...... !51! 5.2.1"BiasUCorrected"Efficiency"Scores"...... "53! 5.2.2"Confidence"Intervals"...... "54! 5.2.3."Scale"Efficiencies"...... "55!

5.3!MERGER!ANALYSIS!...... !56! 5.3.1"Total"Economic"Effects"...... "56! 5.3.2"Learning"Effects"...... "59! 5.3.3"Harmony"Effects"...... "61! 5.3.4"Size"Effects"...... "62!

5.3.5!PURE!MERGER!EFFECTS!...... !63!

5.4!SUMMARY!...... !64!

6)DISCUSSION)...... )65! 6.1!DATA!ENVELOPMENT!ANALYSIS!...... !65!

6.2!POSTJMERGER!ANALYSIS!...... !65!

6.3!SUMMARY!...... !69!

7)CONCLUSION)...... )71! 7.1!FURTHER!RESEARCH!...... !73!

8)LITERATURE)...... )74! 9)APPENDIX)...... )80! 9.1!ABBREVIATIONS!...... !80!

9.2!DATA!SAMPLES!...... !81!

9.3!RESULTS!FROM!R!SOFTWARE!...... !84!

9.4!MERGER!EFFECTS!...... !96!

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List)of)Figures)and)Tables) 1)INTRODUCTION)...... )6! TABLE!1.1!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS,!2009!...... !10!

TABLE!1.2!MEDICAL!DEPARTMENTS,!PREJ!AND!POSTJMERGER!...... !11!

2)LITERATURE)REVIEW)...... )13! 3)METHODOLOGY)...... )21! FIGURE!3.1!FREE!DISPOSABILITY!...... !23!

FIGURE!3.2!CONVEXITY!...... !23!

FIGURE!3.3!CONSTANT!RETURNS!TO!SCALE!...... !24!

FIGURE!3.4!NONJINCREASING!RETURNS!TO!SCALE!...... !24!

FIGURE!3.5!NONJDECREASING!RETURNS!TO!SCALE!...... !25!

FIGURE!3.6!ADDITIVITY!...... !25!

TABLE!3.7!DEA!MODEL!ASSUMPTIONS!...... !26!

FIGURE!3.8!DEA!MODELS!...... !27!

FIGURE!3.9!TOTAL!ECONOMIC!EFFECTS!...... !33!

FIGURE!3.10!LEARNING!EFFECTS!...... !33!

FIGURE!3.11!HARMONY!EFFECTS!...... !34!

FIGURE!3.12!SIZE!EFFECTS!...... !34!

4)DATA)...... )37! TABLE!4.1!DATA!SAMPLE!...... !37!

TABLE!4.2!DESCRIPTIVE!STATISTICS!FOR!DATA!SAMPLE!1!(2011!DRGJTARIFFS)!...... !38!

TABLE!4.3!DESCRIPTIVE!STATISTICS!FOR!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!(2011!DRGJTARIFFS)!.!40!

TABLE!4.4!DESCRIPTIVE!STATISTICS!FOR!DATA!SAMPLE!2!(2012!DRGJTARIFFS)!...... !42!

TABLE!4.5!DESCRIPTIVE!STATISTICS!FOR!DATA!SAMPLE!3!(POSTJMERGER)!...... !44!

5)ANALYSIS)...... )46! TABLE!5.1!HOSPITAL!EFFICIENCY!SCORES!(2011!DRGJTARIFFS)!...... !48!

TABLE!5.2!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!EFFICIENCIES!(2012!DRGJTARIFFS)!...... !49!

TABLE!5.3!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!SCALE!EFFICIENCIES!...... !49!

TABLE!5.4!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!PEER!UNITS!(2011!DRGJTARIFFS)!...... !50!

TABLE!5.5!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!PEER!UNITS!(2012!DRGJTARIFFS)!...... !51!

TABLE!5.6!STANDARD!ERROR!OF!THE!MEDIAN!AT!DIFFERENT!BOOTSTRAP!SAMPLES!B!...... !52!

TABLE!5.7!HOSPITAL!EFFICIENCIES,!BIASJCORRECTED!(2011!DRGJTARIFFS)!...... !53!

TABLE!5.8!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!EFFICIENCIES,!BIASJCORRECTED!(2012!DRGJTARIFFS) !...... !54!

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TABLE!5.9!CONFIDENCE!INTERVALS,!BIASJCORRECTED!HOSPITAL!EFFICIENCIES!...... !55!

TABLE!5.10!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!SCALE!EFFICIENCIES,!BIASJCORRECTED!...... !56!

TABLE!5.11!MERGER!ANALYSIS!CALCULATIONS!...... !57!

TABLE!5.13!CONFIDENCE!INTERVALS,!TOTAL!ECONOMIC!EFFECTS!AND!LEARNING!EFFECTS!...... !58!

TABLE!5.12!TOTAL!ECONOMIC!EFFECTS,!E!...... !58!

TABLE!5.14!LEARNING!EFFECTS,!LE!...... !59!

TABLE!5.15!CONFIDENCE!INTERVALS,!HARMONY!EFFECTS,!SIZE!EFFECTS!AND!PURE!MERGER!EFFECTS!...... !60!

TABLE!5.16!HARMONY!EFFECTS,!HA!...... !61!

TABLE!5.17!SIZE!EFFECTS,!SI!...... !62!

TABLE!5.18!PURE!MERGER!EFFECTS,!E*!...... !63!

6)DISCUSSION)...... )65! TABLE!6.1!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!EFFICIENCIES!(2012!DRGJTARIFFS)!...... !66!

TABLE!6.2!BISPEBJERG!AND!FREDERIKSBERG!HOSPITALS!EFFICIENCIES,!BIASJCORRECTED!(2012!DRGJTARIFFS) !...... !67!

TABLE!6.3!MERGER!EFFECTS!...... !68!

TABLE!6.4!MERGER!EFFECTS,!BIASJCORRECTED!...... !68!

TABLE!6.5!MERGER!EFFECTS,!CONFIDENCE!INTERVALS!...... !69!

7)CONCLUSION)...... )71! 8)LITERATURE)...... )74! 9)APPENDIX)...... )80! !

! 5! !

1)Introduction) A!functional!healthcare!system!is!undeniably!important!in!a!welfare!state,!socially!and!ecoJ nomically!(Acemoglu!&!Johnson!2006).!There!is!a!correlation!between!gross!domestic!product! (GDP)!per!capita!and!life!expectancy.!Countries!with!higher!GDP!per!capita!have!higher!life! expectancy!and!vice!versa!(Deaton!2003;!Becker!et!al.!2005).!Further,!improved!health!condiJ tions!and!higher!life!expectancy!result!in!additional!economic!growth.!Fogel!(2004)!concludes! that!approximately!50.0%!of!economic!growth!in!Great!Britain!since!1790!is!due!to!improving! health!conditions.! Since! the! early! 1990s,! life! expectancy! in! OECD1Jcountries! has! increased! by! one! year! every! four!years.!In!OECD!countries,!life!expectancy!at!birth!is!clearly!correlated!to!a!number!of!inJ dicators,!including!total!expenditure!on!health!per!capita!(OECD!2010).!! During! the! 1990s! the! average! total! health! expenditure! in! OECD! countries! increased! from! 7.3%!of!GDP!in!1990!to!8.4%!of!GDP!in!2001.!In!2011,!close!to!oneJthird!of!OECD!countries2! spend!more!than!10.0%!of!their!GDP!on!total!health!expenditure!and!the!average!total!health! expenditure!had!increased!to!9.3%!of!GDP!(Huber!&!Orosz!2003;!OECD!2013a).!! The!structure!of!the!healthcare!systems!varies!throughout!the!countries!in!OECD.!Böhm!et!al.! (2013)!classify!national!healthcare!systems!in!thirty!OECD!countries!based!on!regulation,!fiJ nancing!and!service!provision,!which!are!run!by!three!types!of!actors:!state,!societal,!and!priJ vate!actors.!The!thirty!countries!are!divided!into!five!healthcare!system!types3.!The!first!type! of!healthcare!systems!is!the!National!Health!Service!(NHS),!where!regulation,!financing!and! service!provision!are!governed!by!the!state.!We!find!the!NHS!healthcare!system!in!the!five! Nordic!countries,!the!two!Iberian!countries!and!the!United!Kingdom.!Like!the!NHS,!the!NaJ tional!Health!Insurance!(NHI)!healthcare!system!is!tax!financed!and!regulated!by!the!state.! However,!the!NHI!differentiates!as!service!provision!is!privately!run.!The!NHI!is!found!in!CanJ ada,!Australia,!New!Zealand,!Ireland!and!Italy.!Most!of!Europe’s!GermanJspeaking!countries4! rely!on!a!Social!Health!Insurance!(SHI)!healthcare!system.!This!third!type!of!healthcare!sysJ tem!is!financed!and!regulated!by!societal!actors,!while!service!provision!is!private.!The!fourth!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1!Organisation!for!Economic!CoJoperation!and!Development! 2!Data!from!the!Japan,!Australia!and!Mexico!refers!to!2010.!Data!from!Turkey!refers!to!2008.!! 3!According!to!Böhm!et!al.!(2013)!the!Slovenian!healthcare!system!is!a!SocialJbased!mixedJtype!system,!and! therefore!a!sixth!healthcare!system.!However,!they!find!this!system!implausible!and!indicate!that!Slovenia!is! evolving!into!a!Social!Health!Insurance!system.!The!socialJbased!mixedJtype!system!is!therefore!not!included.! 4!Social!Health!Insurance!countries!include!Austria,!Germany,!Luxembourg!and!Switzerland.!

! 6! !

healthcare! system! is! also! the! most! common! among! the! OECD! countries.! The! Etatist! Social! Health!Insurance!(ESHI)!is!a!mix!with!state!regulation,!financing!by!societal!actors!and!private! service!provision.!Böhm!et!al.!(2013)!find!that!the!ESHI!is!the!only!plausible!completely!mixed! healthcare!system.!The!ESHI!healthcare!system!is!found!in!eleven!of!the!thirty!OECD!counJ tries5.! As! the! only! remaining! OECD! country! the! United! States! use! a! Private! Health! System! (PHS).!Financing,!regulation!and!service!provision!are!all!handled!by!private!actors,!and!rely! on!market!mechanisms.!However,!the!deficiency!of!the!PHS!has!resulted!in!public!insurance! programmes!such!as!Medicaid!and!Medicare6.!With!the!introduction!of!the!Patient!Protection! and!Affordable!Care!Act,!also!known!as!Obamacare,!the!United!States!has!moved!closer!to!an! etatist!healthcare!system.!All!five!healthcare!systems!have!had!increasing!healthcare!expendiJ tures!during!the!last!decade.!Efficiency!estimates!vary!within!the!different!healthcare!systems,! and!there!is!no!superior!healthcare!system!(OECD!2010).!! ! 1.1)Public)healthcare)expenditure) The!growth!in!healthcare!expenditure!is!seen!as!one!of!the!largest!threats!to!public!finances!in! the!years!to!come.!The!upcoming!retirement!of!the!baby!boom!generation!of!1945J1965!will! result! in! further! increases! in! public! healthcare! expenditure! (Fogel! 2004;! Hagist! &! Kotlikoff! 2005).!However,!OECD!(2013b)!specify!that!of!the!average!4.3%!growth!in!public!health!exJ penditure!in!OECD!countries!from!1995!to!2009,!only!0.5%!was!due!to!demographic!effects.! The!expenditure!growth!due!to!income!effect!is!1.8%,!while!the!residual!expenditure!growth! is! 2.0%.! Likewise,! the! demographic! effect! is! questioned! by! Arnberg! &! Bjørner! (2010),! who! indicate!that!the!main!expense!is!terminal!costs!in!the!final!years!of!a!person’s!life.!A!higher! life!expectancy!merely!postpones!the!healthcare!expenditure.!Arnberg!&!Bjørner!(2010)!find! that!increasing!healthcare!expenditures!are!mainly!due!to!nonJdemographic!effects.! In!2013,!OECD!projected!increasing!public!healthcare!expenditure7!from!an!average!of!5.5%! of!GDP!in!2006J2010!to!between!7.9%!and!11.8%!of!GDP!in!2060.!Meanwhile,!projected!pubJ lic!healthcare!expenditures!for!BRIICS8!countries!increase!to!between!4.4%!and!8.3%!of!GDP!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5!Etatist!Social!Health!Insurance!countries!include!Belgium,!Czech!Republic,!Estonia,!France,!Hungary,!Israel,! Japan,!Korea,!Netherlands,!Poland!and!Slovakia.! 6!Medicaid!is!a!publicly!funding!social!health!insurance!for!people!with!limited!income.!Medicare!is!a!health!care! coverage!for!people!over!65!years.!The!state!covers!medical!expenses,!but!not!longJterm!care.!! 7!Projected!public!healthcare!cost!does!not!including!longJterm!care.! 8!BRIICS:!Brazil,!Russia,!India,!Indonesia,!China!and!South!Africa.!

! 7! !

in! 2060! from! an! average! of! 2.4%! of! GDP! in! 2006J2010! (OECD! 2013b).! Hagist! &! Kotlikoff! (2005)!show!that!public!healthcare!expenditure!in!the!United!States!could!rise!from!6.6%!of! GDP!in!2002!to!a!staggering!18.9%!of!GDP!in!2042.!The!public!healthcare!expenditures!mereJ ly!cover!the!projected!costs!of!Medicaid!and!Medicare.!! ! 1.2)The)Danish)healthcare)system) In!the!1980s!and!1990s,!the!Danish!healthcare!system!was!characterized!by!low!expenditure! growth!and!no!radical!reforms.!Total!healthcare!expenditures!declined!from!9.1%!of!GDP!in! 1980!to!8.3%!of!GDP!in!2000.!During!the!same!period,!the!average!total!healthcare!expendiJ tures!in!OECD!countries!increased!from!7.0%!to!8.4%!of!GDP.!As!mentioned!earlier,!the!DanJ ish!healthcare!system!is!publicly!administrated!in!regulation,!financing!and!service!provision.! Until!2007,!the!Danish!healthcare!sector!was!highly!decentralized!and!the!fourteen!counties! together! with! the! Copenhagen! Hospital! Corporation! were! politically,! financially! and! operaJ tionally! responsible.! In! 2007,! the! Structural! Reform! was! implemented! in! Denmark,! which! meant!an!increased!centralization,!as!the!central!government!wanted!more!uniformity!in!the! healthcare!sector.!The!fourteen!counties!and!the!Copenhagen!Hospital!Corporation!were!disJ solved!and!merged!into!five!regions!with!their!main!responsibility!being!service!provision!of! the!healthcare!sector.!The!Danish!healthcare!sector!is!mainly!financed!through!municipal!coJ payment! and! national! block! grants.! The! healthcare! sector! is! regulated! on! a! national! level,! which!means!that!the!regions!operate!within!a!fixed!budget!framework.!In!2011,!89.0%!of!all! medical!services!in!Denmark!were!publicly!paid.!The!five!regions!operate!all!public!hospitals,! and!the!number!of!private!hospitals!is!limited.!General!practitioners!are!selfJemployed!gateJ keepers!under!contract!with!the!regions!and!are!in!this!context!not!seen!as!private!providers! (Pedersen!et!al.!2005;!Huber!&!Orosz!2003).!However,!this!study!will!not!include!preJ!or!postJ treatments,!but!be!limited!to!the!economic!effect!at!hospitals.!All!Danish!private!hospitals!are! excluded!from!this!study,!as!they!only!handle!planned!treatments,!and!are!a!supplement!to! the!public!healthcare!system.!! ! In!2011,!the!total!Danish!healthcare!expenditure!rose!to!10.9%!of!GDP,!and!were!among!the! ten! highest! in! the! world! (OECD! 2013a).! The! increase! in! healthcare! expenditure! followed! a! decade! where! healthcare! had! become! a! political! focus.! Waiting! lists! were! brought! down! through!investments!and!the!already!exciting!free!choice!of!hospital!was!extended.!It!meant!

! 8! !

that!patients!could!now!freely!choose!hospitals!abroad!or!private!hospitals!if!waiting!lists!at! public!hospitals!exceeded!two!months!(Pedersen!et!al.!2005).!! The!Danish!Ministry!of!Health!introduced!a!caseJmix!system!in!2002.!A!caseJmix!system!had! already!been!used!since!1996!as!a!benchmarking!tool!to!compare!performance!at!Danish!hosJ pitals.!However,!the!new!caseJmix!system!is!used!for!payment!purposes.!It!was!supplementJ ing!the!free!choice!of!hospital!as!the!funding!was!now!based!on!the!diagnosis!and!therefore! following!the!patient.!Previously,!hospitals!had!been!fully!financed!by!state!block!grants.!DiJ agnosis!Related!Groups!(DRG)!was!introduced!for!inpatient!treatments,!while!the!Danish!AmJ bulatory!Grouping!System!(DAGS)!applied!to!all!outpatient!treatments.!Some!diagnoses!are! treated!either!as!inpatient!or!outpatient,!and!in!these!cases!grey!zone!DRG!are!used,!which!are! calculated!based!on!DRG!and!DAGSJtariffs9.!The!caseJmix!system!accounts!for!20.0%!of!the! hospitals’! budget,! while! the! remaining! 80.0%! still! comes! from! state! block! grants.! DRG! and! DAGS! were! introduced! as! an! incentive! for! hospitals! to! improve! productivity! and! efficiency! (AnkjærJJensen!et!al.!2006).!In!this!study,!we!use!the!terms!DRG!inpatient!and!DRG!outpatient! to!differentiate!between!inpatient!and!ambulant!treatments.!The!grey!zone!DRG!is!included!in! DRG!inpatient!and!DRG!outpatient.!! One!objective!of!the!Structural!Reform!in!2007!is!to!ensure!a!more!efficient!healthcare!system.! The! investment! in! fewer,! but! more! modern! hospitals! is! expected! to! generate! synergies! (Regeringen!2007).!OECD!(2010)!estimate!that!a!more!efficient!Danish!healthcare!system!reJ sult!in!potential!savings!equal!of!approximately!2.8%!of!GDP.!! ! 1.3)Bispebjerg)and)Frederiksberg)Hospitals) The!Capital!Region!of!Denmark!is!the!largest!of!the!five!Danish!regions,!in!terms!of!economy! and!population!(Region!Hovedstaden!2007;!Danske!Regioner!2011).!In!2011,!the!Capital!ReJ gion! of! Denmark! presented! Hospitalsplan! 2020! that! define! the! future! structure! for! the! reJ gion’s!hospitals.!The!purpose!was!to!ensure!higher!quality!in!the!treatments!by!bringing!toJ gether!medical!specialities!at!nine!hospitals!instead!of!the!existing!twelve!hospitals!(Region! Hovedstaden!2011).!One!of!the!two!mergers10!is!the!horizontal!merger!between!Bispebjerg!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

(! ×! )!(! ×! ) 9 ! ! ! ! !!! = ! ,!where!R!is!the!tariff!of!the!grey!zone!consisting!of!DRGi!and!DAGSj,!Ni!is!the!number!of!disJ !!!!! charges!in!DRGi,!Nj!is!the!number!of!visits!in!DAGSj,!Ri!is!the!tariff!for!DRGi,!Rj!is!the!tariff!for!DAGSj.! 10!Hillerød,!Frederikssund!and!Helsingør!Hospitals!also!merged!in!2012,!and!will!move!to!New!Hospital!North! Zealand,!which!is!a!Greenfield!hospital!scheduled!for!completion!in!2020.!Furthermore,!management!at!Amager!

! 9! !

and!Frederiksberg!Hospitals.!The!two!hospitals!merged!on!January!1st!2012,!but!treatments! remain!at!two!locations!until!the!construction!of!New!Bispebjerg!Hospital!is!completed11.!The! psychiatric!departments!at!Bispebjerg!and!Frederiksberg!Hospitals!also!merged!as!a!conseJ quence!of!Hospitalsplan!2020.!However,!this!study!will!be!limited!to!the!somatic!departments! of!the!two!hospitals.!In!the!Capital!Region!of!Denmark!the!somatic!and!psychiatric!hospitals! are!divided!in!terms!of!administration!and!economy.!! In!2009,!the!central!government!approved!plans!of!New!Bispebjerg!Hospital!as!a!Greenfield! hospital!to!service!Central!Copenhagen.!Bispebjerg!and!Frederiksberg!Hospitals!together!have! about!4,100!employees!and!an!annual!budget!close!to!2,150!million!Danish!kroner!(DKK).!As! seen!in!table!1.1,!Bispebjerg!Hospital!is!the!larger!of!the!two!hospitals!with!a!budget!almost! 2.5! times! greater! than! Frederiksberg! Hospital.! The! two! hospitals! service! approximately! 416,000!inhabitants,!and!had!more!than!61,000!discharges!and!315,000!outpatient!treatJ!

Table)1.1)Bispebjerg!and!Frederiksberg!Hospitals,!2009) ! Bispebjerg!Hospital! Frederiksberg!Hospital! Employees1!(fullJtime!equivalents)! 3,030! 1,134! Number!of!beds2! 510! 310! Outpatient!treatments3! 207,348! 108,509! Acute!treatments3! 44,693! 27,319! Discharged!patients3! 36,644! 24,588! Total!budget1!(in!1,000!DKK)! 1,510,711! 632,365! Total!result1!(in!1,000!DKK)! 1,491,574! 656,929! Excl.!research!funds! 1)"Source:"http://www.regionh.dk/NR/rdonlyres/D2C6E68EUF1C2U45BFUB5F2U3823A691E74B/0/Regnskab_2009.pdf" 2)"Source:"http://www.ssi.dk/Sundhedsdataogit/Dataformidling/Sundhedsdata/Sengepladser.aspx" 3)"Source:"http://www.ssi.dk/Sundhedsdataogit/Dataformidling/Sundhedsdata/Behandling%20ved%20sygehuse/U Sygehusaktivitet%20Offentlig%20og%20privat.aspx"

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! and!Hvidovre!Hospitals!merged!in!2012,!but!treatments!will!remain!at!the!two!hospitals!without!any!major! changes.! 11!New!Bispebjerg!Hospital!was!originally!scheduled!for!completion!in!2020.!This!is!now!postponed!to!2025.!

! 10! !

Table)1.2!Medical!Departments,!PreJ!and!PostJMerger) ! 20071! 20202! Bispebjerg! Frederiksberg! New!Bispebjerg! ! Hospital! Hospital! Hospital! Acute)Treatment! ! ! ! Joint!Emergency!Department! !! ! !! Emergency!Department! ! !! ! Internal)Medicine) ! ! ! Endocrinology! !! !! !! Gastroenterology! !! !! !! Cardiology! !★! !! !! Pulmonology! !! !! !"! Infectious!Disease! !! ! !! Geriatrics! !! !! !! Rheumatology! #! !! !"! Nephrology! ! ★! ! Surgical)Departments) ) ! ! ! Surgery! !! ! !"! Urology! ! $! ! Orthopaedic!Surgery! !! $! !"! Other)Clinical)Specialities/Units! ! ! ! Neurology! !! ! !"! Ophthalmology! ! $! ! Dermatology!&!Venereology! !"! ! !"! Occupational!and!Environmental!Medicine! !"! ! !"! Palliative!Unit! !! ! !! Dementia!Unit! !! ! !! Interdisciplinary)Specialities) ! ! ! Anaesthetics! !! $! !"! !!!Intensive!Care!Unit! !! ! !! Pathological!Anatomy!&!Cytology! !! ! #! Diagnostic!Radiology! !! $! !"! Clinical!Biochemistry! !! $! !"! Clinical!Microbiology! ! ! #! Clinical!Pharmacology! !! ! "! Clinical!Physiology!and!Nuclear!Medicine! !! !! !! Clinical!Immunology! !"! #! #! !!!!!!Main!Department! "!!!!Specialized!Department! # External!Unit! ★!!!!!Satellite!Unit! $!!!!!Elective!Unit!(daytime!only)! 1)"Source:"Hospitalsplan"2007,"Region"Hovedstaden" 2)"Source:"HospitalsU"og"Psykiatriplan"2020,"Region"Hovedstaden"

! 11! !

ments!in!2009!(Bispebjerg!og!Frederiksberg!Hospitaler!2012).! ! As!one!of!the!larger!hospital!in!the!Capital!Region!of!Denmark,!Bispebjerg!Hospital!has!a!wide! range! of! main! departments! and! specialized! departments.! The! specialized! department! also! treat!patients!from!outside!the!normal!catchment!area.!At!Frederiksberg!Hospital!a!range!of! elective! units! supplemented! the! main! departments.! These! elective! units! only! performed! planned!and!nonJacute!treatments!in!daytime.!In!addition!to!the!exciting!departments,!other! specialized!departments!will!be!established!at!New!Bispebjerg!Hospital!as!seen!in!table!1.2.! In!addition!to!higher!quality!in!treatments!and!more!specialized!departments,!the!Capital!ReJ gion!of!Denmark!finds!that!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!will! result!in!economies!of!scale!and!operational!optimization!of!resources!(Region!Hovedstaden! 2011).!! In!section!2,!we!present!similar!studies!within!the!field!of!hospital!mergers.!Based!on!the!litJ erature!review,!we!derive!four!hypotheses.!Section!3!introduces!the!methodological!frameJ work!of!the!merger!study.!We!utilize!Data!Envelopment!Analysis!(DEA)!to!estimate!the!preJ merger!efficiency!frontier!and!inferred!effects!of!the!merger!between!Bispebjerg!and!FrederJ iksberg!Hospitals.!In!section!4,!we!introduce!the!alternative!data!samples!that!consist!of!adJ justed!operational!costs!and!DRG!income!from!twentyJseven!Danish!public!hospitals.!We!anaJ lyse!the!preJmerger!efficiency!frontier!of!the!data!samples!in!section!5.!The!efficiency!scores! allow! us! to! estimate! the! total! economics! effects! of! the! merger.! These! are! decomposed! into! learning! effects,! harmony! effects! and! size! effects.! In! section! 6,! we! introduce! a! postJmerger! analysis!to!test!and!discuss!the!results!of!the!merger!analysis.!Final!conclusions!and!further! research!are!presented!in!section!7.!

! 12! !

2)Literature)Review) In!this!section,!we!build!the!theoretical!frame!for!the!empirical!work.!We!introduce!the!genJ eral!aspects!of!horizontal!mergers!before!introducing!the!studies!in!the!field!of!hospital!merJ gers.!A!limited!number!of!studies!deal!with!Danish!hospitals!mergers.!We!therefore!include! merger!studies!from!other!NHSJcountries!as!well!as!countries!with!other!healthcare!systems.! The!literature!is!divided!into!four!areas:!total!economic!effects,!learning!effects!(technical!effiJ ciency),!harmony!effects!(scope!economies)!and!size!effects!(scale!economies)12.!Based!on!the! four!merger!effects,!we!derive!four!hypotheses!to!guide!the!empirical!work.! ! 2.1)Horizontal)mergers) The!general!economic!literature!concur!that!horizontal!mergers!do!have!consequences!for!the! implicated!firms.!However,!it!is!unclear!if!a!horizontal!merger!will!result!in!gains!or!losses! (Farrell!&!Shapiro!1990;!Perry!&!Porter!1985;!Salant!et!al.!1983).!Salant!et!al.!(1983)!find!limJ ited!incentives!to!merge!in!a!Cournot!competition,!since!a!horizontal!merger!is!likely!to!deJ crease!profits!for!the!merging!firms.!The!only!profitable!merger!is!from!duopoly!to!monopoly.! Perry!&!Porter!(1985)!concur!with!Salant!et!al.,!and!find!that!a!horizontal!merger!in!Cournot! competition!increase!prices!and!lower!the!output!for!the!merging!firms.!Perry!&!Porter!indiJ cate!that!the!decrease!in!output!is!lower!than!stated!by!Salant!et!al.,!and!the!horizontal!merger! result!in!higher!profits.!Likewise,!the!competing!firms!will!benefit!from!the!rising!prices.!! Horizontal! mergers! in! Cournot! competition! potentially! lower! prices.! However,! Farrell! &! Shapiro! (1990)! find! that! large! economies! of! scale! or! learning! effects! are! required! to! lower! prices.! They! concur! that! horizontal! mergers! typically! result! in! higher! prices,! and! a! merger! that!creates!no!synergies!will!result!in!higher!prices.!Farrell!&!Shapiro!indicate!that!the!synerJ gies! of! a! merger! need! to! be! considerable! to! lower! prices.! Further,! the! higher! the! merging! firms’!market!share!is,!the!higher!the!economies!of!scale!or!learning!effects!need!to!be!to!genJ erate!the!lowering!in!prices.!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 12!The!terms!learning!effects!and!technical!efficiency!are!used!in!the!literature.!There!will!not!be!differentiated! between!the!two!terms,!and!will!used!throughout!this!study.!The!same!applies!to!harmony!effects!and!scope! economies,!and!to!size!effects!and!scale!economies.!

! 13! !

! 2.2)Hospital)Mergers) A! limited! number! of! studies! deal! with! the! economic! effects! of! Danish! hospital! mergers! (Kristensen!et!al.!2010).!Most!studies!deal!with!hospital!mergers!in!the!United!States,!but!this! section!will!include!studies!of!hospital!mergers!in!all!five!healthcare!systems.!As!with!the!genJ eral!economic!literature,!there!is!no!consensus!when!it!comes!to!the!potential!effects!of!hospiJ tal!mergers!(Preyra!&!Pink!2006;!Dranove!&!Lindrooth!2003;!Goddard!&!Ferguson!1997).! ! Many!of!the!studies!dealing!with!U.S.!hospital!mergers!examine!effect!of!prices.!Antitrust!adJ vocates!find!that!mergers!results!in!less!competition!and!higher!prices!for!the!consumer.!MerJ ger!advocates!find!that!the!potential!efficiency!gains!reduce!prices.!Connor!et!al.!(1998)!find! that!mergers!of!U.S.!hospitals!in!the!period!from!1986!to!1994!result!in!a!shift!away!from!nonJ competition! to! increasing! competition.! Using! HerfindahlJHirschman! Index! to! calculate! the! market!concentration!and!investigating!the!merger!effects!on!cost!and!price!inflation,!Connor! et!al.!find!that!horizontal!hospital!mergers!potentially!result!in!cost!savings!of!approximately! 5.0%.!Further,!they!find!that!cost!savings!are!higher!at!similarJsize!hospitals!and!at!hospitals! with!similar!service!provision.!! Dranove! (1998)! find! limitations! in! hospital! mergers.! Estimating! a! cost! function! at! fourteen! nonJrevenue! hospitals! found! that! there! are! substantial! economies! of! scale.! However,! these! economies!are!exhausted!at!hospitals!with!more!than!10,000!discharges!annually.!Aletras!et! al.!(1997)!compare!studies!of!the!optimal!number!of!beds,!and!find!that!the!most!productive! scale!size!is!between!200!and!620!beds.!The!mean!bed!size!and!the!most!productive!scale!size! differentiates!between!the!studies,!but!diseconomies!are!found!at!hospitals!below!200!beds! and!above!620!beds!(Aletras!et!al.!1997).!Kristensen!et!al.!(2012)!point!to!that!number!of!beds! is!a!questionable!measurement!for!hospitals,!as!increasingly!more!patients!are!treated!as!outJ patients.!In!Denmark,!the!number!of!beds!decreased!by!approximately!20.0%!between!1998! and! 2007.! New! Bispebjerg! Hospital! is! planned! to! have! 14.9%! fewer! beds! compared! to! Bispebjerg!and!Frederiksberg!Hospitals!combined!in!2009.!! Sinay! &! Campbell! (1995)! test! the! hypothesis! that! many! late! 1980s! hospital! mergers! in! the! United!States!were!an!attempt!to!improve!efficiency.!A!hybrid!translog!cost!function!estimate! economies!of!scale!and!scope!at!merging!hospital!and!control!hospitals.!The!study!finds!that! the! merging! hospitals! eliminate! diseconomies! by! lowering! output! to! more! efficient! levels.!

! 14! !

Economies!of!scope!are!visible!in!acute!and!subJacute!care!days!at!merging!hospitals.!Sinay!&! Campbell! find! scale! economies! at! control! hospitals! that! would! improve! efficiency! through! mergers.! Like!Sinay!and!Campbell,!Lynk!(1995)!tests!the!assumption!that!hospital!mergers!will!result! in!higher!efficiency.!Lynk!found!that!improved!efficiency!could!be!found!as!a!result!of!hospital! mergers.!E.g.!through!consolidations!of!clinics!would!improve!efficiency!since!the!cost!of!staffJ ing!for!peak!periods!is!now!reduced.! Harris!et!al.!(2000)!use!Data!Envelopment!Analysis!(DEA)!to!estimate!preJ!and!postJmerger! technical!efficiencies!at!hospitals.!This!study!use!data!from!U.S!hospitals!in!the!years!before! and!after!1990,!where!many!hospitals!were!forced!to!restructure!due!the!increasing!pressure! on!prices!(Sinay!&!Campbell!1995;!Harris!et!al.!2000).!Using!a!Constant!Returns!to!Scale!(CRS)! model!and!a!Variable!Returns!to!Scale!(VRS)!model,!Harris!et!al.!find!that!horizontal!mergers! do!result!in!a!reduction!of!input.!Scale!efficiency!is!the!overall!reason!for!this!improved!effiJ ciency!rather!than!technical!efficiency.!! Using!DEA,!Ferrier!&!Valdmanis!(2004)!find!that!efficiency!and!productivity!increase!on!U.S.! hospitals!that!merged!in!1997.!The!VRS!model!is!applied!on!preJ!and!postJmerger!data!from! 1996!to!1998.!Ferrier!&!Valdmanis!use!a!control!group!of!nonJmerging!hospitals!to!compare! the!results,!and!this!show!the!same!efficiency!and!productivity!gain!where!found!at!the!conJ trol!hospitals.!Ferrier!&!Valdmanis!conclude!that!mergers!do!not!lead!to!improving!efficiency! or!productivity.!! Dranove!and!Lindrooth!(2003)!define!a!merger!in!healthcare!as!the!combination!of!several! facility!licenses!into!a!single!license,!where!also!financial!reporting!is!consolidated.!This!difJ ferentiates!from!system!consolidation!as!in!Connor!et!al.!(1998).!Using!a!translog!cost!funcJ tion,!Dranove!&!Lindrooth!find!that!while!no!savings!are!generated!in!system!consolidations,! savings!of!approximately!14.0%!are!generated!two,!three!and!four!years!after!a!merger.! Harrison! (2011)! agrees! with! Connor! et! al.! and! Dranove! &! Lindrooth! that! hospital! mergers! generate!economic!gains.!In!the!years!following!a!merger!potential!cost!savings!are!found,!and! cost!savings!are!realized!by!the!involved!hospitals.!However,!Harrison!also!found!that!the!cost! savings!decline!a!few!years!after!the!merger.!Further,!the!proportion!of!hospitals!that!experiJ ence!cost!savings!decrease.!! Inspired!by!the!large!amount!of!hospital!mergers!in!the!United!States,!Preyra!&!Pink!(2006)! examine!the!economic!effects!of!hospital!mergers!in!the!Canadian!province!of!Ontario.!The!

! 15! !

restructuring! of! the! hospitals! in! Ontario! was! a! consequence! of! massive! funding! cuts! in! healthcare.!In!1996,!it!was!announced!that!15.0%!of!the!funding!was!cut!over!the!next!three! years.!It!was!expected!that!a!restructure!would!offset!large!efficiency!gains.!Preyra!&!Pink!find! potential!economies!of!scope!and!scale!in!the!Canadian!healthcare!system,!but!indicate!that! further!research!is!necessary!to!find!the!actual!economic!effects!of!the!hospital!restructuring! in!Ontario.!! ! Studies!of!hospital!mergers!in!NHSJcountries!are!as!inconclusive!as!the!literature!above.!AletJ ras!(1999)!find!neither!economies!or!diseconomies!in!the!Greek!healthcare!system.!Aletras! apply!a!shortJrun!cost!function!and!longJrun!cost!function!to!the!data!from!the!Greek!hospiJ tals.!Aletras!found!that!the!longJrun!cost!function!tended!to!indicate!trivial!economies!of!scale,! and!the!study!should!not!be!basis!for!policy!making.!The!potential!economic!gains!from!hospiJ tal!mergers!are!just!as!inconclusive!in!the!United!Kingdom!(Goddard!&!Ferguson!1997).!Like! Aletras,!also!Ferguson! &! Goddard!(1997)!find!it!worrying!that!policy!makers!view!hospital! mergers!as!way!to!a!achieve!cost!savings,!even!though!cost!reduction!from!mergers!are!unJ documented.!! Wagstaff!&!Lopez!(1996)!utilized!a!stochastic!frontier!analysis!(SFA)!to!examine!efficiency!at! 43!private!and!public!hospitals!in!Catalonia.!Even!though!none!of!the!hospitals!have!merged! or!plan!to!merge,!Wagstaff!&!Lopez!find!economies!of!scale!and!scope!in!all!hospitals.!The!five! public!hospitals!included!in!the!study!have!higher!inefficiency!levels!than!the!private!hospiJ tals.!Wagstaff!&!Lopez!find!that!it!is!mainly!due!to!the!higher!degree!of!freedom!at!private! hospitals!in!contracting!with!medical!and!nonJmedical!manpower.!! Using!DEA,!Kjekshus!&!Hagen!(2007)!compare!merged!and!nonJmerged!Norwegian!hospitals! in!short!and!medium!term.!A!CRS!model!is!applied!to!estimate!technical!efficiency!and!cost! efficiency.!Kjekshus!&!Hagen!find!increasing!costs!between!2.0%!and!2,8%!in!all!hospitals!exJ pect!one.!No!technical!efficiencies!are!found!as!a!result!of!the!mergers.!The!only!merger!that! result! in! cost! reduction! and! technical! efficiency! gains! is! a! consolidation! of! five! hospitals,! where!administration!and!acute!services!are!centralized.!The!result!is!significant!with!a!6.0%! gain!in!technical!efficiency!and!5.0%!cost!reduction.!! ! The!Danish!hospital!mergers!are!either!not!yet!fully!implemented!or!have!not!been!in!place! long!enough!to!measure!the!economic!gains.!The!literature!on!Danish!hospital!mergers!priJ

! 16! !

marily! estimates! the! potential! economic! effects! and! whether! the! mergers! should! be! impleJ mented.!! Based!on!data!from!2004,!Kristensen!et!al.!(2009)!find!economies!and!diseconomies!at!Danish! hospitals.!Using!SFA!to!estimate!the!potential!gains!at!thirtyJthree!Danish!hospital!units,!KrisJ tensen!et!al.!identify!economies!of!scale!and!scope!at!hospitals!with!less!than!200!beds.!At! hospitals!with!more!than!200!beds!economies!of!scale!and!diseconomies!of!scope!are!identiJ fied.!Kristensen!et!al.!(2009)!do!not!conclude!whether!Danish!hospitals!should!merger!or!not.! The!comparison!with!previous!international!merger!studies!makes!it!difficult!to!give!a!clear! conclusion!on!any!potential!economies!of!scale.!Further!research!is!needed!to!provide!a!clear! recommendation!and!Kristensen!et!al.!(2009)!suggest!the!use!of!alternative!methods,!e.g.!DEA.!! In!another!study!of!the!potential!effects!of!Danish!hospital!mergers,!DEA!is!applied!to!estimate! the!cost!frontier!(Kristensen!et!al.!2010).!A!nonJdecreasing!returns!to!scale!(NDRS)!model!and! a!variable!returns!to!scale!(VRS)!model!is!utilized!to!examine!the!potential!gains.!Kristensen!et! al.!(2010)!examine!five!potential!mergers!as!a!consequence!of!the!Structural!Reform!in!2007.! They!find!that!economic!gains!could!be!realized!from!learning!effects!and!harmony!effects,!but! indicate! that! the! merging! hospitals! become! too! large! and! will! experience! diseconomies! of! scale.!The!merging!hospitals!realize!higher!potential!gains!from!applying!best!practice!instead! of!a!fullJscale!merger.!! Using!a!quadratic!cost!function,!Kristensen!et!al.!(2012)!conclude!that!fewer!Danish!hospitals! could!result!in!higher!efficiency.!However,!Kristensen!et!al.!(2012)!indicate!that!postJmerger! studies!show!that!horizontal!integration!fails,!e.g.!in!the!United!States!and!the!United!KingJ dom.! Based!on!the!literature!review!four!hypotheses!are!derived.!Four!merger!effects!are!the!basis! of!the!derived!hypotheses.!First!of!all,!we!include!the!total!economic!effects!of!the!merger!beJ tween!Bispebjerg!and!Frederiksberg!Hospitals.!Further,!the!total!economic!effects!are!decomJ posed!into!learning!effects,!harmony!effects!and!size!effects.! ! 2.3)Hypothesis)1:)Total)Economic)Effects) In!all!five!healthcare!systems!the!economic!effects!of!hospital!mergers!are!inconclusive.!LikeJ wise,!the!merger!studies!based!on!DEA!derived!different!conclusions.!Harris!et!al.!(2000)!and! Kjekshus!&!Hagen!(2007)!find!no!economics!gains!from!hospital!mergers.!However,!Ferrier!&! Valdmanis! (2004)! find! scale! economies! at! merging! U.S.! hospitals.! Even! though! the! general!

! 17! !

literature!is!inconclusive!the!majority!of!Danish!studies!indicate!overall!economic!gains!from! hospital!mergers.!Bogetoft!(2012)!defines!the!total!economic!effects! !! !of!a!merger!J!is!a! function!of!learning!effects! !"! ,!harmony!effects! !"! !and!size!effects! !"! ,! ! !! = !"!!×!!"!!×!!"!! ! In!Kristensen!et!al.!(2010)!the!majority!of!the!potential!mergers!indicate!potential!cost!reducJ tions.! The! total! size! of! Bispebjerg! and! Frederiksberg! Hospitals! potentially! generates! scale! economies.!However,!the!literature!indicates!that!learning!effects!will!ensure!an!overall!ecoJ nomic!gain!from!the!merger.!Based!on!these!studies,!the!first!hypothesis!is:! ! ! The"merger"between"Bispebjerg"and"Frederiksberg"Hospitals"will"result"in"cost"reductions" from"total"economic"effects." ! 2.4)Hypothesis)2:)Learning)Effects) As!concluded!by!Farrell!&!Shapiro!(1990),!large!gains!from!learning!effects!are!necessary!to! ensure!an!overall!economic!gain!from!mergers.!The!literature!shows!that!there!are!potential! gains!to!be!found!from!learning!effects!or!technical!efficiency.!Varabyova!&!Schreyögg!(2013)! conclude!that!countries!with!higher!healthcare!cost!per!capita!have!lower!potential!technical! efficiency!gains.!However,!the!potential!gains!are!estimated!to!be!approximately!5.0J10.0%!in! the!Danish!healthcare!system.!Even!though!Kjekshus!&!Hagen!(2007)!find!no!technical!effiJ ciency!from!Norwegian!hospital!mergers,!the!results!in!Kristensen!et!al.!(2010)!indicate!sigJ nificant!economic!gains.!The!VRS!model!displays!cost!reductions!from!mean!learning!effects! of!12.7%!in!the!uncorrected!data!sample!and!20.9%!in!the!biasJcorrected!data!sample.!The! NDRS!model!indicates!similar!results!with!mean!cost!reductions!of!14.9%!and!21.4%,!respecJ tively.!Learning!effects!indicate!the!potential!economic!gains!that!can!be!realized!if!hospitals! remain! independent! and! apply! best! practice.! Based! on! the! literature! the! second! of! the! hyJ potheses!is:! ! The"merger"between"Bispebjerg"and"Frederiksberg"Hospitals"will"result"in"cost"reductions" from"learning"effects."" !

! 18! !

2.5)Hypothesis)3:)Harmony)Effects) The! harmony! effects! or! scope! economies! are! an! essential! part! of! realizing! cost! reductions! from!a!merger.!Dranove!&!Lindrooth!(2003)!conclude!that!the!degree!of!mergers!differentiJ ates.!Mergers!where!e.g.!administration!and!acute!services!merge!result!in!scope!economies.! Connor,!Feldman!&!Dowd!(1998)!concluded!that!similarJsize!hospitals!and!similarity!in!serJ vice!provision!increase!the!economic!gains!from!mergers.!Bispebjerg!Hospital!is!significantly! larger!than!Frederiksberg!Hospital,!but!we!find!a!number!of!similar!medical!departments,!as! shown!in!table!1.2.!! In!Kristensen!et!al.!(2010)!mean!harmony!effects!between!0.6%!and!1.4%!are!found!at!potenJ tial!mergers!of!Danish!hospitals.!Likewise,!Kristensen!et!al.!(2012)!find!potential!economies!of! scope!in!Danish!hospital!mergers.!Based!on!these!studies,!the!third!hypothesis!is:! ! The"merger"between"Bispebjerg"and"Frederiksberg"Hospitals"will"result"in"cost"reductions" from"harmony"effects."" ! 2.6)Hypothesis)4:)Size)Effects) The!literature!shows!that!size!affect!the!potential!gains!from!mergers.!Smaller!hospitals!have! higher!economic!gains!from!mergers,!while!economic!gains!are!lower!at!larger!hospitals.!The! optimal!number!of!beds!or!most!productive!scale!size!differentiates,!but!diseconomies!of!scale! are!identified!at!hospitals!with!more!than!620!beds.!With!a!planned!capacity!of!675!beds,!New! Bispebjerg!Hospital!will!exceed!this!number!of!beds.!Kristensen!et!al.!(2010)!support!this,!as! efficiency!gains!from!size!effects!are!found!at!the!three!potential!hospital!mergers!with!less! than!620!beds!combined.!Meanwhile!the!two!potential!hospital!mergers!with!more!than!620! beds!combined!shows!increasing!costs!of!9.4%!and!12.2%!as!result!of!size!effects.!In!2009,! more!than!61,000!patients!were!discharged!at!Bispebjerg!and!Frederiksberg!Hospitals!,!which! indicates! potential! diseconomies! according! to! the! results! in! Dranove! (1998).! Based! on! the! literature,!the!fourth!and!final!hypothesis!is:!! ! The"merger"between"Bispebjerg"and"Frederiksberg"Hospitals"will"not"result"in"cost"reducU tions"from"size"effects." " !

! 19! !

2.7)Summary) We!find!that!the!studies!within!the!field!of!hospital!merger!are!inconclusive!on!the!economic! effects!of!a!merger.!As!the!number!of!studies!on!Danish!hospital!mergers!is!limited!we!include! studies!from!all!five!healthcare!system.!Four!hypotheses!are!derived!based!on!total!economic! effects,!learning!effects,!harmony!effects!and!size!effects.!In!the!following!section,!we!introJ duce!the!methodology!utilized!to!confirm!or!refute!the!four!hypotheses.!

! 20! !

3)Methodology) As!indicated!in!the!literature!review,!data!envelopment!analysis!(DEA)!is!a!commonly!applied! method! in! studies! of! hospital! mergers.! This! nonparametric! method! use! mathematical! proJ gramming! methods,! and! in! this! study! we! use! DEA! to! analyse! the! effects! of! the! merger! beJ tween!Bispebjerg!and!Frederiksberg!Hospitals!(Charnes!et!al.!1994;!Bogetoft!2012).!In!this! section!we!introduce!DEA!and!the!different!underlying!models!and!their!restrictions.!We!utiJ lize!DEA!to!estimate!the!minimal!input!of!producing!an!output.!The!input!variable!is!the!adJ justed!operational!costs!of!Danish!hospitals!and!the!two!output!variables!consist!of!DRG!inJ come!from!inpatient!treatments!and!outpatient!treatments.!This!will!be!elaborated!in!section! 4.1.!Based!on!the!cost!function,!we!estimate!efficiencies!and!gains!of!the!merger!in!terms!of! total!economic!effects,!learning!effects,!harmony!effects!and!size!effects.!The!bootstrap!methJ od! will! be! introduced! to! biasJcorrect! the! alternative! data! sample! using! R! software! package! Benchmarking.!! ! 3.1)Data)Envelopment)Analysis) Charnes!et!al.!(1978)!introduce!the!basics!of!DEA,!which!is!originally!a!tool!for!efficiency!analJ ysis!of!public!sector!entities.!Through!the!usage!of!mathematical!programming!methods,!DEA! estimates!efficiency!frontiers!and!best!practice!frontiers!between!different!entities.!These!enJ tities!are!typically!referred!to!as!decisionJmaking!units!(DMUs)!in!the!DEA!literature,!as!they! choose!their!own!production!plan!(Bogetoft!2012).!However,!we!will!refer!to!these!DMUs!as! firms!or!hospitals.!! DEA!is!a!nonparametric!approach!and!differentiates!from!parametric!approaches!by!focusing! on! the! performance! measure! of! the! individual! firms.! Where! a! single! optimized! regression! equation!applies!to!all!firms!as!an!average,!DEA!creates!a!best!practice!frontier!based!on!the! ParetoJefficient!firms.!As!the!true!production!plan!!!of!a!firm!is!unknown,!DEA!help!to!estiJ mate!a!substituted!production!plan!or!technology!set!!∗!based!on!historical!data.!Another!difJ ference! between! the! two! approaches! is! the! utilization! of! a! functional! form.! The! parametric! approach!uses!a!functional!form!to!relate!the!independent!variable!to!the!dependent!variable.! Further,! the! functional! form! requires! specific! assumptions! about! the! distribution! of! error! terms!and!other!restrictions.!DEA!does!not!require!the!same!functional!form!and!the!included! assumptions.! A! maximal! performance! measure! is! based! on! the! performance! of! the! other!

! 21! !

firms,! and! the! only! requirement! is! that! the! firm! is! located! below! the! efficiency! frontier! (Charnes!et!al.!1994).!! DEA!builds!on!Farrell!efficiency,!where!technical!efficiency!of!firm!!!is!measured!and!comJ pared! to! a! sample! of! firms! !! in! the! industry.! Farrell! efficiency! is! the! single! most! used! apJ proach! for! measuring! the! degree! of! efficiency! (Charnes! et! al.! 1978;! Bogetoft! 2012).! Farrell! (1957)!compares!a!firm’s!actual!input!with!the!minimal!input!to!estimate!the!technical!effiJ ciency.!The!purpose!is!to!reduce!a!firm’s!input!without!a!change!in!output!(input!efficiency!E),! or!to!increase!the!output!with!the!same!amount!of!input!(output!efficiency!F).!Bogetoft!(2012)! defines!input!efficiency!and!output!efficiency!as,!! ! ! = !"#$$%&'!!!!"#ℎ!!ℎ!"!!!!!!"!!"#$!!"!!"#$%&'!!"#$"#!!!! ! = !"#$%&'!!!!"#ℎ!!ℎ!"!!!!!"#!!"#$%&'!!"#$"#!!!!! ! If!! < 1!the!firm!is!not!fully!efficient!and!would!benefit!from!adopting!the!same!production! plan!as!the!more!efficient!firms.!Likewise,!if!! > 1!the!firm!could!produce!more!output!with! their!current!input.!Danish!hospitals!aim!to!reduce!input!costs,!and!the!focus!of!this!study!will! therefore!be!the!estimation!of!!.!The!firm!can!change!the!production!plan!to!become!more! efficient!within!the!feasible!combinations!of!inputs!and!outputs,!as!previously!referred!to!as! the! technology! set! T.! Bogetoft! (2012)! expands! the! technology! set! by! adding! reasonable! asJ sumptions.!These!are!free!disposability,!convexity,!scaling!and!additivity,!and!will!be!elaboJ rated!below.! We!utilize!DEA!to!calculate!a!cost!function!for!the!Danish!hospitals!!!that!use!the!minimal! amount!of!input!(!!, … , !!)!to!produce!multiple!outputs!(!!, … , !!).!This!cost!function!is!used! to! estimate! total! economic! effects,! learning! effects,! harmony! effects! and! size! effects! of! the! merger.!! ! 3.1.1)Free)Disposability) The! first! of! the! assumptions! is! the! possibility! to! dispose! of! unwanted! input! and! output! for! free.!Meaning!it!is!possible!to!produce!less!output!with!the!same!amount!of!input!and!to!use! more!input!to!produce!the!same!amount!of!output.!A!firm!will!of!course!not!pursue!this,!but!it! remains!a!technological!possibility.!It!is!be!useful!for!a!firm!that!wants!to!reduce!an!unattracJ tive!output.!For!a!hospital,!this!could!be!the!total!number!of!days!that!patients!are!admitted.!

! 22! !

Figure)3.1)Free!Disposability) ! Figure)3.2)Convexity) !

y y (x3 ,y3 ) ! (x2 ,y2 ) 4 4

2 2 (x ,y ) (x ,y ) ! ! 1 1 ! 1 1 ! (x ,y ) (x ,y )! ! ! ! ! ! ! x x ! ! Source:!Performance!Benchmarking,!Measuring!and!ManJ ! Source:!Performance!Benchmarking,!Measuring!and!ManJ aging!Performance!(Bogetoft!2012)! aging!Performance!(Bogetoft!2012)!

In!DEA!literature,!a!technology!based!on!a!set!of!observation!and!free!disposability!is!called! free!disposable!hull!(FDH).!In!figure!3.1,!the!technology!set!of!free!disposability!is!illustrated! with!four!different!production!plans!(!!, !!),!(!!, !!),! !!, !! !and!(!!, !!).!The!feasible!inputJ output!combinations!are!inside!the!shaded!area,!and!the!(x4,!y4)!production!plan!is!only!possiJ ble!due!to!the!assumption!of!free!disposability!(Bogetoft!2012).!! ) 3.1.2)Convexity) In!an!analysis!with!few!observations,!convexity!is!a!way!to!enlarge!the!technology.!All!classical! DEA!models!assume!convexity.!This!assumption!makes!it!feasible!to!take!a!weighted!average! of! two! production! plans,! e.g.! !! + !! ! and! !! + !! .! This! convex! combination! use! the! weights!!!and!1 − !,!where!0! < !! < 1,!! ! 1 − ! !!, !! + !(!!, !!)! ! As!seen!in!figure!3.2,!all!points!between! !! + !! !and! !! + !! !are!feasible.!Bogetoft!(2012)! indicate!that!convexity!makes!it!possible!to!rely!on!fewer!observations,!and!still!be!able!to! conclude!whether!a!firm!is!fully!efficient.!It!is!difficult!for!an!inefficient!firm!to!find!a!fully!effiJ cient!peer!unit,!as!it!might!not!be!a!real!observation,!but!merely!a!result!of!the!assumption.!In! figure! 3.2,! we! see! how! convexity! enhance! the! shaded! area! and! thereby! also! the! number! of! feasible!inputJoutput!combinations.!Convexity!is!defined!as!a!strong!assumption!with!a!large! potential! impact.! Due! to! this! large! potential! impact! convexity! is! debated! among! DEA! reJ

! 23! !

searchers.! Convexity! is! important! in! economics,! as! it! is! useful! to! examine! market! systems! based!on!prices.!Further,!it!is!argued!that!convexity!occurs!naturally!if!different!processes!are! available,!and!the!firm!can!regulate!time!consumption!and!resources!allocated!for!the!differJ ent!processes!(Bogetoft!2012).!This!is!applicable!for!hospitals,!where!treatments!consist!of! different!processes!and!especially!nonJacute!treatments!are!regulated.!Furthermore,!convexiJ ty!is!a!useful!assumption!in!data!samples!with!firms!consisting!of!subunits,!like!hospital!deJ partments.!The!convexity!assumption!is!questioned,!as!it!does!not!take!into!account!any!poJ tential!economies!of!scale!or!scope.!Additionally,!convexity!requires!divisibility!that!might!not! be! reasonable! to! assume! when! setJup! times! and! switching! costs! is! considered! (Bogetoft! 2012).!Variable!returns!to!scale!(VRS)!combines!free!disposability!and!convexity,!as!seen!in! figure!3.8.! ! 3.1.3)Scaling) The!assumption!of!scaling!is!divided!into!three!returns!to!scale!models;!constant!returns!to! scale! (CRS),! nonJincreasing! returns! to! scale! (NIRS)! and! nonJdecreasing! returns! to! scale! (NDRS).!The!three!returns!to!scale!models!agree!that,! ! !, ! !!"!!"#$%&'"! ⇒ !", !" !!"!!"#$%&'")! ! The! three! returns! to! scale! models! differentiate! on! the! value! of! !.! The! CRS! model! uses! any! !! ≥ 0,!and!as!seen!in!figure!3.3!it!means!that!any!point!between!(!, !)!and!(0,0)!is!feasible.!

Figure)3.3)Constant!Returns!to!Scale) ! Figure)3.4)NonJIncreasing!Returns!to!Scale)

y ! y

! ! ! ! ! ! ! !

x x ! ! Source:!Performance!Benchmarking,!Measuring!and!ManJ ! Source:!Performance!Benchmarking,!Measuring!and!ManJ aging!Performance!(Bogetoft!2012)! aging!Performance!(Bogetoft!2012)!

! 24! !

Figure)3.5)NonJDecreasing!Returns!to!Scale) ! Figure)3.6)Additivity) ! y y 2a ! ! a"+"b ! ! a ! ! 2b! ! b x x ! ! Source:!Performance!Benchmarking,!Measuring!and!ManJ ! Source:!Performance!Benchmarking,!Measuring!and!ManJ aging!Performance!(Bogetoft!2012)! aging!Performance!(Bogetoft!2012)!

Additionally,!the!CRS!model!assumes!free!disposability!as!indicated!by!the!shaded!area!in!figJ ure!3.3.!The!NIRS!model!assumes!the!possibility!of!scaling!down!and!not!up,!which!means!that! 0! ≤ !! ≤ 1.!Conversely,!the!NDRS!model!assumes!! ≥ 1!and!focus!on!scaling!up!the!producJ tion!plan!(Banker!1984;!Bogetoft!2012).!! Bogetoft!(2012)!argues!that!the!NIRS!model!is!found!if!firms!can!reduces!production!speed,! capacity!or!time!consumption.!The!NIRS!model!means!that!output!increase!less!than!the!input! making!it!possible!to!scale!down!production,!but!not!scale!up.! The!NDRS!model!implies!that!output!increase!more!than!input,!as!the!firm!will!benefit!from! i.e.!better!utilization!of!specialization!and!fixed!costs.!Danish!hospitals!cannot!downscale!proJ duction!by!rejecting!treatment!of!patients,!or!quickly!reduce!staff!in!periods!with!fewer!paJ tients.!Furthermore,!as!Danish!hospitals!have!an!incentive!to!produce!more!than!budgeted!in! terms!of!additional!DRGJincome,!NDRS!is!the!most!applicable!for!this!study!of!hospital!merJ gers.!! The!NIRS!and!NDRS!models!are!referred!to!as!decreasing!returns!to!scale!(DRS)!and!increasJ ing!returns!to!scale!(IRS),!respectively.!Bogetoft!(2012)!argues!that!the!terms!DRS!and!IRS!are! less!precise.!However,!as!these!terms!are!utilized!in!R!software!we!will!not!differentiate!beJ tween!NIRS!and!DRS!or!between!NDRS!and!IRS!in!this!study.!! !

! 25! !

3.1.4)Additivity) The!last!of!the!four!assumptions!is!additivity,!where!two!production!plans!are!combined!into! one.!If!two!productions!are!feasible!individually,!then!the!sum!of!the!two!is!also!feasible,!exJ pressed!as,! ! !!, !! !!"#! !!, !! !!"#$%&'"! ⇒ !! + !!, !! + !! !!"#$%&'"!! ! Figure!3.6!indicates!how!two!production!plans!!!and!!!can!be!combined!into!three!feasible! production!plans!2!,!2!!and!! + !.!Furthermore,!other!feasible!production!plans!are!! + 2!,! ! + 2!,!et!cetera.!The!assumption!of!additivity!means!that!two!firms!with!different!production! lines!can!be!combined,!and!additivity!rules!out!any!positive!or!negative!externalities!between! two!productions!lines!(Bogetoft!2012).!The!DEA!model!assuming!free!disposability!and!addiJ tivity!is!entitled!free!replicability!hull!(FRH).!! ! 3.1.5)DEA)Models) Based!on!free!disposability,!convexity,!scaling!and!additivity!six!DEA!models!are!presented!in! table! 3.7.! All! DEA! models! intend! to! estimate! the! unknown! technology! set! !! for! a! group! of! firms,!and!the!models!only!differentiate!in!the!applied!assumptions.!! ! Bogetoft!(2012)!refers!to!this!estimate!of!the!technology!!!as!the!empirical!reference!technolJ ogy!!∗,!which!is!created!according!the!minimal!extrapolation!principle.!Bogetoft!(2012)!deJ fines! the! minimal! extrapolation! principle! as! the! smallest! set! of! inputJoutput! combinations! that!contains!data!from!different!firms!and!satisfying!certain!assumptions!specific!to!the!given!

Table)3.7)DEA!Model!Assumptions) Model) Free)disposability) Convexity) Scaling) Additivity) FDH! ✔! ! ! ! VRS! ✔! ✔! ! ! NIRS!(DRS)! ✔! ✔! Down! ! NDRS!(IRS)! ✔! ✔! Up! ! CRS! ✔! ✔! Any! ! FRH! ✔! ! ! ✔! Source:!Performance!Benchmarking,!Measuring!and!Managing!Performance!(Bogetoft!2012)!

! 26! !

Figure)3.8)DEA!Models) ! y y FDH VRS C C ! B ! ! B ! ! ! ! ! D D ! E ! E A A

x x ! ! ! y y

NIRS NDRS ! C C ! B B

! ! !

D ! D ! ! E E A A x x ! ! ! y y CRS FRH C ! ! ! ! C B B ! ! ! ! ! ! D ! D E

E ! ! ! A A ! x x ! ! Source:!Performance!Benchmarking,!Measuring!and!Managing!Performance!(Bogetoft!2012)! approach.!The!reason!for!using!the!smallest!possible!set!is!to!ensure!that!the!firms!are!evalu! in!the!most!conservative!way.!It!is!important!when!using!DEA!that!there!is!no!noise!in!the!daJ ta.!This!could!result!in!an!unrealistic!estimate!of!the!empirical!reference!technology!!∗,!which! would!make!the!involved!firms!look!more!inefficient!than!they!actually!are.!FDH!is!the!smallJ est!technology!set!of!the!six!DEA!models!in!table!3.7.!Due!to!the!assumption!of!convexity,!VRS! is!marginally!larger!than!FDH.!The!assumption!of!scaling!further!enlarges!the!technology!set! of!NIRS!and!NDRS.!Lastly,!CRS!is!the!largest!of!the!DEA!models.!Bogetoft!(2012)!argues!that!

! 27! !

FRH!is!comparable!to!the!other!DEA!models,!but!is!larger!than!FDH!and!smaller!than!CRS.!The! six!DEA!models!are!graphically!illustrated!in!figure!3.8.! ! The!data!samples!utilized!in!this!study!are!too!small!to!circumvent!the!assumption!of!convexiJ ty.!FDH!and!FRH!are!therefore!excluded!in!the!analysis!of!the!potential!effects!of!the!merger! between!Bispebjerg!and!Frederiksberg!Hospitals.!This!leaves!the!VRS!model!as!the!smallest! technology!set,!and!this!model!will!therefore!be!utilized!in!this!study.!Further,!NDRS!is!includJ ed!in!the!analysis!due!to!the!arguments!presented!in!section!3.1.3.!As!mentioned!in!section!2,! the!VRS!model!was!applied!by!Harris!et!al.!(2000),!Kjekshus!&!Hagen!(2007)!and!Kristensen! et!al.!(2010).!The!latter!also!apply!the!NDRS!model!in!their!analysis!of!potential!gains!from! hospital!mergers.!! ) 3.1.5.1)Variable)Returns)to)Scale)and)Non^Decreasing)Returns)to)Scale) As! seen! in! Figure! 3.8,! the! VRS! model! is! the! lowest! of! the! convexityJassuming! DEA! models.! Kristensen!et!al.!(2010)!express!the!cost!function!utilized!to!calculate!the!efficiency!scores!of! firm!!!in!a!VRS!model!as! ! ! ! ! = !"#!,!!! !. !.! ! !!!! − ! ≤ 0! !!! ! !!!! − !! ≥ 0! !!! ! !! = 1! !!! ! The!cost!function!utilized!under!NDRS!technology!is!very!similar!to!the!cost!function!under! ! ! VRS!technology.!However,!as!seen!below,!it!differentiates!by! !!! ! !equalling!1!or!above!opJ ! ! posite!under!VRS!technology,!where! !!! ! !equals!1.! ! ! ! ! = !"#!,!!!

! 28! !

!. !.! ! !!!! − ! ≤ 0! !!! ! !!!! − !! ≥ 0! !!! ! !! ≥ 1! !!! ! The! difference! between! the! two! DEA! models! means! that,! whereas! there! might! be! disadJ vantages!of!being!either!too!small!or!too!large!in!the!VRS!model,!there!are!no!disadvantages!of! being!too!large!in!the!NDRS!model.!However,!there!might!still!be!disadvantages!of!being!too! small!in!the!NDRS!model!(Kristensen!et!al.!2010).!! ! 3.1.6)Peer)Units) Based!on!efficiency!scores,!we!analyse!peer!weights!under!VRS!and!NDRS!technologies.!Peer! weights! indicate! the! peer! units! for! inefficient! firms.! To! ensure! cost! savings! the! inefficient! firms!should!look!their!peer!unit!for!a!more!efficient!production!plan.!A!peer!unit!is!defined,! as! a! real! firm! situated! at! the! efficiency! frontier! that! the! evaluated! firm! is! projected! onto! (Bogetoft!2012).!We!use!the!efficiency!level!!!of!firm!!!to!estimate!the!peer!weights!!!.! ) min !!! !. !.! !!!×!!! ≥ ! !!, … , !!! !! ≤ ! !!, … . , !!! !! ≥ 0, … , !! ≥ 0, !! ! ≥ 0! ! An!inefficient!firm!may!have!more!than!one!peer!unit.!However,!the!maximum!number!of!peer! units!under!VRS!and!NDRS!technologies!are!restricted!to!! + !,!where!!!is!the!number!of!inJ puts,!and!!!is!the!number!of!outputs.!! !

! 29! !

3.1.7)Scale)Efficiencies) For!some!inefficient!firms!the!inefficiency!is!due!to!scale.!Using!the!different!DEA!models!it!is! possible!to!estimate!how!far!the!firm!is!from!the!most!productive!scale!size.!Bogetoft!(2012)! defines!scale!efficiency!!"!as,! ! !"#$!!"!!"#!!"#$% !!"# !" = ! = ! !"#$!!"!!"#!!"#$% !!"# !. !.! !"! ≤ 1! ! The!higher!the!value!of!!",!the!closer!the!firm!is!to!the!most!productive!scale!size.!Whether! the!firm!is!below!or!above!the!most!productive!scale!size!are!determined!by!including!NDRS! and!NIRS!model!efficiency!scores.!If!the!latter!coincide!with!the!CRS!model!efficiency!score!the! firm!is!below!the!optimal!scale!size.!Likewise,!if!the!NIRS!model!efficiency!score!coincide!with! the!VRS!model!the!firm!is!above!the!optimal!scale!size!(Bogetoft!2012).! ! 3.1.8)Limitations)of)DEA) Newhouse!(1994)!presents!a!series!of!generic!problems!in!utilizing!DEA!to!estimate!cost!funcJ tions!in!the!healthcare!sector.!Newhouse!(1994)!states!that!the!necessary!inputs!are!not!alJ ways!included!in!the!analysis!of!hospitals.!If!inputs!such!as!capital!inputs!or!physician!inputs! are!not!included!in!the!data!sample,!it!results!in!imprecise!estimates!of!the!hospitals!efficienJ cies.!The!same!applies!to!the!outputs,!where!the!registration!of!DRGJtariffs,!even!at!diagnosis! level,!may!vary!between!hospitals.!In!this!study!we!offset!some!of!the!problems!by!utilizing! prices!instead!of!quantities!in!input!and!output!variables.!Further,!adjustments!of!the!operaJ tional! costs! are! made! to! ensure! comparability! between! the! Danish! hospitals.! This! will! be! elaborated!in!the!section!4.1.! Another!generic!problem!of!DEA!is!the!nonJtestable!assumptions.!These!are!necessary,!as!no! measurement! errors! are! assumed! in! this! method! (Newhouse! 1994).! As! mentioned! above,! noise!in!the!data!sample!will!have!significant!effect!on!the!efficiency!frontier!making!the!inefJ ficiency!estimate!inaccurate.!Additionally,!Kristensen!et!al.!(2010)!argue!that!DEA!models!sufJ fer!more!from!bias.!It!is!therefore!necessary!to!biasJcorrect!the!data!sample.!This!study!will! utilize!the!R!software!package!Benchmarking!by!Bogetoft!&!Otto!(2011)!for!bootstrapping.!!

! 30! !

3.1.9)Bootstrapping) Efron!(1977)!introduced!the!bootstrap!method,!which!later!is!applied!to!DEA.!We!apply!the! bootstrap!method!for!biasJcorrecting!DEA!analysis!introduced!by!Bogetoft!&!Otto!(2011).!The! bootstrap!serves!as!a!statistical!method!to!set!up!a!new!“random”!data!sample!based!on!the! observations!in!the!original!data!sample.!Likewise,!the!new!data!sample!consists!of!the!same! number!of!observations!!!as!the!original!data!sample,!and!is!utilized!to!derive!the!necessary! statistics,!e.g.!median!of!the!bootstrap!sample.!These!statistics!are!called!replicates,!and!the! process!is!repeated!to!create!a!sufficient!sample!of!replicates.!The!sufficient!number!of!bootJ strap!replicates!will!be!introduced!below.!! ! 3.1.9.1)How)many)Bootstraps) The!number!of!bootstrap!replicates!!!used!in!an!analysis!will!influence!the!results.!Davidson! &! Mackinnon! (2001)! indicate! that! the! optimal! number! of! bootstrap! replicates! would! be! ! → ∞.!However,!as!this!is!not!possible,!we!introduce!a!method!to!estimate!a!finite!number!of! bootstraps!with!a!low!loss!of!power.!! Bogetoft!&!Otto!(2011)!use!the!standard!error!of!the!median!to!clarify!an!optimal!number!of! bootstrap!replicates.!Nine!different!bootstrap!samples!!,!where!10 ≤ ! ≤ 1,000,000!are!used! to! calculate! the! standard! error! of! the! median! of! a! data! sample.! This! calculation! is! run! four! times! with! changing! outcomes! in! terms! of! the! standard! errors! of! the! median.! The! results! clearly! indicate! that! a! larger! bootstrap! sample! results! in! a! smaller! difference! between! the! standard!errors!of!the!median.!In!the!general!literature!a!bootstrap!sample!between!50!and! 200!is!a!good!standard!error!estimator.!Bogetoft!&!Otto!(2011)!indicate!that!this!is!not!suffiJ cient!when!utilizing!the!bootstrap!method!in!DEA.!! ! 3.1.9.2)Bias^correcting) The!purpose!of!including!bootstrapping!in!this!study!is!to!derive!biasJcorrected!data!samples! for!the!analysis.!As!previously!mentioned,!the!true!technology!set!!!is!unknown,!and!DEA!is! therefore!used!to!derive!an!estimated!technology!set!!∗!for!the!implicated!firms!!.!As!DEA!is! upward!biased!the!estimated!efficiencies!might!be!higher!than!the!true!efficiencies,!and!we! therefore! estimate! the! bias! to! obtain! biasJcorrected! estimated! efficiencies.! Bogetoft! &! Otto! (2011)!defines!this!for!firm!!!as!! !

! 31! !

!"#$! = !! − !!,!where!!!!is!the!DEA!estimated!efficiency!and!!!!is!the!true!efficiency.!! ! As!!!!is!unknown!it!is!necessary!to!use!bootstrapping!to!find!!"#$!.!A!bootstrap!estimate!of! bias!can!be!found!as! ! ! 1 !"#$!∗ = !!" − !! = !!∗ − !!! ! !!! ! The!biasJcorrected!estimator!of!!!!is!then! ! !! = !! − !"#$!∗ = !! − !!∗ + !! = 2!! − !!∗! ! As!the!bootstraps!are!created!based!in!the!original!data!sample!there!is!a!chance!of!spikes!in! the!distribution!if!the!data!sample!is!small.!To!avoid!these!spikes!smoothing!are!introduced!to! smoothen!the!distribution.!A!smoothed!sample!is!used!instead!of!replicating!the!observations! in!the!original!data!sample!(Bogetoft!&!Otto!2011).!As!previously!mentioned,!the!R!software! package! Benchmarking! is! utilized! to! calculate! the! biasJcorrected! efficiencies! of! the! Danish! hospitals!in!the!data!samples.!! ! 3.1.9.3)Confidence)intervals) Bootstrapping!provides!an!opportunity!to!estimate!confidence!intervals!for!the!biasJcorrected! efficiencies.!Gardner!&!Altman!(1986)!present!the!width!of!a!confidence!interval!as!partly!deJ pending!on!the!standard!error!of!a!sample!statistic.!Hence,!the!confidence!interval!depends!on! the!standard!deviation!and!the!sample!size.!In!this!study,!we!utilize!the!95%!confidence!interJ val!on!the!biasJcorrected!data!samples.!The!purpose!of!the!confidence!is!to!test!the!signifiJ cance!of!the!biasJcorrected!efficiency!scores.!! ! 3.2)Merger)Effects) We!estimate!the!effects!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!based! on!the!cost!function!and!efficiency!scores!of!the!Danish!hospitals.!As!introduced!in!sections!

! 32! !

Figure)3.9)Total!Economic!Effects) ! Figure)3.10)Learning!Effects)

! Input!2

T! T!

A*+B*! A+B! A+B! C! y1+y2 B*! C! B! y2 A*! B! A! y1 A!

1 2 1 2 1 2 Input!1 x x E(x +x ) x +x ! ! Source:!Performance!Benchmarking,!Measuring!and!ManJ ! Source:!Performance!Benchmarking,!Measuring!and!ManJ aging!Performance!(Bogetoft!2012)! aging!Performance!(Bogetoft!2012)!

2.3!to!2.6,!the!structure!of!the!analysis!is!based!on!the!four!hypotheses;!total!economic!effects,! learning!effects,!harmony!effects!and!size!effect.!Furthermore,!pure!merger!effects!will!be!inJ! troduced!as!a!function!of!harmony!effects!and!size!effects.!! ! 3.2.1)Total)Economic)Effects) As!introduced!in!section!3.1,!a!main!focus!for!a!firm!is!input!efficiency!!.!Likewise,!the!focus!of! a! horizontal! merger! is! to! produce! an! output! using! the! minimal! amount! of! input.! Bogetoft! (2012)!defines!!!in!a!merger!between!Firm!1!and!Firm!2!can!be!presented!as,! ! !!=!Smallest!!!such!that!!(!! + !!)!can!produce!output!!! + !!! ! The!minimization!of!!!is!graphically!presented!in!figure!3.9.!Production!plan!!!of!Firm!1!and! production!plan!!!of!Firm!2!indicate!that!the!two!firms!are!not!fully!efficient!before!the!merJ ger,!as!they!are!found!below!the!efficiency!frontier!!.!However,!the!postJmerger!production! plan!! + !!contains!even!larger!efficiency!potential.!Production!plan!!!is!the!most!efficient! production!plan,!where!!(!! + !!)!can!produce!output!!! + !!.!This!also!applies!to!the!merJ gers!of!Danish!hospitals.!The!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!!!can! be!defined!as,! !

!! = !( !!)/ !!! !∈! !∈!

! 33! !

! A!score!of!!! < 1!indicate!potential!cost!reductions!from!the!merger,!while!a!score!of!!! > 1! indicate!that!the!merger!increase!costs!at!Bispebjerg!and!Frederiksberg!Hospitals.!It!is!necesJ sary!to!analyse!if!the!total!economic!effects!are!due!to!learning!effects,!harmony!effects!or!size! effects.!These!merger!effects!are!introduced!below.!! ) 3.2.2)Learning)Effects)) The!learning!effects!or!technical!efficiency!is!defined!as!the!potential!gains!from!applying!best! practice.!Many!firms!are!not!fully!efficient!before!the!merger!and!a!high!efficiency!gain!could! be!achieved!by!applying!best!practice!instead!of!merging.!However,!as!shown!in!figure!3.10!a! merger!adds!to!the!potential!gain!from!applying!best!practice.!By!optimizing!the!production! plan!of!Firm!1!we!get!! → !∗,!and!the!same!applies!to!Firm!2,!where!we!get!! → !∗.!The!two! production!plans,!!∗!and!!∗!are!efficient.!However,!if!Firm!1!and!Firm!2!merge!additional!effiJ ciency!gains!could!be!achieved!as!the!production!plan!!∗ + !∗!is!not!fully!efficient!(Bogetoft! 2012).!! The!learning!effects!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!!!can!be! defined!as! !

!"! = ! !! / !!! !∈! !∈! !

Figure)3.11)Harmony!Effects) ! Figure)3.12)Size!Effects)

Input!2 !

A! T

C!

(A+B)/2! y1+y2 A+B! C! B! y2 1 B! y A!

Input!1 x1 x2 E(x1+x2) x1+x2 ! ! Source:!Performance!Benchmarking,!Measuring!and!ManJ ! Source:!Performance!Benchmarking,!Measuring!and!ManJ aging!Performance!(Bogetoft!2012)! aging!Performance!(Bogetoft!2012)!

! 34! !

Similar!to!the!total!economic!effects!a!score!of!!"! < 1!indicate!a!potential!gain!from!the!merJ ger,!while!a!score!of!!"! > 1!will!result!in!increasing!costs!due!to!the!learning!effects.!! ) 3.2.3)Harmony)Effects) The!harmony!effects!or!scope!effects!measure!the!optimal!economic!gains!from!reallocating! the! production! plans! of! merging! firms.! Harmony! effects! are! estimated! as! the! possibility! of! reducing!the!average!cost!of!producing!an!average!output.!To!achieve!harmony!effects!from!a! merger!more!than!one!input!or!one!output!is!needed.!The!data!samples!in!this!study!consist!of! one!input!and!two!outputs,!which!is!introduced!in!section!4.!Figure!3.11!illustrates!the!harJ mony!effects!of!a!merger!of!two!firms!producing!two!outputs.!In!an!outputJmaximizing!merJ ger!!!would!be!the!optimal!production!plan!without!increasing!the!input!(Bogetoft!2012).!The! focus!of!this!study!is!input!minimization,!but!the!potential!reallocation!of!outputs!is!needed!to! estimate!the!harmony!effects!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!!! as! !

!"! = !( ! !! !!)/ ! !! !(!!)! !∈! !∈! ! A! score! of! !"! < 1! indicate! that! Bispebjerg! and! Frederiksberg! Hospitals! realize! potential! gains!from!reallocation!the!hospitals’!two!outputs.!! ! 3.2.4)Size)Effects) The!size!effects!or!scale!efficiencies!compare!the!cost!of!operating!at!full!scale!to!the!cost!of! the! average! scale.! Figure! 3.12! shows! that! firm! 1! and! firm! 2! have! fully! efficient! production! plans,!A!and!B,!respectively.!The!production!plan!of!the!merged!firm!! + !!is!not!fully!efficient! and!economic!gains!can!be!realized!by!changing!to!production!plan!!.!The!firm!can!produce! the!same!output!with!a!lower!amount!of!input.!! !

!"! = !( !!)/ ! !( ! !! !!)! !∈! !∈!

! 35! !

) 3.2.5)Pure)Merger)Effects) The!correlation!between!harmony!effects!and!size!effects!is!defined!as!the!pure!merger!effects! !⋆!.!! ! !⋆! = !"!!×!!"!! ! Learning!effects!can!be!realized!without!a!merger,!but!to!realize!the!pure!merger!effects!a!fullJ scale!merger!is!needed.!As!previously!mentioned,!the!total!economic!effects!are!a!function!of! learning!effects,!harmony!effects!and!size!effects.!The!total!economics!effects!are!defined!as! ! !! = !"!!×!!⋆! = !"!!×!!"!!×!!"!! ! 3.3)Summary) In!this!section,!we!introduce!the!methodological!framework!of!this!study.!The!main!focus!is!to! estimate!the!optimal!input!efficiency.!We!utilize!DEA!to!estimate!the!efficiency!frontier!and! efficiency!scores!of!the!hospitals!in!the!alternative!data!samples.!Based!on!four!assumptions,! we!find!that!DEA!models!under!VRS!and!NDRS!technologies!are!utilized!for!the!analysis!of! merger!effects.!Bootstrapping!is!introduced!to!correct!the!upward!bias!of!the!DEAJapproach.! Based! on! the! efficiency! frontier,! we! derive! the! economic! effects! of! the! merger! between! Bispebjerg!and!Frederiksberg!Hospitals.!We!estimate!the!total!economic!effects!of!the!merger,! and!these!are!decomposed!into!learning!effects,!harmony!effects!and!size!effects.!In!section!4,! we!present!the!alternative!data!samples!utilized!of!this!study.!

! 36! !

4)Data) This! section! introduces! the! data! used! in! this! study.! The! input! and! output! variables! are! deJ scribed!and!the!alterations!to!the!original!data!sample!is!elaborated.!The!data!sample!consists! of!adjusted!operational!costs!and!DRG!income!from!treatments!in!2011.!Furthermore,!data!on! treatments!will!be!presented!to!describe!the!characteristics!of!Bispebjerg!and!Frederiksberg! Hospitals!compared!to!the!other!hospitals!in!the!data!sample.!A!variation!of!the!output!data!is! introduced,!as!2012!DRGJtariffs!are!applied!to!the!2011!DRGJactivities.!This!alternative!data! sample!is!included!to!ensure!an!alternative!and!more!accurate!output!variables!since!2012! DRGJtariffs!are!based!on!the!costs!of!a!previous!year.!The!data!samples!will!additionally!be! biasJcorrected!as!described!in!section!3.!The!quality!of!the!data!will!be!discussed.!This!section! will!only!present!descriptive!statistics!of!the!data!samples.!The!full!data!samples!are!found!in! appendix!9.2.!! ! 4.1)Data)Samples) Data!from!twentyJseven!Danish!hospitals!in!all!five!regions!are!used!in!this!study!to!analyse! the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals.!Since!the!hospitals!merged!on! January!1st!2012,!data!from!2011!will!be!used!to!analyse!the!potential!merger!effects.!Data! related!to!healthcare!expenditures!and!productivity!is!extracted!from!the!annual!productivity! reports!published!by!the!Ministry!of!Health,!Ministry!of!Finance!and!Danish!Regions.!In!addiJ tion,!data!is!extracted!from!SSIs13!online!healthcare!database!to!support!the!data!in!the!annual! productivity!report.!The!Ministry!of!Health!publish!an!annual!productivity!analysis!of!all!DanJ

Table)4.1)Data!Sample) ) ) Input)variable) Output)variables) Hospitals,)!) Data!Sample!1! Adjusted!Operational!Costs,!2011! 2011!Inpatient!and!Outpatient!DRGJ 27! production!at!2011!DRGJtariffs! Data!Sample!2! Adjusted!Operational!Costs,!2011! 2011!Inpatient!and!Outpatient!DRGJ 26! production!at!2012!DRGJtariffs! Data!Sample!3! Adjusted!Operational!Costs,!2012! 2012!Inpatient!and!Outpatient!DRGJ 26! production!at!2012!DRGJtariffs!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 13!Statens!Serum!Institut!(SSI)!is!a!public!institute!under!the!Danish!Ministry!of!Health.!SSI!collects!data!on!e.g.! health!status,!quality!and!economy!in!the!public!healthcare!system.!!

! 37! !

Table)4.2)Descriptive!Statistics!for!Data!Sample!1!(2011!DRGJtariffs)) Variable) Description) Mean) St.)dev.) Minimum) Maximum) Input1! ! ! ! ! ! ! Adjusted!Operational!Costs! 1,815,484.09! 1,394,763.83! 208,926.92! 5,370,703.46! Output1! ! ! ! ! ! ! DRG!J!Inpatient! 1,363,480.57! 1,059,901.59! 195,740.17! 4,194,984.00! ! DRG!J!Outpatient! 794,774.67! 557,767.97! 51,078.00! 2,058,714.00! Treatments2:! ! ! ! ! ! ! Discharged!Patients! 43,735.52! 27,710.70! 7,246.00! 106,440.00! ! Days!Admitted! 150,726.44! 95,314.96! 32,309.00! 360,971.00! ! Days!Admitted!per!Patient! 3.55! 0.48! 2.84! 5.13! ! Outpatient!Treatments! 245,851.16! 179,278.63! 13,950.00! 678,737.00! ! Acute!Treatments! 33,110.80! 16,177.94! 3,059.00! 67,011.00! ! Surgeries! 58,048.72! 41,160.72! 1,289.00! 159,194.00! ! Radiological!Examinations! 184,758.60! 103,504.81! 31,622.00! 406,088.00! ! University!Hospital!(yes/no)! 0.16! 0.37! 0.00! 1.00! Other:! ! ! ! ! ! ! Cost!per!Patient! 5,364.15! 1,156.02! 3,879.16! 8,613.73! ! Income!per!Inpatient! 27,675.15! 6,207.44! 20,119.91! 46,428.32! ! Income!per!Outpatient! 2,628.55! 453.92! 1,293.03! 3,360.78! ! Income!per!Patient! 6,207.53! 1,351.79! 4,243.82! 10,819.54! 1)"Input"and"output"variables"are"in"1,000"DKK" 2)"Treatments"from"Region"Zealand"is"not"included"as"data"is"only"provided"as"a"total"for"the"region’s"hospitals" ish!public!hospitals.!To!secure!a!basis!for!comparison!adjustments!are!made!in!the!productiviJ ty!analysis.!Many!of!the!same!adjustments!are!used!in!this!study,!and!will!be!introduced!in! section!4.1.2.! A!few!hospitals!have!been!excluded!from!the!data!sample!in!addition!to!the!psychiatric!hospiJ tals.!In!Region!Zealand,!Garantiklinikken!is!excluded!as!it!only!handles!nonJacute!and!planned! treatments.!For!the!same!reasons,!De!Vestdanske!Friklinikker!in!the!Region!of!Southern!DenJ mark! is! excluded.! Finally,! Hammel! Neurocenter! in! the! Central! Denmark! Region! is! omitted! from!the!data!sample,!as!it!is!a!crossJregional!neurological!rehabilitation!hospital.!! Many!of!the!hospitals!in!the!data!sample!consist!of!hospitals!located!at!different!geographical! locations,!but!with!a!joint!management.!In!Region!Zealand,!the!seven!hospitals!are!combined! in!two!administrative!centres.!Hospital!North!includes!four!of!the!region’s!hospitals,!while!the! three!remaining!hospitals!form!Hospital!South.!In!Region!of!Southern!Denmark,!Odense!UniJ

! 38! !

versity!Hospital!and!Svendborg!Hospital!have!joint!management,!but!remaining!independent! in!the!data!sample.!The!same!applies!to!Lillebælt!Hospital,!which!include!the!hospitals!in!FreJ dericia,!Kolding,!Vejle!and!Give.!In!this!study!Fredericia!&!Kolding!Hospitals!is!an!independent! entity.!Likewise,!Vejle!&!Give!Hospitals!is!seen!as!an!independent!entity.!In!the!Central!DenJ mark!Region!and!the!North!Denmark!Region!all!hospitals!are!situated!at!more!than!one!geoJ graphical!location.!The!Capital!Region!of!Denmark!differentiates!from!the!other!regions,!as!a! majority!of!the!hospitals!are!independent!entities.!Only!Hospital!North!Zealand!is!situated!at! three!different!geographical!locations.! In!Kristensen!et!al.!(2010),!hospitals!with!joint!management!are!exclude!from!the!data!samJ ple.!A!similar!approach!in!this!study!would!result!in!a!data!sample!limited!to!nine!hospitals.! To!ensure!that!the!data!sample!is!comparable,!adjustments!will!be!made!to!equalize!any!efJ fects! of! a! joint! management! and! differences! in! organization.! This! will! be! elaborated! below.! Table!4.2!summarizes!the!descriptive!data!of!the!twentyJseven!hospitals.! ! 4.1.1)Bispebjerg)and)Frederiksberg)Hospitals) The!Danish!hospitals!in!the!data!sample!vary!significantly!in!budget!and!productivity.!ComJ pared! to! the! other! hospitals! in! the! data! sample! Bispebjerg! and! Frederiksberg! Hospital! are! below!mean!value!in!input!and!output!variables.!However,!this!reflects!the!fact!that!many!of! the!entities!in!the!data!sample!consist!of!geographically!separated!hospitals!with!joint!manJ agement.!Comparing!the!hospitals’!adjusted!operational!costs;!Bispebjerg!and!Frederiksberg! Hospitals!are!thirteenth!and!twentyJthird,!respectively.!Bispebjerg!Hospital!has!the!eleventh! highest!DRGJincome!from!inpatient!treatments!and!17th!highest!from!outpatient!treatments.! Frederiksberg! Hospital! is! twentyJthird! in! DRGJincome! from! inpatient! and! outpatient! treatJ ments.!! As!seen!in!Table!4.3,!Frederiksberg!Hospital!is!below!the!mean!value!of!the!full!data!sample! on!all!variables.!Furthermore,!Frederiksberg!Hospital!is!below!the!twentyJfifth!percentile!on! all!variables,!but!three.!These!are!acute!treatments,!days!admitted!per!patient!and!income!per! inpatient.! The! data! for! Frederiksberg! Hospitals! reflects! a! relatively! high! number! of! acute! treatments,! while! the! low! cost! and! income! per! patient! indicate! a! low! complexity! in! treatJ ments.!Bispebjerg!Hospital!only!surpasses!the!mean!value!of!the!data!sample!on!a!few!variaJ bles.!In!2011,!Bispebjerg!Hospital!had!a!relatively!high!number!of!acute!treatments.!With!a! total!of!45,489!acute!treatments,!Bispebjerg!Hospital!is!above!the!seventyJfifth!percentile!of!

! 39! !

Table)4.3)Descriptive!Statistics!for!Bispebjerg!and!Frederiksberg!Hospitals!(2011!DRGJtariffs)) Bispebjerg)Hos^ Frederiksberg) Variable) Description) Mean) pital) Hospital) Input1! ! ! ! ! ! Adjusted!Operational!Costs! 1,815,484.09! 1,557,444.83! 651,992.39! Output1! ! ! ! ! ! DRG!J!Inpatient! 1,363,480.57! 1,270,234.00! 491,086.38! ! DRG!J!Outpatient! 794,774.67! 577,626.00! 267,276.00! Treatments2:! ! ! ! ! ! Discharged!Patients! 43,735.52! 42,573.00! 19,840.00! ! Days!Admitted! 150,726.44! 157,696.00! 67,549.00! ! Days!Admitted!per!Patient! 3.55! 3.70! 3.40! ! Outpatient!Treatments! 245,851.16! 219,111.00! 106,558.00! ! Acute!Treatments! 33,110.80! 45,489.00! 23,674.00! ! Surgeries! 58,048.72! 51,649.00! 22,170.00! ! Radiological!Examinations! 184,758.60! 108,744.00! 65,956.00! ! University!Hospital!(yes/no)! 0.16! 0.00! 0.00! Other:! ! ! ! ! ! Cost!per!Patient! 5,364.15! 5,070.25! 4,344.53! ! Income!per!Inpatient! 27,675.15! 29,836.61! 24,752.34! ! Income!per!Outpatient! 2,628.55! 2,183.02! 2,052.31! ! Income!per!Patient! 6,207.53! 6,015.70! 5,053.32! 1)"Input"and"output"variables"are"in"1,000"DKK" 2)"Treatments"from"Region"Zealand"is"not"included"as"data"is"only"provided"as"a"total"for"the"region’s"hospitals" the!data!sample.!Meanwhile,!the!number!of!outpatient!treatments!is!lower!than!the!mean!valJ ue,!and!this!is!also!reflected!in!the!income!per!outpatient,!which!is!below!the!twentyJfifth!perJ centile.!Furthermore,!table!4.3!show!that!while!the!number!of!discharges!is!below!the!mean! value,!the!days!admitted!is!above.!This!higher!number!of!days!admitted!per!patient!is!also!reJ flected!in!the!income!per!inpatient,!as!Bispebjerg!Hospital!on!these!two!variables!is!ranged! seventh!and!eighth,!respectively.! ) 4.1.2)Variables) Bogetoft!(2012)!argues!that!the!number!of!fully!efficient!firms!in!a!DEAJapproach!is!correlatJ ed!to!the!number!of!input!and!output!variables.!Only!relevant!variables!should!be!included!in!

! 40! !

the! model.! DEA! researchers! have! suggested! rules! of! thumbs! for! the! relationship! between! firms! K,! input! m! and! output! n.! Two! of! the! traditional! rules! for! this! relationship! are! !! > 3(! + !)!and!!! > !!×!!.!The!two!rules!are!clearly!met!in!this!study.!Bogetoft!(2012)!also! point!to!that!these!rules!are!at!the!low!end.!! The!input!variable!in!the!data!sample!is!the!adjusted!operational!costs!associated!with!somatJ ic!treatments.!The!operational!costs!include!salaries,!goods!and!services.!Like!Kristensen!et!al.! (2009)!this!study!assumes!that!input!prices!are!constant!across!hospitals.!Even!though!hospiJ tals!have!independent!procurement!departments!the!authorities!regulate!prices!on!medicaJ tion!and!other!nonJwage!inputs.!Union!agreements!are!made!nationally!for!all!the!relevant! professions.!As!hospital!costs!only!vary!on!a!limited!number!of!goods!this!is!a!reasonable!asJ sumption.!! To!ensure!operational!costs!are!comparable!these!are!adjusted!for!outpatient!medication,!inJ ternal!financed!research!and!other!costs!not!related!to!somatic!treatments.!The!latter!includes! among!others,!expenses!for!leasing!of!medical!equipment,!cost!of!rent!and!patient!transportaJ tion.!To!ensure!accordance!between!costs!and!productivity,!outpatient!medication!is!omitted! from!the!data!sample.!This!is!due!to!inconsistency!in!registration!of!outpatient!medication.!At! some!hospitals!these!costs!are!distributed!between!departments!based!on!productivity,!and! this! may! result! in! misleading! expenditures! (Ministry! of! Health! 2012).! Internal! financed! reJ search!is!excluded!from!the!data!sample!as!research!in!some!regions!is!limited!to!a!few!hospiJ tals,!and!these!costs!are!not!directly!associated!to!somatic!treatments.!Lastly,!payments!from! the!State,!other!regions!and!municipalities!are!omitted!from!the!operational!costs.!! Staff!salaries!account!for!more!than!half!of!all!operational!costs,!as!seen!in!appendix!9.2.!An! alternative!input!variable!is!the!hospitals!usage!of!doctors!and!nurses.!Bogetoft!(2012)!argues! that!this!is!an!advantage!if!firms!face!different!labour!market!conditions,!which!will!affect!salJ aries.!A!disadvantage!is!that!this!does!not!reflect!differences!in!skills,!which!is!displayed!in! salaries.!Doctor!salaries!are!often!higher!in!the!peripheral!areas!of!Denmark.!However,!KrisJ tensen!et!al.!(2009)!indicate!that!these!differences!are!not!significant!compared!to!the!total! staff!salaries.!Therefore,!salaries!are!a!more!accurate!input!variable.!! As! introduced! in! section! 1.2,! the! Danish! caseJmix! system! consists! of! three! variables;! DRG,! DAGS!and!grey!zone!DRG.!However,!the!income!from!grey!zone!DRGJdiagnoses!is!split!on!DRG! and!DAGS.!Therefore,!the!output!variables!are!specified!as:!DRG!income!from!inpatient!treatJ ments!and!DRG!income!from!outpatient!treatments.!

! 41! !

Table)4.4)Descriptive!Statistics!for!Data!Sample!2!(2012!DRGJtariffs)) Variable) Description) Mean) St.)dev.) Minimum) Maximum) Input1! ! ! ! ! ! ! Adjusted!Operational!Costs! 1,922,695.01! 1,487,129.60! 208,926.92! 5,370,703.46! Output1! ! ! ! ! ! ! DRG!J!Inpatient! 1,400,320.69! 1,115,474.39! 194,241.00! 4,257,551.00! ! DRG!J!Outpatient! 758,102.15! 565,676.80! 46,863.00! 2,210,896.00! Treatments2:! ! ! ! ! ! ! Discharged!Patients! 45,556.79! 30,161.89! 7,246.00! 107,746.00! ! Days!Admitted! 157,006.71! 104,619.63! 32,309.00! 384,829.00! ! Days!Admitted!per!Patient! 3.55! 0.49! 2.84! 5.13! ! Outpatient!Treatments! 256,105.38! 196,076.64! 13,950.00! 768,774.00! ! Acute!Treatments! 34,489.38! 18,486.66! 3,059.00! 77,496.00! ! Surgeries! 60,466.38! 46,104.51! 1,289.00! 180,201.00! ! Radiological!Examinations! 192,456.88! 119,647.26! 31,622.00! 527,767.00! ! University!Hospital!(yes/no)! 0.17! 0.38! 0.00! 1.00! Other:! ! ! ! ! ! ! Cost!per!Patient! 5,365.56! 1,180.73! 3,879.16! 8,613.73! ! Income!per!Inpatient! 27,303.93! 6,337.54! 18,905.62! 47,120.78! ! Income!per!Outpatient! 2,401.28! 412.93! 1,136.53! 3,000.50! ! Income!per!Patient! 5,988.49! 1,430.69! 3,818.75! 10,781.74! 1)"Input"and"output"variables"are"measured"in"1,000"DKK" 2)"Treatments"from"Region"Zealand"is"not"included"as"data"is"only"provided"as"a"total"for"the"region’s"hospitals"

DRGJtariffs!are!calculated!on!the!basis!of!the!previous!year’s!reported!costs.!Additionally,!a! required!productivity!increase!of!2.0%!is!deducted!from!these!costs!(Christiansen!2012).!It!is! therefore!assumed!in!this!study!that!DRG!income!from!inpatient!and!outpatient!treatments! are!the!most!accurate!output!variables.!Alternative!variables,!such!as!outpatient!treatments! and!discharges!do!not!capture!the!complexity!in!treatments.!The!output!variables!are!adjustJ ed!like!the!input!variable!to!ensure!basis!for!comparison.!The!difference!in!hospital!organizaJ tion!is!adjusted!in!the!data!sample!to!ensure!a!better!basis!for!comparison.!The!Ministry!of! Health!(2012)!indicate!that!the!structure!at!some!hospitals!affects!the!DRG!income!from!inpaJ tient!treatments.!As!the!DRG!caseJmix!system!was!introduced!as!a!benchmarking!tool,!DRG! activities!are!registered!at!hospital!and!department!level.!Patients!transferred!between!two! hospitals!with!a!joint!management!will!be!registered!twice!as!DRG!productivity!is!measured! per!hospital.!To!ensure!that!this!does!not!affect!DRGJtariffs,!the!DRG!income!from!inpatient!

! 42! !

treatments!is!adjusted.!Finally,!the!DRG!income!from!outpatient!treatments!is!like!the!input! variable!adjusted!for!outpatient!medication.! ) 4.1.3)2012)DRG)Tariffs) Since!DRGJtariffs!are!calculated!based!on!reported!costs!from!the!previous!year,!this!study! will!include!an!additional!data!sample,!as!seen!in!Table!4.4.!DRGJtariffs!from!2012!will!be!apJ plied!to!the!hospitals’!DRGJactivities!in!2011.!This!is!to!ensure!an!even!more!accurate!estiJ mate!of!the!total!DRGJproduction.!This!additional!data!sample!contains!only!twentyJsix!hospiJ tals!as!Odense!University!Hospital!and!Svendborg!Hospitals!fully!merged!in!2012.!Therefore,! 2012Jdata!from!the!Ministry!of!Health!define!this!as!one!entity,!including!2011!DRG!income!at! 2012!DRGJtariffs.!The!input!data!remain!the!same!as!in!the!first!data!sample,!but!is!marginally! affected!by!change!from!twentyJseven!to!twentyJsix!hospitals.!! ! 4.2)Data)Quality) The!overall!quality!of!the!data!is!estimated!to!be!high.!As!public!institutions,!all!Danish!hospiJ tals!are!obliged!to!report!costs!and!productivity!to!the!Ministry!of!Health.!Unlike!private!firms,! hospitals!do!not!need!to!safeguard!economic!data,!such!as!fixed!and!variable!costs.!However,! the!Ministry!of!Health!(2012)!emphasize!that!there!are!limitations!to!the!data.! Firstly,!the!restricted!number!of!Danish!hospitals!limits!the!data.!Along!with!the!geographical! limitations!the!large!number!of!hospitals!with!joint!management!also!affects!the!data!sample.! A!larger!sample!size!would!provide!a!more!accurate!analysis!of!the!potential!economic!effects.!! Secondly,!the!difference!in!the!accounting!of!operational!costs!could!affect!the!data!quality.! The!data!indicate!clear!differences!between!the!regions!accounting!of!costs!and!coJpayments.! This!makes!it!difficult!to!split!the!operational!costs!into!subgroups,!like!salaries,!services!and! purchase!of!goods.!Therefore,!the!input!variable!is!restricted!to!the!total!adjusted!operational! costs.! Thirdly,!the!registration!of!DRGJproductivity!affects!the!quality!of!the!data.!Complex!and!rare! treatments!might!not!be!grouped!independently,!which!means!that!they!will!be!compared!too! less!complex!and!expensive!treatments.!While!this!accommodates!the!smaller!hospitals!where! more!frequent!and!simple!treatments!are!performed,!it!will!not!sufficiently!compensate!the! highly!specialized!hospitals!(Ministry!of!Health!2012).!More!detailed!DRGJgroups!are!introJ duced!yearly,!which!gradually!rectifies!these!inequalities!in!the!caseJmix!system.!

! 43! !

Lastly,!there!are!uncertainties!related!to!the!costs!of!internal!financed!research.!The!Ministry! of!Health!(2012)!emphasizes!that!the!five!regions!have!been!working!on!a!common!methodJ ology!to!ensure!a!better!basis!for!comparison.!This!focus!has!resulted!in!a!significant!increase! in!costs!between!2010!and!2011.!However,!cost!of!internal!financed!research!for!2011!is!more! accurate!than!data!from!prior!years.!! ! 4.3)Post^Merger)Data)Sample) The! merger! between! Bispebjerg! and! Frederiksberg! Hospitals! is! a! thoroughgoing! process,! where! departments! are! moved! in! stages,! and! the! merger! is! fully! implemented! when! New! Bispebjerg!Hospital!is!completed!in!2025.!As!a!basis!for!discussion!of!the!results!of!this!study,! input! and! outputs! from! 2012! will! be! presented! and! analysed.! These! adjusted! operational!

Table)4.5)Descriptive!Statistics!for!Data!Sample!3!(PostJMerger)) Variable) Description) Mean) St.)dev.) Minimum) Maximum) Input1! ! ! ! ! ! ! Adjusted!Operational!Costs! 1,903,776.36! 1,582,365.21! 250,159.69! 5,597,703.46! Output1! ! ! ! ! ! ! DRG!J!Inpatient! 1,361,926.00! 1,169,917.12! 206,791.00! 4,387,531.00! ! DRG!J!Outpatient! 764,799.38! 611,008.67! 48,930.00! 2,395,846.00! Treatments2:! ! ! ! ! ! ! Discharged!Patients! 46,500.17! 30,993.94! 8,357.00! 111,934.00! ! Days!Admitted! 154,014.21! 105,911.65! 31,908.00! 378,213.00! ! Days!Admitted!per!Patient! 3.34! 0.42! 2.49! 4.14! ! Outpatient!Treatments! 265,846.83! 201,240.00! 14,180.00! 797,568.00! ! Acute!Treatments! 33,393.79! 19,511.87! 1,291.00! 89,393.00! ! Surgeries! 62,426.79! 48,260.45! 1,330.00! 189,480.00! ! Radiological!Examinations! 197,533.96! 125,989.76! 32,284.00! 559,523.00! ! University!Hospital!(yes/no)! 0.17! 0.38! 0.00! 1.00! Other:! ! ! ! ! ! ! Cost!per!Patient! 5,454.84! 1,332.00! 3,912.33! 9,792.52! ! Income!per!Inpatient! 27,318.98! 6,909.23! 17,289.30! 46,334.76! ! Income!per!Outpatient! 2,463.44! 468.54! 1,046.58! 3,162.69! ! Income!per!Patient! 6,012.85! 1,400.37! 4,099.04! 10,543.49! 1)"Input"and"output"variables"are"measured"in"1,000"DKK" 2)"Treatments"from"Region"Zealand"is"not"included"as"data"is"only"provided"as"a"total"for"the"region’s"hospitals"

! 44! !

costs!and!DRG!income!from!inpatient!and!outpatient!treatment!are!solely!included!as!a!comJ parison!to!the!results!derived!in!the!analysis.!We!include!the!2012!data!in!data!sample!3!to! examine! if! the! potential! economic! effects! found! in! the! analysis! are! reflected! in! the! postJ merger!analysis!in!section!6.!The!descriptive!data!of!this!postJmerger!data!sample!are!found! in! table! 4.5.! Like! the! original! data! samples! 1! and! 2,! this! data! is! based! on! the! Ministry! of! Health’s! annual! productivity! report.! Not! only! Bispebjerg! and! Frederiksberg! Hospitals! were! subject!to!restructuring!in!2012.!Like!data!sample!2,!only!twentyJsix!hospitals!are!included!in! the!data!sample!3!compared!to!the!twentyJseven!hospitals!in!data!sample!1.!! Bispebjerg!and!Frederiksberg!Hospitals!remain!as!two!independent!hospitals!in!the!Ministry! of!Health’s!annual!productivity!report.!However,!adjustments!have!been!made!to!compensate! for! the! effects! of! the! merger.! This! includes! salaries! and! services,! which! is! adjusted! in! data! sample!3.!! ! 4.4)Summary) In!section!4,!we!introduce!the!alternative!data!samples!for!the!analysis!of!the!merger!between! Bispebjerg!and!Frederiksberg!Hospitals.!We!find!that!the!two!hospitals!are!below!the!mean! value!on!most!of!the!variables!in!table!4.3.! In!data!sample!1,!we!present!adjusted!operational!costs!from!2011!as!the!input!variable.!The! two!output!variables!are!2011!DRG!income!from!inpatient!and!outpatient!treatments.!Data! sample!2!differs!from!data!sample!1!by!applying!2012!DRGJtariffs!to!the!2011!DRGJactivities.! Finally,!data!sample!3!consists!of!postJmerger!data,!as!the!input!variable!is!adjusted!operaJ tional! costs! from! 2012,! and! the! output! variables! are! 2012! DRG! income! from! inpatient! and! outpatient! treatments.! Data! sample! 3! is! used! in! section! 6,! where! the! results! of! the! merger! analysis!are!discussed!and!tested.!! We!estimate!that!the!overall!quality!of!the!variable!is!high.!The!variables!are!adjusted!to!enJ sure!comparison!of!hospital!between!regions.!!

! 45! !

5)Analysis) In!this!section,!we!use!DEA!to!analyse!the!economic!effects!of!the!merger!between!Bispebjerg! and!Frederiksberg!Hospitals.!Firstly,!we!conduct!a!preJmerger!analysis!of!the!individual!hosJ pitals!in!the!applied!data!samples.!We!estimate!individual!efficiency!score!under!Variable!ReJ turns!to!Scale!(VRS)!and!NonJDecreasing!Returns!to!Scale!(NDRS)!technologies.!Potential!inefJ ficiencies! at! Bispebjerg! and! Frederiksberg! Hospitals! are! decomposed! through! analyses! of! peer!units!and!scale!efficiencies.!! As!introduced!in!sections!3!and!4,!two!alternative!approaches!and!data!samples!are!utilized!in! the!analysis.!Data!sample!1!include!of!adjusted!operational!cost!as!the!input!variable.!The!outJ put!variables!include!DRG!income!from!inpatient!and!outpatient!treatment!at!2011!DRGJtariff.! Data!sample!2!differs!by!applying!2012!DRGJtariffs!to!the!2011!DRGJactivity.!As!an!alternative! to! the! DEAJapproach,! we! introduce! biasJcorrected! efficiency! scores! through! bootstrapping.! This!ensures!a!more!accurate!estimation!of!preJmerger!and!merger!effects.!! Based! on! the! preJmerger! efficiency! scores,! we! estimate! total! economic! effects,! learning! efJ fects,!harmony!effects!and!size!effects!of!merger!between!Bispebjerg!and!Frederiksberg!HosJ pitals.!The!merger!effects!are!compared!to!the!literature!review,!as!we!confirm!or!refute!the! hypotheses! introduced! in! section! 2.! The! analysis! includes! deliberations! on! the! degree! to! which!the!results!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals,!resemble!or! deviate!from!other!similar!studies!within!in!the!field!of!hospital!mergers.! To! test! the! significance! of! the! analysis! results,! we! include! confidence! intervals! of! the! biasJ corrected!efficiency!scores!and!merger!effects.!Further,!we!introduce!a!postJmerger!analysis! in! section! 6! to! test! and! discuss! the! merger! effects! derived! from! the! horizontal! merger! beJ tween!Bispebjerg!and!Frederiksberg!Hospitals.!! ! As!the!focus!of!this!study!is!input!efficiency,!efficiency!scores!below!1.0000!indicate!potential! cost!reductions,!while!efficiency!scores!above!1.0000!indicate!potential!increase!in!costs!for! the!implicated!hospital(s).!! We!utilize!the!R!software!package!Benchmarking!presented!in!Bogetoft!&!Otto!(2011)!in!the! DEAJapproach!of!the!efficiency!frontier!and!the!inferred!merger!effects.!The!full!extent!of!the! statistical!computed!efficiency!scores!and!merger!effects!are!found!in!appendix!9.2.! !

! 46! !

5.1)Pre^Merger)Analysis) To!estimate!the!total!economic!effects!of!the!merger!between!Bispebjerg!and!Frederiksberg! Hospitals,! we! need! to! calculate! the! efficiency! frontiers! and! individual! efficiencies! !! for! all! Danish!hospitals!in!the!data!sample.!This!includes!calculating!the!efficiency!score!of!all!hospiJ tals!in!the!data!sample!1!and!data!sample!2.!! ! 5.1.1)Efficiency)scores) As!presented!in!Section!3.1.5.1,!the!cost!function!for!calculating!the!efficiency!score!under!VRS! and!NDRS!technologies!is!expressed!as,! ! ! ! ! = !"#!,!!! !. !.! ! !!!! − ! ≤ 0! !!! ! !1!!! − !1! ≥ 0! !!! ! !2!!! − !2! ≥ 0! !!! ! ! !! = 1 !!"#!!"#, !! ≥ 1!!"#!!"#$! !!! !!! ! Where!the!input!variable!!!equals!the!adjusted!operational!cost,!while!the!output!variables!!1! and!!2! equal! DRG! inpatient! and! DRG! outpatient,! respectively.! The! number! of! hospitals! !! equals!twentyJseven!or!twentyJsix!depending!on!the!applied!data!sample,!as!shown!in!table! 4.1.!! In!table!5.1,!we!find!the!efficiency!scores!of!the!hospitals!in!data!sample!1.!Bispebjerg!Hospital! is!inefficient!under!VRS!and!NDRS!technologies!with!efficiency!scores!at!0.9650!and!0.9191,! respectively.!This!indicates!potential!gains!of!3.5%!and!8.1%,!respectively.!Likewise,!FrederJ iksberg!Hospital!is!inefficient!in!the!two!applied!DEA!models.!Efficiency!scores!of!0.9075!and! 0.8926!indicate!that!Frederiksberg!Hospital!have!even!higher!potential!economic!gains!than! Bispebjerg!Hospital.!Comparing!these!potential!economic!gains!to!the!adjusted!operational!!

! 47! !

Table)5.1)Hospital!Efficiency!Scores!(2011!DRGJtariffs)) Hospital/Region) VRS) NDRS) Hospital/Region) VRS) NDRS) Capital"Region"of"Denmark" " " Region"Zealand" " " Rigshospitalet! 1.0000! 0.8661! Sygehus!Syd! 0.9004! 0.8380! Bispebjerg!Hospital! 0.9650! 0.9191! Sygehus!Nord! 1.0000! 0.9377! Hvidovre!Hospital! 1.0000! 0.9459! " ! ! Amager!Hospital! 0.8482! 0.8381! Region"of"Southern"Denmark! ! ! Frederiksberg!Hospital! 0.9075! 0.8926! Odense!Universitetshospital! 1.0000! 0.9261! Gentofte!Hospital! 0.8493! 0.8337! Svendborg!Sygehus! 0.8971! 0.8781! Glostrup!Hospital! 0.9595! 0.9466! Sygehus!Sønderjylland! 0.8600! 0.8470! Herlev!Hospital! 1.0000! 0.9738! Sydvestjysk!Sygehus! 0.9062! 0.8882! Nordsjællands!Hospital! 0,9010! 0.8579! Fredericia!&!Kolding!Sygehuse! 0.9270! 0.9067! Bornholms!Hospital! 0.8140! 0.8140! Vejle!&!Give!Sygehuse! 1.0000! 1.0000! " ! ! ! ! ! Central"Denmark"Region" ! ! North"Denmark"Region! ! ! Regionshospitalet!Horsens! 0.9842! 0.9673! Sygehus!Thy! 0.7610! 0.7610! Hospitalsenhed!Vest! 0.8965! 0.8753! Aalborg!Sygehus! 0.8990! 0.8493! Århus!Universitetshospital! 1.0000! 0.8676! Sygehus!Vendsyssel! 0.9187! 0.8867! Regionshospitalet!Randers! 0.9636! 0.9446! Sygehus!Himmerland! 1.0000! 1.0000! Hospitalsenhed!Midt! 0.8993! 0.8751! ! ! ! Source:!Appendix!9.3!for!calculations!in!R! costs! for! 2011! indicate! that! Bispebjerg! Hospital! could! reduce! costs! by! approximately! 54.5! million!DKK!according!to!the!VRS!model,!while!the!NDRS!model!show!potential!savings!of!apJ proximately!126.0!million!DKK.!Likewise!the!potential!savings!for!Frederiksberg!Hospital!in! the!VRS!and!NDRS!models!are!approximately!60.3!million!DKK!and!70.0!million!DKK,!respecJ tively.! ! Table!5.1!indicate!that!eight!of!the!Danish!hospitals!are!situated!at!the!efficiency!frontier!unJ der!VRS!technology,!meaning!that!they!are!fully!efficient.!Under!NDRS!technology,!only!Vejle! &! Give! Sygehuse! and! Sygehus! Himmerland! are! fully! efficient.! We! find! that! particularly! the! largest!hospitals!in!the!data!sample!become!inefficient!in!the!NDRS!model.!! ! In!data!sample!2,!where!2012!DRGJtariffs!are!applied!to!the!2011!DRGJactivities!even!larger! potential!economic!gains!are!found!at!Bispebjerg!and!Frederiksberg!Hospitals.!As!seen!in!taJ

! 48! !

Table)5.2)Bispebjerg!and!Frederiksberg!Hospitals!Efficiencies!(2012!DRGJtariffs))

Hospital) VRS)) NDRS))

Efficiency"Scores" ! ! Bispebjerg!Hospital! 0.9476! 0.8892!

Frederiksberg!Hospital! 0.8650! 0.8538!

! ! !

Potential"savings,"in"million"DKK" ! !

Bispebjerg!Hospital! 81.6299! 172.5281! Frederiksberg!Hospital! 87.9977! 95.3252!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals! ble!5.2,!Bispebjerg!Hospital!could!save!between!81.6!million!DKK!and!172.5!million!DKK!by! applying!best!practice.!Frederiksberg!Hospital!could!save!between!88.0!million!DKK!and!95.3! million!DKK!of!the!adjusted!operational!costs!in!2011.!Compared!to!data!sample!1,!Sygehus! Nord!and!Århus!Universitetshospital!are!no!longer!fully!efficient!under!VRS!technology.!Under! NDRS!technology,!Vejle!&!Give!Sygehuse!and!Sygehus!Himmerland!remain!the!only!fully!effiJ cient!hospitals.!! ! The!high!efficiency!scores!of!Vejle!&!Give!Sygehuse!and!Sygehus!Himmerland!are!explained!by! their!predominant!focus!on!either!outpatient!or!inpatient!treatments.!A!total!of!57.3%!of!the! DRG!income!at!Vejle!&!Give!Sygehuse!comes!from!outpatient!treatments.!As!the!only!hospital,! more!than!half!of!their!income!is!related!to!outpatient!treatments.!Conversely,!80.5%!of!the! DRG!income!at!Sygehus!Himmerland!comes!from!inpatient!treatments.!!

Table)5.3)Bispebjerg!and!Frederiksberg!Hospitals!Scale!Efficiencies) Hospital) CRS) VRS)) SE) NIRS) Data"Sample"1"(2011"DRGUtariffs)" ! ! ! ! Bispebjerg!Hospital! 0.9191! 0.9650! 0.9524! 0.9650! Frederiksberg!Hospital! 0.8962! 0.9075! 0.9875! 0.9075! ! ! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! ! ! Bispebjerg!Hospital! 0.8892! 0.9476! 0.9384! 0.9476! Frederiksberg!Hospital! 0.8538! 0.8650! 0.9871! 0.8650! Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals!

! 49! !

By!applying!2012!DRGJtariffs!to!2011!DRGJproductivity!in!data!sample!2,!an!even!higher!perJ centage!of!DRG!income!comes!from!inpatient!treatments!at!all!Danish!hospitals.!Vejle!&!Give! Sygehuse!remains!the!only!hospital,!where!more!than!half!of!the!income!is!related!to!outpaJ tient!treatments.!Likewise,!Sygehus!Himmerland!remains!the!only!hospital,!where!more!than! threeJfourth!of!the!DRG!income!comes!from!inpatient!treatments.!These!outlying!outputs!exJ plain!the!high!efficiency!scores!for!the!two!hospitals.! ! 5.1.2)Scale)Efficiencies) As!seen!in!figure!3.8,!the!potential!number!of!production!plans!(!, !)!are!higher!in!the!NDRS! model! than! in! the! VRS! models.! This! is! confirmed! by! the! results! in! section! 5.1.1,! where! the! larger! hospitals! are! inefficient! under! NDRS! technology.! Scale! efficiencies! estimate! to! which! degree!inefficiencies!are!due!to!size.!In!table!5.3,!we!find!that!the!inefficiencies!at!Bispebjerg! Hospital!are!mainly!due!to!scale!efficiencies.!This!also!explains!Bispebjerg!Hospital’s!increasJ ing!inefficiencies!from!data!samples!1!to!2.!The!inefficiencies!at!Frederiksberg!Hospital!are! not!merely!related!to!scale!efficiencies.!We!find!that!efficiency!scores!similar!under!VRS!and! NIRS! technologies,! which! indicates! that! Bispebjerg! and! Frederiksberg! Hospitals! are! above! their!optimal!scale!size.! ! 5.1.3)Peer)Units) As!indicated!in!Section!3,!the!peer!units!are!calculated!for!the!inefficient!hospitals.!As!the!maxJ imum! number! of! peer! units! in! VRS! and! NDRS! models! equal! ! + !,! we! find! a! maximum! of!

Table)5.4)Bispebjerg!and!Frederiksberg!Hospitals!Peer!Units!(2011!DRGJtariffs)) Hvidovre)) Herlev)) Vejle)&)Give) Sygehus)) Hospital) Hospital) Hospital) Sygehuse) Himmerland) Variable"Returns"to"Scale" ! ! ! ! Bispebjerg!Hospital! 0.6297! 0.0932! 0.0000! 0.2772! Frederiksberg!Hospital! 0.0000! 0.1444! 0.0411! 0.8144! ! ! ! ! ! NonUDecreasing"Returns"to"Scale" ! ! ! ! Bispebjerg!Hospital! 0.0000! 0.0000! 0.3344! 4,8459! Frederiksberg!Hospital! 0.0000! 0.0000! 0.1836! 1.6844!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals!

! 50! !

Table)5.5)Bispebjerg!and!Frederiksberg!Hospitals!Peer!Units!(2012!DRGJtariffs)) Hvidovre)) Herlev)) Vejle)&)Give) Sygehus)) Hospital) Hospital) Hospital) Sygehuse) Himmerland) Variable"Returns"to"Scale" ! ! ! ! Bispebjerg!Hospital! 0.5830! 0.1154! 0.0000! 0.3015! Frederiksberg!Hospital! 0.0000! 0.1139! 0.0835! 0.8026! ! ! ! ! ! NonUDecreasing"Returns"to"Scale" ! ! ! ! Bispebjerg!Hospital! 0.0000! 0.0000! 0.3489! 4.5367! Frederiksberg!Hospital! 0.0000! 0.0000! 0.2041! 1.4402!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals! three!peer!units!in!this!study.!The!results!in!tables!5.4!and!5.5!confirm!this.! In!table!5.4,!we!find!the!peer!unit!weights!!!!for!Bispebjerg!and!Frederiksberg!Hospitals!using! 2011! DRGJtariffs.! In! the! VRS! model,! Bispebjerg! Hospital! should! primarily! look! to! Hvidovre! Hospital! for! a! more! efficient! production! plan,! while! it! is! clear! that! Frederiksberg! Hospital! should!primarily!look!to!Sygehus!Himmerland!for!a!production!plan!closer!to!the!efficiency! ! ! frontier.!We!see!that!while! !!! ! = 1!under!VRS!technology,!there!is!no!upper!limit!under! ! ! NDRS!technology!as! !!! ! ≥ 1,!which!is!also!reflected!in!table!5.4.!! As!neither!Hvidovre!nor!Herlev!Hospitals!are!fully!efficient!under!NDRS!technology,!Sygehus! Himmerland!becomes!the!primary!peer!unit!for!Bispebjerg!and!Frederiksberg!Hospitals.! If!we!compare!the!input!and!output!variables!of!Bispebjerg!and!Hvidovre!Hospitals,!we!find! that!the!two!hospitals!are!relatively!similar!in!operational!cost!and!DRG!income.!The!same! applies! to! Frederiksberg! Hospital! and! Sygehus! Himmerland.! In! table! 5.5,! we! find! trivial! changes!compared!to!the!peer!units!in!table!5.4.!We!find!that!Hvidovre!Hospital!and!Sygehus! Himmerland!are!still!the!primary!peer!units!for!Bispebjerg!and!Frederiksberg!Hospitals,!reJ spectively.! ) 5.2)Bias^Corrected)Pre^Merger)Analysis) As!indicated!in!Section!3,!the!DEA!model!suffers!from!upward!bias,!and!we!therefore!include! an!alternative!approach,!where!we!estimate!biasJcorrected!efficiencies!of!the!hospitals!in!the! data!samples.!The!biasJcorrected!efficiencies!are!calculated!by!applying!a!smoothed!bootstrap!

! 51! !

Table)5.6)Standard!Error!of!the!Median!at!different!Bootstrap!Samples!B) B6 25) 50) 100) 250) 500) 1,000) 2,500) 5,000) 10,000) 1st!run! 221,638! 234,851! 239,843! 250,814! 250,042! 243,929! 240,635! 245,288! 247,390! 2nd!run! 188,664! 280,852! 239,103! 242,439! 244,562! 239,691! 250,002! 242,441! 246,911! 3rd!run! 253,966! 216,107! 247,945! 260,370! 246,935! 240,405! 245,983! 246,309! 241,336! 4th!run! 308,167! 240,962! 224,850! 230,277! 243,288! 256,236! 249,552! 242,829! 246,783! 5th!run! 203,570! 233,136! 276,253! 238,735! 275,208! 244,611! 245,271! 248,675! 239,913! 6th!run! 194,873! 232,325! 259,902! 256,775! 227,190! 249,583! 254,675! 245,957! 247,944! 7th!run! 281,354! 267,723! 229,820! 238,893! 240,239! 244,048! 247,925! 245,112! 245,386! 8th!run! 214,323! 238,271! 259,773! 242,416! 238,649! 250,556! 245,055! 243,778! 250,014! 9th!run! 309,232! 207,962! 236,494! 231,010! 234,374! 253,141! 243,001! 244,331! 244,538! 10th!run! 182,291! 233,698! 264,340! 249,268! 249,633! 248,437! 250,769! 241,751! 245,097! Source:!See!appendix!9.3!for!calculations!in!R! sample!based!on!data!sample!1!and!data!sample!2.!Firstly,!it!is!relevant!to!calculate!the!optiJ mal!number!of!replicates!!!to!be!used!in!the!analysis.!! As!presented!in!section!4.1.2,!the!optimal!number!of!replicates!!!can!be!found!by!calculating! the!standard!error!of!the!median!at!different!scenarios.!Using!nine!different!bootstrap!samJ ples!!!ranging!from!25!to!10,000,!we!calculate!the!standard!error!of!the!median!and!run!these! calculations!ten!times!to!ensure!a!sufficient!basis!for!comparison.!The!results!in!table!5.6,!inJ dicate!that!at!! = 25!the!standard!error!of!the!median!varies!from!a!minimum!of!182,291!to!a! maximum!of!309,232.!As!mentioned!in!section!3,!Bogetoft!&!Otto!(2011)!indicate!that!the!reJ quired! number! of! bootstrap! samples! in! a! DEA! analysis! is! significantly! higher! than! in! other! approaches,!where!a!bootstrap!sample!between!50!and!200!is!sufficient.!This!is!supported!by! the!results!in!Table!5.6.!A!minimum!of!1,000!bootstraps!is!required!to!ensure!a!standard!error! of!the!median!without!large!fluctuations.!At!! = 5,000,!the!standard!error!of!the!median!varJ ies!by!only!6,924!in!the!ten!runs.!This!is!compared!to!the!standard!errors!of!the!median!at! ! = 10,000,!which!vary!by!10,101.!Based!on!these!results,!a!bootstrap!sample!of!5,000!is!used! in!the!biasJcorrected!preJmerger!analysis.!!

!

! 52! !

5.2.1)Bias^Corrected)Efficiency)Scores) The!biasJcorrected!efficiency!scores!of!Danish!hospitals!in!table!5.7!show!a!higher!degree!of! inefficiencies!than!the!results!presented!in!table!5.1.!We!find!that!none!of!the!hospitals!are! fully!efficient!when!estimating!the!biasJcorrected!efficiency!scores!in!data!samples!1!and!2.! The! efficiency! score! of! Bispebjerg! Hospital! under! VRS! technology! decrease! from! 0.9650! to! 0.9361!in!the!biasJcorrected!data!sample.!Similarly,!the!efficiency!score!under!NDRS!technolJ ogy!decrease!from!0.9191!to!0.8924.!These!biasJcorrected!efficiency!scores!are!equivalent!to! potential!cost!reductions!of!99.6!million!DKK!under!VRS!technology!and!167.5!million!DKK! under!NDRS!technology.!Likewise,!the!efficiencies!scores!of!Frederiksberg!Hospital!decrease! under!VRS!and!NDRS!technologies,!from!0.9075!to!0.8870!and!from!0.8926!to!0.8586,!respecJ tively.!The!biasJcorrected!efficiency!scores!of!Frederiksberg!Hospital!are!equivalent!to!potenJ tial!savings!of!73.7!million!DKK!and!92.2!million!DKK!under!VRS!and!NDRS!technologies,!reJ

Table)5.7)Hospital!Efficiencies,!BiasJCorrected!(2011!DRGJtariffs)) Hospital/Region) VRS) NDRS) Hospital/Region) VRS) NDRS) Capital"Region"of"Denmark" " " Region"Zealand" " " Rigshospitalet! 0.9225! 0.8327! Sygehus!Syd! 0.8642! 0.8140! Bispebjerg!Hospital! 0.9361! 0.8924! Sygehus!Nord! 0.9637! 0.9198! Hvidovre!Hospital! 0.9584! 0.9162! " ! ! Amager!Hospital! 0.8036! 0.7687! Region"of"Southern"Denmark! ! ! Frederiksberg!Hospital! 0.8870! 0.8586! Odense!Universitetshospital! 0.9220! 0.9048! Gentofte!Hospital! 0.8321! 0.8040! Svendborg!Sygehus! 0.8804! 0.8543! Glostrup!Hospital! 0.9316! 0.9010! Sygehus!Sønderjylland! 0.8266! 0.8005! Herlev!Hospital! 0.9570! 0.9565! Sydvestjysk!Sygehus! 0.8851! 0.8595! Nordsjællands!Hospital! 0.8661! 0.8323! Fredericia!&!Kolding!Sygehuse! 0.9103! 0.8853! Bornholms!Hospital! 0.7660! 0.7362! Vejle!&!Give!Sygehuse! 0.9209! 0.8953! " ! ! ! ! ! Central"Denmark"Region" ! ! North"Denmark"Region! ! ! Regionshospitalet!Horsens! 0.9683! 0.9395! Sygehus!Thy! 0.6981! 0.6654! Hospitalsenhed!Vest! 0.8741! 0.8546! Aalborg!Sygehus! 0.8557! 0.8304! Århus!Universitetshospital! 0.9216! 0.8473! Sygehus!Vendsyssel! 0.8931! 0.8538! Regionshospitalet!Randers! 0.9493! 0.9214! Sygehus!Himmerland! 0.9215! 0.8967! Hospitalsenhed!Midt! 0.8734! 0.8561! ! ! ! Source:!Appendix!9.3!for!calculations!in!R!

! 53! !

Table)5.8!Bispebjerg!and!Frederiksberg!Hospitals!Efficiencies,!BiasJCorrected!(2012!DRGJtariffs)) Hospital) VRS)) NDRS)) Efficiency"Scores" ! ! Bispebjerg!Hospital! 0.9172! 0.8543! Frederiksberg!Hospital! 0.8375! 0.8039! ! ! ! Potential"savings,"in"million"DKK" ! ! Bispebjerg!Hospital! 128.9555! 226.8982! Frederiksberg!Hospital! 105.9246! 127.8521!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals! spectively.!This!confirms!that!DEA!estimates!are!upward!biases,!and!the!biasJcorrected!are! closer!to!the!true!efficiencies!of!the!Danish!hospitals.!! The!biasJcorrect!analysis!of!data!sample!2!indicates!the!same!pattern!as!in!the!analysis!of!data! sample! 1.! None! of! the! hospitals! in! the! data! sample! are! fully! efficient! under! VRS! and! NDRS! technologies.!In!section!5.1.1,!the!efficiency!scores!of!Bispebjerg!and!Frederiksberg!Hospitals! are!decrease!in!data!sample!2!compared!to!data!sample!1.!Table!5.8!indicate!the!same!tendenJ cy!in!the!biasJcorrected!efficiency!scores.!Bispebjerg!Hospital’s!efficiency!score!of!0.9172!unJ der!VRS!technology!indicates!potential!savings!of!128.6!million!DKK.!Similarly,!the!efficiency! score!under!NDRS!technology!indicate!an!efficiency!score!of!0.8543!and!potential!savings!of! 226.9!million!DKK.!! Likewise,!the!biasJcorrected!data!sample!2!indicates!even!larger!potential!savings!at!FrederJ iksberg!Hospital!compared!to!data!sample!1.!This!applies!under!VRS!and!NDRS!technologies! with!efficiency!scores!of!0.8375!and!0.8039,!respectively.!! ) 5.2.2)Confidence)Intervals) As!introduced!in!section!3.1.9.3,!we!introduce!95%!confidence!intervals!in!the!merger!analJ yses!of!the!biasJcorrected!data!samples.!In!table!5.9,!we!find!that!the!width!of!the!confidence! intervals!ranges!between!0.0334!and!0.0632.!The!confidence!intervals!of!the!biasJcorrected! efficiency!scores!have!an!average!width!of!approximately!0.0500.!We!find!trivial!variations! when! comparing! the! average! width! of! the! confidence! intervals! of! the! alternative! hospitals,! alternative!data!samples!and!alternative!returnsJtoJscale!technologies.!!

! 54! !

Table)5.9!Confidence!Intervals,!BiasJCorrected!Hospital!Efficiencies) Hospital) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Bispebjerg!Hospital! 0.8999!J!0.9631! 0.8635!J!0.9173! Frederiksberg!Hospital! 0.8684!J!0.9053! 0.8381!J!0.8887! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Bispebjerg!Hospital! 0.8859!J!0.9450! 0.8252!J!0.8867! Frederiksberg!Hospital! 0.8194!J!0.8627! 0.7866!J!0.8487!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals!

As!the!confidence!intervals!are!based!on!the!efficiency!scores!in!section!5.2.1,!we!find!that!the! lowest!efficiency!scores!are!found!at!Frederiksberg!Hospitals!in!data!sample!2!under!NDRS! technology.!Based!on!results!in!table!5.9,!we!can!almost!certainly!conclude!that!potential!cost! savings!at!Bispebjerg!and!Frederiksberg!Hospitals!do!exist.!In!some!scenarios,!we!find!nonJ trivial!potential!cost!reductions.! ) 5.2.3.)Scale)Efficiencies) Estimating!the!biasJcorrected!scale!efficiencies!in!table!5.10,!we!find!the!same!pattern!as!the! uncorrected!scale!efficiencies!in!table!5.3.!Part!of!the!inefficiency!at!Bispebjerg!Hospital!is!exJ plained!by!scale!efficiencies!!",!while!scale!efficiencies!at!Frederiksberg!Hospital!seems!to!be! minimal.! Likewise,! the! higher! degree! of! inefficiency! at! Bispebjerg! Hospital! in! the! biasJ corrected!analysis!of!data!sample!2!compared!to!data!sample!1!can!be!explained!by!scale!effiJ ciencies.!! Neither!the!CRS!nor!VRS!efficiency!scores!coincide!with!the!NIRS!efficiency!score.!However,!as! the! difference! between! the! VRS! and! NIRS! efficiency! score! are! fairly! small! we! find! that! Bispebjerg!and!Frederiksberg!Hospitals!are!above!the!optimal!scale!size.!The!difference!is!exJ plained!by!the!use!of!a!finite!number!of!bootstrap!samples!!.!! )

! 55! !

Table)5.10)Bispebjerg!and!Frederiksberg!Hospitals!Scale!Efficiencies,!BiasJCorrected) Hospital) CRS) VRS)) SE) NIRS) Data"Sample"1"(2011"DRGUtariffs)" ! ! ! ! Bispebjerg!Hospital! 0.8937! 0.9361! 0.9547! 0.9332! Frederiksberg!Hospital! 0.8749! 0.8870! 0.9864! 0.8877! ! ! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! ! ! Bispebjerg!Hospital! 0.8570! 0.9172! 0.9343! 0.9146! Frederiksberg!Hospital! 0.8310! 0.8375! 0.9922! 0.8420!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals!

5.3)Merger)Analysis) Based!on!the!results!of!the!DEA!analyses!in!sections!5.1!and!5.2,!we!calculate!the!potential! economic!effects!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals.!This!section! tests!the!four!hypotheses!introduces!in!sections!2.3!to!2.6,!and!calculate!the!mergers!effects! based!on!total!economic!effects,!learning!effects,!harmony!effects!and!size!effects.!The!merger! analysis!includes!the!uncorrected!and!biasJcorrected!data!sample!1!and!the!data!sample!2.! In!table!5.11,!we!present!the!data!and!calculations!required!for!analyse!the!economic!effects! of!merger!between!Bispebjerg!Hospital!(BBH)!and!Frederiksberg!Hospital!(FBH).!! ) 5.3.1)Total)Economic)Effects) As!introduced!in!section!3.1,!the!focus!of!this!analysis!is!to!calculate!the!input!efficiency!of!the! merger!between!Bispebjerg!and!Frederiksberg!Hospitals!!!!"!!"#.!We!define!input!efficiency! as!the!minimal!amount!of!input,!at!which!the!two!hospitals!can!produce!the!current!amount!of! output,!! ! !!!"!!"#!=!Smallest!!!such!that!!(!!!" + !!!")!can!produce!output!!!!" + !!"#! !

! 56! !

Table)5.11)Merger!Analysis!Calculations) Hospital) VRS) NDRS)) BiasCor^VRS) BiasCor^NDRS) Data"Sample"1"(2011"DRGUtariffs)" ! ! ! ! !(!!!")! 1,502,934! 1,431,448! 1,457,924! 1,389,864! !(!!"#)! 591,683! 581,968! 578,317! 559,801! !(!!!" + !!"#)! 2,121,883! 2,013,367! 2,054,396! 1,959,849! !!!"! 1,557,445! 1,557,445! 1,557,445! 1,557,445! !!"#! 651,992! 651,992! 651,992! 651,992! !!!" + !!"#! 2,209,437! 2,209,437! 2,209,437! 2,209,437! !"#!!"#!"#$%"!!" + !"#!!"#$%&'"%!"#! 1,761,320! 1,761,320! 1,761,320! 1,761,320! !"#!!"#$%#&'(#!!" + !"#!!"#$%#&'(#!"#! 844,902! 844,902! 844,902! 844,902! !(0.5(!!!" + !!"#))! 1,045,877! 1,006,684! 1,018,560! 976,687! ! ! ! ! ! Data"Sample"2"(2012"DRGUtariffs)! ! ! ! ! !(!!!")! 1,475,835! 1,384,880! 1,428,488! 1,330,525! !(!!"#)! 563,973! 556,671! 546,044! 524,137! !(!!!" + !!"#)! 2,063,976! 1,941,584! 1,993,223! 1,875,675! !!!"! 1,557,445! 1,557,445! 1,557,445! 1,557,445! !!"#! 651,992! 651,992! 651,992! 651,992! !!!" + !!"#! 2,209,437! 2,209,437! 2,209,437! 2,209,437! !"#!!"#$%&'"%!!" + !"#!!"#$%&'"%!"#" 1,693,846! 1,693,846! 1,693,846! 1,693,846! !"#!!"#$%#&'(#!!" + !"#!!"#$%#&'(#!"#! 777,308! 777,308! 777,308! 777,308! !(0.5(!!!" + !!"#))! 1,014,750! 970,792! 984,863! 933,383!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals!

The!total!economic!effects!!!are!derived!from!the!optimal!cost!function!for!the!two!merging! hospitals,!!(!!!" + !!"#).!Compared!to!the!input!of!the!two!hospitals!!!!" + !!"#,!this!alJ lows!us!to!calculate!the!total!economic!effects!!,!as! ! ! = !(!!!" + !!"#)/(!!!" + !!"#)! !

! 57! !

Table)5.12)Total!Economic!Effects,!E) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Total!Economic!Effects! 0.9604! 0.9113! Total!Economic!Effects,!biasJcorrected! 0.9298! 0.8824! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Total!Economic!Effects! 0.9342! 0.8788! Total!Economic!Effects,!biasJcorrected! 0.9021! 0.8394!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

In!table!5.12,!we!find!that!there!clearly!is!a!total!economic!effect!from!the!merger!between!the! Bispebjerg!and!Frederiksberg!Hospitals.!However,!the!degree!of!economic!gains!differentiates! between!the!alternative!returns!to!scale!and!data!samples.!Furthermore,!the!biasJcorrected! analyses!indicate!even!larger!economic!gains!from!the!hospital!merger.!! The!total!economic!effects!differentiate!significantly!between!the!different!scenarios.!AccordJ ing! to! the! results! in! table! 5.12,! the! hospital! merger! will! result! in! cost! reductions! between! 4.0%!and!11.8%!for!data!sample!1,!and!between!6.6%!and!16.1%!for!data!sample!2.!As!the! total!input!of!the!two!hotels!combined!equals!2,209.4!million!DKK,!the!potential!savings!difJ fers!from!87.6!million!DKK!to!259.8!million!DKK!for!data!sample!1.!For!data!sample!2,!the!poJ tential!saving!differs!from!145.5!million!DKK!to!354.8!million!DKK.!! ! In!section!2.3,!we!find!that!based!on!the!general!literature!there!will!be!a!potential!reduction!

Table)5.13)Confidence!Intervals,!Total!Economic!Effects!and!Learning!Effects) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Total!Economic!Effects,!biasJcorrected! 0.8971!J!0.9574! 0.8560!J!0.9087! Learning!Effects,!biasJcorrected! 0.8906!J!0.9460! 0.8560!J!0.9089! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Total!Economic!Effects,!biasJcorrected! 0.8724!J!0.9310! 0.8139!J!0.8755! Learning!Effects,!biasJcorrected! 0.8663!J!0.9207! 0.8139!J!0.8755!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

! 58! !

in!costs!from!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals.!The!results!in!taJ bles!5.12!to!5.13!confirm!this!hypothesis.!! Even!though!the!similar!studies!within!the!field!of!hospital!mergers!is!inconclusive!on!the!efJ fects!of!hospital!mergers,!the!majority!of!Danish!studies!indicate!cost!reductions!from!mergJ ing!hospitals.!The!analysis!reaches!the!same!conclusion!in!terms!of!estimating!potential!savJ ings!from!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals.! The! total! economic! effects! in! tables! 5.12! to! 5.13! resemble! the! results! of! Kristensen! et! al.! (2010).!!The!economic!gain!from!the!merger!between!Bispebjerg!and!Frederiksberg!Hospital! deviate!from!the!more!significant!mean!economic!gains!in!Kristensen!et!al.!(2010).!However,! there! is! a! clear! correlation! as! the! two! studies! indicate! higher! economic! gains! under! NDRS! technologies! compared! to! VRS! technologies.! Further,! the! biasJcorrected! analyses! leads! to! higher! potential! saving! than! the! upward! biased! analyses.! The! confidence! intervals! in! table! 5.13!emphasize!the!cost!reduction,!and!indicate!that!the!merger!could!results!in!nonJtrivial! economic!effects.! However,!it!is!unclear!what!the!basis!of!these!cost!reductions!is.!To!decompose!the!total!ecoJ nomic!effects!of!the!merger!an!analysis!of!learning!effects,!harmony!effects!and!size!effects!are! introduced! below.! As! previously! mentioned,! these! three! merger! effects! are! the! basis! of! the! total!economic!effects.! ) 5.3.2)Learning)Effects) As!previously!introduced,!the!learning!effects!(technical!efficiency)!estimate!economic!effects! that!hospitals!will!obtain!by!applying!best!practice.!The!learning!effects!!"!of!the!merger!beJ

Table)5.14)Learning!Effects,!LE) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Learning!Effects! 0.9481! 0.9113! Learning!Effects,!biasJcorrected! 0.9216! 0.8824! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Learning!Effects! 0.9232! 0.8788! Learning!Effects,!biasJcorrected! 0.8937! 0.8394!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

! 59! !

tween!Bispebjerg!and!Frederiksberg!Hospitals!are!defined!as,! ! !" = (! !!!" + ! !!"# )/(!!!" + !!"#)! ! In!section!2.4,!we!present!the!hypothesis!that!the!merger!between!Bispebjerg!and!FrederiksJ berg! Hospitals! will! result! in! cost! reductions! from! learning! effects.! This! hypothesis! is! conJ firmed!by!the!results!in!table!5.14.!! Varabyova!&!Schreyögg!(2013)!estimate!potential!gains!from!learning!effects!to!be!approxiJ mately!5.0J10.0%!in!the!Danish!healthcare!system.!This!corresponds!to!the!results!under!VRS! technology! in! table! 5.14,! whereas! even! higher! potential! savings! are! indicated! under! NDRS! technology.!In!Kristensen!et!al.!(2010)!mean!learning!effects!of!0.7906!and!0.8735!are!found! under!VRS!technology,!while!mean!learning!effects!under!NDRS!technology!fairly!similarly!are! ranging!from!0.7859!to!0.8514.!! ! Comparing! the! potential! learning! effects! in! table! 5.14! to! the! total! economic! effects! in! table! 5.12,!we!find!that!the!results!only!differentiate!marginally.!For!the!majority!of!the!learning! effects,!the!potential!cost!reductions!are!even!larger!than!the!total!economic!effects.!As!the! total!economic!effects!are!based!on!learning!effects,!harmony!effects!and!size!effects,!this!indiJ cate! that! the! potential! economic! gain! of! the! merger! between! Bispebjerg! and! Frederiksberg! Hospitals!is!mainly!due!to!learning!effects.!This!resembles!the!conclusion!of!Farrell!&!Shapiro!

Table)5.15)Confidence!Intervals,!Harmony!Effects,!Size!Effects!and!Pure!Merger!Effects) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Harmony!Effects,!biasJcorrected! 0.9979!J!1.0068! 0.9998!J!1.0000! Size!Effects,!biasJcorrected! 1.0005!J!1.0142! 1.0000!J!1.0000! Pure!Merger!Effects,!biasJcorrected! 1.0073!J!1.0120! 0.9998!J!1.0000! ! ! ! Data"Sample"2"(2012"DRGUtariffs)! ! ! Harmony!Effects,!biasJcorrected" 0.9946!J!1.0051! 1.0000!J!1.0000! Size!Effects,!biasJcorrected! 1.0020!J!1.0167! 1.0000!J!1.0000! Pure!Merger!Effects,!biasJcorrected! 1.0071!J!1.0112! 1.0000!J!1.0000!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

! 60! !

(1990),!where!large!learning!effects!are!necessary!for!a!merger!to!result!in!economic!gains.! The!potential!learning!effects!in!table!5.14!deviate!from!the!results!in!Harris!et!al.!(2000),!as! they!conclude!that!economic!gains!from!merger!is!mainly!due!to!size!effects.!Comparing!this! to!the!confidence!intervals!of!the!size!effects!in!table!5.15,!we!find!that!this!further!deviates! from!the!results!in!Harris!et!al.!(2000).!The!harmony!effects!and!size!effects!will!be!introduced! in!the!following!sections.! ! 5.3.3)Harmony)Effects) In!section!2.5,!we!derive!the!hypothesis!that!the!merger!between!Bispebjerg!and!FrederiksJ berg! Hospitals! will! result! in! cost! reductions! from! harmony! effects! (scope! economies).! The! results!in!table!5.15!refute!this!hypothesis,!as!the!economic!effects!are!fairly!trivial.!Under!VRS! technology,!we!find!economic!effects!ranging!from!0.9949!to!1.0005.!As!presented!in!section! 3.1.5.1,!a!merger!under!NDRS!technology!has!no!disadvantages!of!being!too!large.!Therefore! harmony!effects!under!NDRS!technology!in!table!5.15!are!equal!to!1.0000!in!the!uncorrected! analysis.!Comparing!these!results!to!the!confidence!intervals!in!table!5.15,!we!find!that!the! harmony!effects!almost!certainly!range!very!close!to!1.0000.!We!find!that!the!harmony!effects! are!more!likely!to!result!in!increasing!costs!instead!of!cost!reductions.!The!harmony!effects!of! the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!are!defined!as,! ! !" = !(0.5 !!!" + !!"# )/0.5(! !!!" + ! !!"# )! ! The!inconclusive!harmony!effects!in!table!5.16!concur!with!the!results!in!Connor!et!al.!(1998).!

Table)5.16)Harmony!Effects,!HA) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Harmony!Effects! 0.9986! 1.0000! Harmony!Effects,!biasJcorrected! 1.0005! 1.0000! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Harmony!Effects! 0.9949! 1.0000! Harmony!Effects,!biasJcorrected! 0.9976! 1.0000!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

! 61! !

The!similarity!in!medical!departments!is!not!sufficient!to!exceed!the!dissimilarJsize!hospitals! in!this!merger!analysis.!! In!Kristensen!et!al.!(2010),!mean!harmony!effects!between!0.6%!and!1.4%!are!found!at!the! five! potential! hospital! mergers.! These! economic! gains! deviate! from! the! harmony! effects! in! table! 5.16! under! VRS! and! NDRS! technologies.! However,! a! resemblance! is! found! as! the! two! analyses!indicate!higher!economic!gains!under!VRS!technologies!compared!to!NDRS!technolJ ogies.!!! ! 5.3.4)Size)Effects) In!section!2.6,!we!derived!the!hypothesis!that!the!merger!between!Bispebjerg!and!FrederiksJ berg!Hospital!would!not!result!in!cost!reduction!from!size!effects!(scale!economies).!The!reJ sults! in! table! 5.17! confirm! this! hypothesis,! as! size! effects! vary! between! 1.0085! and! 1.0170! under! VRS! technology.! Under! NDRS! technology,! the! size! effects! are! limited! to! 1.0000.! The! NDRS!technology!has!no!disadvantage!of!being!too!large,!which!explains!the!neutral!size!efJ fects.!The!confidence!intervals!in!table!5.15!emphasize!that!the!merger!between!Bispebjerg! and!Frederiksberg!Hospitals!will!result!in!increasing!costs!due!to!size!effects.!The!size!effects! of!the!merger!are!defined!as,! ! !" = ! !!!" + !!"# /2!(0.5(!!!" + !!"#))! ! The!results!in!table!5.17!correspond!to!the!general!literature!on!size!effects!presented!in!secJ tion!2.!The!potential!loss!from!size!effects!resembles!the!results!in!Dranove!(1998)!and!KrisJ

Table)5.17)Size!Effects,!SI) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Size!Effects! 1.0144! 1.0000! Size!Effects,!biasJcorrected! 1.0085! 1.0000! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Size!Effects! 1.0170! 1.0000! Size!Effects,!biasJcorrected! 1.0119! 1.0000!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

! 62! !

tensen,!Bogetoft!and!Pedersen!(2010).! In!Kristensen!et!al.!(2010),!mean!size!effects!under!uncorrected!and!biasJcorrected!VRS!techJ nologies! equal! 1.0681! and! 1.0448,! respectively.! Meanwhile,! mean! size! effects! under! uncorJ rected!and!biasJcorrected!NDRS!technologies!equal!0.9907!and!0.9916,!respectively.!HowevJ er,!the!mean!potential!gains!under!NDRS!technology!are!based!on!results!from!five!potential! mergers! of! Danish! hospitals.! Mergers! 1,! 4! and! 5! have! size! effects! below! 1.0000! and! are! all! characterized!by!have!less!than!650!beds.!Mergers!2!and!3!have!more!than!650!beds!and!size! effects!equal!to!1.0000.!! ) 5.3.5)Pure)Merger)Effects) As!introduced!in!section!3.2.5,!the!pure!merger!effects!!∗!indicate!the!effects!of!an!actual!merJ ger.!Learning!effects!could!be!achieved!by!applying!best!practice!instead!of!merging.!Harmony! effects!and!size!effect!depend!on!an!actual!merger.! The!pure!merger!effects!for!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!are! defined!as,! ! !∗ = !" ∗ !" = ! !!!" + !!"# /(! !!!" + ! !!"# )! ! The! results! in! table! 5.18! indicate! a! potential! loss! from! pure! merger! effects! under! VRS! and! NDRS!technologies.!These!results!resembles!the!mean!pure!merger!effects!under!VRS!techJ nology!in!Kristensen!et!al.!(2010).!!

Table)5.18!Pure!Merger!Effects,!E*) ) VRS)) NDRS)) Data"Sample"1"(2011"DRGUtariffs)" ! ! Pure!Merger!Effects! 1.0130! 1.0000! Pure!Merger!Effects,!biasJcorrected! 1.0090! 1.0000! ! ! ! Data"Sample"2"(2012"DRGUtariffs)" ! ! Pure!Merger!Effects! 1.0118! 1.0000! Pure!Merger!Effects,!biasJcorrected! 1.0095! 1.0000!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

! 63! !

5.4)Summary) To!ensure!robustness!of!the!analysis,!we!apply!two!alternative!data!samples,!two!alternative! returnsJtoJscale!technologies!and!two!alternative!approaches.!We!consistently!find!economic! gains!in!the!analyses!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals.!! The!preJmerger!analysis!indicates!that!Bispebjerg!and!Frederiksberg!Hospital!are!below!the! efficiency!frontier.!We!find!that!eight!and!six!Danish!hospitals!are!fully!efficient!under!VRS! technology! in! data! sample! 1! and! data! sample! 2,! respectively.! Under! NDRS! technology! only! two!hospitals!are!fully!efficient.!In!analysing!scale!efficiencies,!we!find!that!inefficiencies!at! Bispebjerg!and!Frederiksberg!Hospitals!are!partly!due!to!size.!The!two!hospitals!are!too!large! compared! to! the! other! hospitals! in! the! data! samples.! Peer! units! indicate! from! which! other! hospitals!best!practice!should!be!applied!to!achieve!a!fully!efficient!production!plan.!The!peer! unit!analyses!indicate!that!depending!on!the!returnJtoJscale!and!data!samples,!Bispebjerg!and! Frederiksberg! Hospitals! should! primarily! look! to! Hvidovre! Hospital! and! Sygehus! HimmerJ land,!respectively.!! The! total! economic! effects! of! the! merger! between! Bispebjerg! and! Frederiksberg! Hospitals! indicate!nonJtrivial!potential!cost!reductions!in!certain!scenarios.!! Decomposing! the! total! economic! effects,! we! find! that! the! potential! gains! of! the! merger! are! largely!due!to!learning!effects.!We!find!trivial!gains!from!harmony!effects!and!size!effects,!but! in! overall! the! pure! merger! effects! indicate! that! the! actual! merger! will! result! in! increasing! costs.!The!reduction!in!adjusted!operational!costs!would!be!larger!if!Bispebjerg!and!FrederJ iksberg!Hospitals!apply!best!practice!from!their!peer!unit!instead!of!a!fullJscale!merger.! We!conclude!that!the!economic!effects!in!this!study!of!the!merger!between!Bispebjerg!and! Frederiksberg! Hospital! largely! resemble! the! results! derived! in! similar! studies! of! this! field.! These!conclusions!are!discussed!and!tested!against!a!postJmerger!analysis!in!section!6.!! ! ! !

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6)Discussion) In!this!section,!we!discuss!the!efficiency!scores!and!merger!effects!derived!in!section!5.!We! compare!these!results!to!an!analysis!of!the!postJmerger!data!sample!presented!in!section!4.3,! to!see!if!the!estimated!mergers!effects!recur!and!if!any!immediate!postJmerger!cost!savings! are!found!at!Bispebjerg!and!Frederiksberg!Hospitals.!! ! 6.1)Data)Envelopment)Analysis) As!introduced!in!section!3.1.8,!Newhouse!(1994)!found!that!the!necessary!inputs!are!not!inJ cluded!in!a!DEA!analysis!of!the!healthcare!sector.!We!offset!this!by!utilizing!adjusted!operaJ tional!costs!and!DRGJtariffs!instead!of!e.g.!the!number!of!doctors,!nurses!and!discharged!paJ tients!as!inputs!and!outputs.!The!operational!costs!are!adjusted!to!ensure!a!basis!of!compariJ son!within!and!between!regions.!Likewise,!the!DRGJtariffs!ensure!uniform!principles!of!payJ ment.!However,!the!DRG!tariffs!are!not!without!limitations!as!introduced!in!section!4.2.!The! DRGJtariffs!tend!to!accommodate!the!simple!treatments,!and!do!not!sufficiently!compensate! the!highly!specialized!hospitals.!Table!5.1!confirms!this,!as!Vejle!&!Give!Sygehuse!and!Sygehus! Himmerland!are!the!only!Danish!hospitals!to!be!fully!efficient!under!NDRS!technology.!None! of! the! two! hospitals! are! university! hospitals.! Further,! Sygehus! Himmerland! has! the! lowest! adjusted!operational!costs!of!the!twentyJseven!Danish!Hospital,!while!Vejle!&!Give!Sygehuse! is!eighteenth!in!that!context.!This!would!indicate!few!highly!specialized!treatments.! A!limitation!to!DEA!is!the!correlation!between!variables!and!efficiency!levels.!As!presented!in! section!4.1,!a!higher!number!of!outputs!result!in!more!firms!being!fully!efficient.!As!indicated! in!section!5.1.1,!Vejle!&!Give!Sygehuse!has!the!highest!percentage!of!DRGJincome!from!outpaJ tient! treatments! among! the! twentyJseven! Danish! hospitals.! Likewise,! Sygehus! Himmerland! has! the! highest! percentage! of! DRGJincome! from! inpatient! treatments.! These! outliers! could! explain!the!optimal!efficiency!scores!of!the!two!hospitals.!! Despite! of! the! limitations,! we! find! no! basis! to! reject! the! analysis! of! the! merger! between! Bispebjerg!and!Frederiksberg!Hospitals!in!section!5.!! ! 6.2)Post^Merger)Analysis) As!introduced!in!section!4.3,!we!utilize!data!sample!3!for!a!postJmerger!analysis!to!estimate!if! any!merger!gains!are!realized!within!the!first!year!of!the!hospital!merger.!As!previously!menJ

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Table)6.1)Bispebjerg!and!Frederiksberg!Hospitals!Efficiencies!(2012!DRGJtariffs)) Hospital) VRS)) NDRS)) Efficiency"Scores" ! ! Bispebjerg!Hospital! 0.9742! 0.9742! Frederiksberg!Hospital! 0.9463! 0.9463! ! ! ! Potential"savings,"in"million"DKK" ! ! Bispebjerg!Hospital! 41.4893! 41.4893! Frederiksberg!Hospital! 34.6835! 34.6835!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals! tioned,!the!Bispebjerg!and!Frederiksberg!Hospitals!merged!in!January!2012,!but!for!remained! two! independent! hospitals! in! terms! of! registration! of! treatments! and! economy! throughout! 2012.!! ! In!table!6.1,!we!find!that!Bispebjerg!and!Frederiksberg!Hospitals!are!not!fully!efficient!in!the! DEA!analysis!of!the!twentyJsix!Danish!hospitals.!However,!the!analysis!indicates!a!nonJtrivial! difference!in!the!efficiency!levels!of!the!two!hospitals!in!data!sample!3!compared!to!data!samJ ple!1!and!data!sample!2.!The!efficiency!scores!of!Bispebjerg!Hospital!increase!to!0.9742!under! VRS!technology!from!0.9650!and!0.9476!in!data!sample!1!and!data!sample!2,!respectively.!The! same!tendency!applies!under!NDRS!technology,!where!the!efficiency!score!increase!to!0.9742! from!0.9191!in!data!sample!1!and!0.8892!in!data!sample!2.!! Likewise,!the!increase!in!efficiency!scores!at!Frederiksberg!Hospitals!is!significant.!In!2012,! the!estimated!efficiency!score!of!Frederiksberg!Hospital!is!0.9463!under!VRS!and!NDRS!techJ nologies.!We!find!that!efficiency!scores!have!increase!from!0.9075!and!0.8926!in!data!sample! 1!under!VRS!and!NDRS!technologies,!respectively.!Compared!to!data!sample!2,!the!increase!in! efficiency!scores!is!even!more!significant!from!0.8650!under!VRS!technology,!and!0.8538!unJ der!NDRS!technology.!! The!improved!efficiency!score!obviously!minimize!the!savings!potential!at!the!two!hospitals.! However,!the!results!in!table!6.1!indicate!significant!potential!reduction!in!costs!of!41.5!milJ lion!DKK!and!34.7!million!DKK!at!Bispebjerg!and!Frederiksberg!Hospitals,!respectively.! In! table! 6.2,! we! find! that! the! increase! in! efficiency! scores! is! reflected! in! the! biasJcorrected! analysis!of!the!postJmerger!data!sample.!!

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Table)6.2)Bispebjerg!and!Frederiksberg!Hospitals!Efficiencies,!BiasJCorrected!(2012!DRGJtariffs)) Hospital) VRS)) NDRS)) Efficiency"Scores" ! ! Bispebjerg!Hospital! 0.9546! 0.9587! Frederiksberg!Hospital! 0.9262! 0.9235! ! ! ! Confidence"Intervals,"95%" ! ! Bispebjerg!Hospital! 0.9265!J!0.9727! 0.9390!J!0.9724! Frederiksberg!Hospital! 0.9080!J!0.9447! 0.9037!J!0.9442!

Source:!See!Appendix!9.3!for!calculations!in!R!and!other!Danish!hospitals!

Further,!the!95%!confidence!intervals!in!table!6.2!indicate!that!the!biasJcorrected!efficiency! score!almost!certainly!increased!from!2011!to!2012.!We!find!that!the!width!of!the!confidence! interval!has!decreased!compared!results!in!table!5.9.!! Based!on!the!results!in!tables!6.1!and!6.2,!we!conclude!that!the!efficiency!scores!at!Bispebjerg! and!Frederiksberg!Hospitals!increase!significantly!from!2011!to!2012.!However,!whether!theJ se!efficiency!gains!are!derived!from!the!hospital!merger!remain!uncertain,!and!would!require! a!more!detailed!analysis!of!the!data!samples.!! There! has! been! no! postJmerger! analysis! of! effects! of! the! merger! between! Bispebjerg! and! Frederiksberg!Hospitals.!However,!a!memorandum!from!the!Capital!Region!of!Denmark!supJ ports! the! conclusion! above.! The! memorandum! states! that! savings! of! 5.0! million! DKK! were! realized!in!2012!at!Bispebjerg!and!Frederiksberg!Hospitals!due!to!the!reduction!of!fullJtime! equivalents!in!the!administration.!Further!savings!was!realized!in!2013!and!2014!equalling!a! total!of!14.8!million!DKK.!However,!the!Capital!Region!of!Denmark!emphasize!that!it!is!uncerJ tain! whether! these! cost! savings! are! directly! linked! to! the! merger! between! Bispebjerg! and! Frederiksberg!Hospitals!(Region!Hovedstaden!2014).!! ! Based!on!the!results!in!tables!6.1!and!6.2,!we!analysis!the!potential!economic!effects!of!the! merger!between!Bispebjerg!and!Frederiksberg!Hospitals.!These!merger!effects!based!on!postJ merger!data!form!the!basis!for!a!discussion!of!the!merger!effects!derived!in!section!5.!! In!table!6.3,!we!find!that!the!hospital!merger!generate!total!economic!effects!at!0.9550!under! VRS!and!NDRS!technologies!in!the!uncorrected!analysis.!The!biasJcorrected!analysis!of!data! sample!3!indicates!total!economic!effects!of!0.9345!and!0.9402!under!VRS!and!NDRS!technolJ

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Table)6.3)Merger!Effects) ) VRS)) NDRS)) Total!Economic!Effects" 0.9550! 0.9550! Learning!Effects! 0.9662! 0.9662! Harmony!Effects! 0.9926! 0.9926! Size!Effects! 0.9959! 0.9959! Pure!Merger!Effects! 0.9885! 0.9885!

Source:!See!Appendix!9.3!for!more!detailed!calculations! ogies,!respectively.!By!comparing!the!total!economic!effects!in!tables!6.3!and!6.4!to!the!results! in!section!5.3.1,!we!find!that!the!potential!gains!from!total!economic!effects!have!decreased!in! all!scenarios,!but!one.!This!correlates!to!the!increased!efficiency!scores!in!tables!6.1!and!6.2.! ! In!section!5,!we!find!that!the!potential!gain!from!the!between!Bispebjerg!and!Frederiksberg! Hospitals!is!mainly!due!to!learning!effects!ranging!from!0.8394!to!0.9481.!In!table!6.3,!we!find! that!the!potential!gains!from!learning!effects!in!the!uncorrected!analysis!are!limited!to!3.4%! under!VRS!and!NDRS!technologies.!Likewise,!the!potential!gains!from!learning!effect!in!the! biasJcorrected!analysis!of!data!sample!3!is!5.3%!and!5.1%!under!VRS!and!NDRS!technologies,! respectively.!This!decrease!in!potential!gains!from!learning!effects!indicate!that!a!best!pracJ tice!have!been!applied!to!a!greater!extend.!Despite!the!treatments!remain!at!two!locations!in! 2012,!the!larger!learning!effects!is!a!plausible!outcome!of!the!merger!between!Bispebjerg!and! Frederiksberg!Hospitals.! We!find!it!unclear!whether!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals!reJ sults!in!potential!gains!from!harmony!effects.!The!estimated!harmony!effects!in!tables!6.3!and!

Table)6.4)Merger!Effects,!biasJcorrected) ) VRS)) NDRS)) Total!Economic!Effects" 0.9345! 0.9402! Learning!Effects! 0.9465! 0.9486! Harmony!Effects! 0.9949! 0.9940! Size!Effects! 0.9923! 0.9971! Pure!Merger!Effects! 0.9873! 0.9912!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

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Table)6.5)Merger!Effects,!Confidence!Intervals) ) VRS)) NDRS)) Total!Economic!Effects! 0.9095!J!0.9532! 0.9263!J!0.9532! Learning!Effects! 0.9212!J!0.9646! 0.9289!J!0.9643! Harmony!Effects! 0.9923!J!1.0027! 0.9926!J!0.9972! Size!Effects! 0.9846!J!0.9958! 0.9959!J!1.0000! Pure!Merger!Effects! 0.9873!J!0.9882! 0.9884!J!0.9972!

Source:!See!Appendix!9.3!for!more!detailed!calculations!

6.4!indicate!potential!gains!from!the!merger.!This!is!predominately!supported!by!the!results! in!table!6.5,!but!the!confidence!intervals!indicate!potential!losses!due!to!harmony!effects.!! Overall,!we!must!conclude!that!Bispebjerg!and!Frederiksberg!Hospitals!are!increasingly!harJ monized!from!2011!to!2012.!! ! In!section!5,!we!confirm!the!hypothesis!that!the!merger!between!Bispebjerg!and!FrederiksJ berg!Hospital!results!in!a!potential!loss!from!size!effects.!However,!the!analyses!of!data!samJ ple!3!indicate!a!clear!potential!gain!from!size!effects.!The!number!of!beds!at!Bispebjerg!and!! Frederiksberg!Hospitals!are!not!radically!downsized!after!the!merger,!so!the!postJmerger!size! effects!deviate!from!Aletras!et!al.!(1997),!where!above!620!beds!cause!diseconomies!of!scale.! As!the!pure!merger!effects!are!correlated!to!harmony!effects!and!size!effects,!we!find!potential! gains!from!the!postJmerger!analysis!of!data!sample!3.!Unlike!the!results!in!section!5,!the!postJ merger! analysis! indicate! that! Bispebjerg! and! Frederiksberg! Hospitals! will! not! achieve! ecoJ nomic! gains! by! solely! exploiting! the! learning! effects! and! apply! best! practice.! Based! on! the! analysis!of!data!sample!3,!we!conclude!that!the!full!merger!at!the!planned!Greenfield!hospital! adds!to!the!potential!gains.!! ! 6.3)Summary) In! the! discussion! of! the! results! in! section! 5,! we! find! that! there! are! limitations! to! the! DEAJ approach.!However,!we!find!no!basis!to!reject!the!conclusions!of!the!merger!analysis.! The!postJmerger!analysis!of!data!sample!3!still!indicates!potential!cost!reductions!from!the! merger! between! Bispebjerg! and! Frederiksberg! Hospitals.! Decomposing! the! total! economic! effects,!we!find!that!the!potential!cost!reduction!is!mainly!due!to!learning!effects!like!in!secJ tion!5.!However,!the!potential!postJmerger!learning!effects!are!less!significant.!The!pure!merJ

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ger!effects!in!the!postJmerger!analysis!deviate!from!the!preJmerger!analysis.!In!tables!6.3!to! 6.5,!we!find!that!harmony!effects!and!size!effect!indicate!potential!cost!savings!from!the!merJ ger!between!Bispebjerg!and!Frederiksberg!Hospitals.!Despite!of!the!few!deviations,!the!postJ merger!analysis!supports!the!conclusions!in!section!5.!!

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7)Conclusion) Since!the!1990s!healthcare!expenditures!in!all!OECD!countries!have!significantly!increased.! We!find!that!these!increasing!expenditures!are!mainly!due!to!the!increasing!GDP!per!capita,! and!to!some!extend!the!prolonged!life!expectancy.!The!projections!indicate!that!the!healthcare! expenditures!will!continue!to!increase.!! In!Denmark,!the!Structural!Reform!was!implemented!in!2007!with!the!purpose!to!centralize! the!healthcare!system.!One!objective!was!to!generate!scale!economies!through!hospital!merJ gers.!Bispebjerg!and!Frederiksberg!Hospitals!merged!in!2012,!and!plan!to!fully!merge!in!2025,! when!New!Bispebjerg!Hospital!is!planned!for!completion.!! ! We!find!that!the!studies!within!the!field!of!hospital!merger!are!inconclusive!on!the!economic! effects!of!a!merger.!As!the!number!of!studies!on!Danish!hospital!mergers!is!limited!we!include! studies!from!all!five!healthcare!system.!In!this!study!we!base!your!theoretical!framework!on! four!different!merger!effects,!which!are!total!economic!effects,!learning!effects,!harmony!efJ fects!and!size!effects.!Based!on!these!four!merger!effects!we!derive!four!hypotheses!that!serve! as!the!structure!of!this!study.!The!total!economic!effects!are!the!general!merger!effects!and! are!decomposed!into!learning!effects,!harmony!effects!and!harmony!effects.!Based!on!the!litJ erature!review,!we!expect!the!total!economic!effects,!learning!effects!and!harmony!effect!to! result!in!potential!cost!reduction.!Meanwhile,!we!expect!the!merger!between!Bispebjerg!and! Frederiksberg!Hospital!to!result!in!increasing!costs!from!size!effects.!! ! The!main!focus!of!this!study!is!to!estimate!the!optimal!input!efficiency.!We!utilize!DEA!models! under!variable!returns!to!scale!(VRS)!and!nonJdecreasing!returns!to!scale!(NDRS)!technoloJ gies!to!estimate!the!efficiency!frontier!and!efficiency!scores!of!the!hospitals!in!the!alternative! data!samples.!We!introduce!bootstrapping!to!biasJcorrect!the!upward!biased!DEAJapproach.!! ! We!introduce!the!alternative!data!samples!for!the!analysis!of!the!merger!between!Bispebjerg! and! Frederiksberg! Hospitals.! The! input! variable! of! the! data! samples! is! the! adjusted! operaJ tional!costs!of!the!hospitals,!while!the!tow!output!variables!are!DRG!income!from!inpatient! and!outpatient!treatments.!! !

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To!ensure!robustness!of!the!analysis,!we!apply!two!alternative!data!samples,!two!alternative! returnsJtoJscale!technologies!and!two!alternative!approaches.!We!consistently!find!economic! gains!in!the!analyses!of!the!merger!between!Bispebjerg!and!Frederiksberg!Hospitals.!! The!results!of!the!preJmerger!analysis!indicate!overall!inefficiencies!at!Bispebjerg!and!FrederJ iksberg!Hospitals.!In!some!scenarios!these!inefficiencies!are!nonJtrivial.!We!find!that!the!preJ merger!inefficiency!at!Bispebjerg!Hospital!is!mainly!due!to!scale!efficiencies,!as!the!hospital!is! above!the!optimal!scale!size.!At!Frederiksberg!Hospitals!inefficiencies!are!partly!due!to!scale! efficiencies,!as!Frederiksberg!is!above!the!optimal!scale!size.!In!general,!we!find!that!the!true! biasJcorrected!efficiency!scores!are!significantly!lower!than!the!uncorrected!efficiencies.!! The! analysis! of! the! merger! between! Bispebjerg! and! Frederiksberg! Hospitals! indicate! conJ sistent!cost!reductions!from!total!economic!effects.!! Decomposing! the! total! economic! effects,! we! find! that! the! potential! gains! of! the! merger! are! largely!due!to!learning!effects.!We!find!trivial!gains!from!harmony!effects!and!size!effects,!but! in! overall! the! pure! merger! effects! indicate! that! the! actual! merger! will! result! in! increasing! costs.!The!biasJcorrected!merger!effects!and!confidence!intervals!support!the!conclusions,!as! increasing!costs!due!to!harmony!effects!and!size!effects!are!more!likely!than!cost!reductions.!! Based!on!the!results!in!section!5,!we!conclude!that!the!merger!between!Bispebjerg!and!FredJ eriksberg!Hospitals!do!result!in!cost!reduction.!However,!the!potential!cost!reductions!would! be!even!more!significant,!if!Bispebjerg!and!Frederiksberg!Hospital!had!applied!best!practice! instead!of!a!fullJscale!merger.!The!conclusion!resembles!the!results!of!the!few!other!studies!on! Danish!hospital!mergers.!! ! We! find! that! there! are! limitations! to! the! DEAJapproach! and! the! alternative! data! samples.! However,!in!the!discussion!of!this!study,!we!find!no!reason!to!reject!the!conclusions!of!the! merger!analysis.!A!postJmerger!analysis!supports!the!results!in!section!5.!Decomposing!the! postJmerger!analysis,!we!find!that!cost!reduction!are!mainly!due!to!learning!effect.!However,! the!analysis!indicates!potential!cost!reduction!from!harmony!effects!and!size!effects.!! !! !

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7.1)Further)Research) In!this!section,!we!discuss!some!of!the!questions!that!are!problematized,!but!not!elaborated!in! this!study.!This!includes!the!potential!of!applying!best!practice,!mergers!at!other!hospitals!and! the!regional!economic!effects!of!quality!in!the!healthcare!sector.!! ! We! conclude! that! the! potential! cost! reduction,n! from! the! merger! between! Bispebjerg! and! Frederiksberg!is!mainly!due!to!learning!effects.!However,!it!is!uncertain!how!these!learning! effects! are! implemented! to! ensure! cost! reductions.! The! peer! unit! analysis! indicate! that! Bispebjerg! Hospitals! could! learn! from! Hvidovre! Hospital,! while! could! learn! from! Sygehus! Himmerland.!! Kristensen!et!al.!(2010)!argue!that!low!measurements!of!learning!effects!would!be!due!to!a! range!of!reasons.!It!is!unclear!whether!the!potential!gains!from!learning!effects!should!be!obJ tained!through!better!management,!better!incentives!for!the!staff!or!other!reasons.!A!more! detailed!analysis!of!the!learning!effects!would!therefore!be!interesting!in!order!to!realize!poJ tential!efficiency!gains.! ! Further,!these!learning!effects!are!possible!to!implement!without!a!fullJscale!merger,!it!would! be!possible!to!look!at!other!hospital!mergers!in!Denmark.!As!presented!in!section!1,!Amager! and!Hvidovre!merged!in!2012,!but!treatments!remain!at!two!hospitals.!It!would!be!interesting! to!see!if!this!merger!has!resulted!in!any!cost!reductions.!Any!potential!gains!from!the!merger! would!be!possible!to!compare!to!the!potential!gains!from!New!Bispebjerg!Hospitals.! ! A!newly!published!study!shows!that!Denmark!have!a!high!quality!in!treatments!compared!to! other!OECD!countries,!but!there!are!large!regional!differences!in!quality!and!patient!satisfacJ tion!(Ministry!of!Health!2014).!As!indicate!in!section!1,!health!conditions!do!have!an!effect!on! economic!growth.!It!would!therefore!be!interesting!to!elaborate!on!the!regional!economic!efJ fects!of!the!hospital!mergers.!!

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8)Literature)

Acemoglu,!D.!&!Johnson,!S.,!2006.!Disease"and"Development"U"the"Effect"of"Life"Expectancy"on" Economic"Growth,!Available!at:!http://www.nber.org/papers/w12269![Accessed!March! 21,!2014].!

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! 79! !

9)Appendix) ! 9.1)Abbreviations) BBH! ! Bispebjerg!Hospital! CRS! ! Constant!Returns!to!Scale! DAGS! ! Danish!Ambulatory!Grouping!System! DEA! ! Data!Envelopment!Analysis! DKK! ! Danish!Kroner! DMU! ! Decision!Making!Unit! DRG! ! Diagnosis!Related!Groups! E! ! Total!Economic!Effects! E*! ! Pure!Merger!Effects! ESHI! ! Etatist!Social!Health!Insurance! FBH! ! Frederiksberg!Hospital! FDH! ! Free!Disposable!Hull! FRH! ! Free!Replicability!Hull! GDP! ! Gross!Domestic!Product! HA! ! Harmony!Effects! LE! ! Learning!Effects! NDRS! ! NonJDecreasing!Returns!to!Scale! NHI! ! National!Health!Insurance! NHS! ! National!Health!Service! NIRS! ! NonJIncreasing!Returns!to!Scale! OECD! ! Organisation!for!Economic!CoJoperation!and!Development! PHS! ! Private!Health!Insurance! SFA! ! Stochastic!Frontier!Analysis! SHI! ! Social!Health!Insurance! SI! ! Size!Effects! SSI! ! Statens!Serum!Institut! VRS! ! Variable!Returns!to!Scale! !

! 80! ! 9.2$Data$Samples$ !

Data sample 1 Input Output 2011/2011 No. Hospital Salaries Purchase of Goods Services Others Research Drug Correction Total Input DRG inpatient DRG outpatient Total Output 1301 Rigshospitalet 3.900.620 2.145.382 1.272.446 -846.503 175.460 925.781 5.370.703 4.194.984 1.790.612 5.985.596 1309 Bispebjerg Hospital 1.444.059 330.281 112.487 -214.173 53.972 61.237 1.557.445 1.270.234 577.626 1.847.860 1330 Hvidovre Hospital 1.573.090 449.912 220.940 -132.733 62.787 132.362 1.916.060 1.628.580 705.293 2.333.873 1351 Amager Hospital 259.708 28.139 80.963 1.872 605 1.742 368.336 291.717 101.800 393.517 1401 Frederiksberg Hospital 460.158 150.405 111.376 -9.623 1.330 58.993 651.992 491.086 267.276 758.362 1501 Gentofte Hospital 836.583 368.463 143.844 -91.649 31.656 66.724 1.158.860 763.704 509.845 1.273.549 1502 Glostrup Hospital 1.061.054 392.256 124.823 -54.542 59.185 206.619 1.257.788 858.642 733.960 1.592.602 1516 Herlev Hospital 2.083.002 763.808 401.185 -264.093 121.911 300.695 2.561.295 1.998.618 1.281.288 3.279.906 2000 Nordsjællands Hospital 1.790.015 400.089 256.212 -167.101 32.824 108.176 2.138.215 1.610.853 761.941 2.372.794 4001 Bornholms Hospital 264.682 65.828 80.235 -38.476 0 22.150 350.119 195.740 119.279 315.019 Region Hovedstaden 13.672.970 5.094.563 -1.817.019 539.730 1.884.482 17.330.814 13.304.158 6.848.920 20.153.078 2500 Sygehus Syd 2.415.107 604.762 305.035 -148.369 7.399 188.036 2.981.099 2.171.922 1.065.855 3.237.777 2501 Sygehus Nord 2.361.455 679.333 357.990 83.703 35.720 308.319 3.138.442 2.473.641 1.364.215 3.837.856 Region Sjælland 4.776.562 1.284.095 663.025 -64.667 43.119 496.355 6.119.541 4.645.563 2.430.070 7.075.633 4202 Odense Universitetshospital 3.228.548 1.292.410 472.920 -428.212 194.758 413.060 3.957.847 2.885.422 1.949.127 4.834.549 4212 OUH Svendborg Sygehus 824.178 114.157 137.614 -3.016 6.523 21.744 1.044.666 756.601 443.673 1.200.274 5000 Sygehus Sønderjylland 1.222.396 346.830 241.743 -81.624 1.988 98.371 1.628.986 1.000.829 843.043 1.843.872 5501 Sydvestjysk Sygehus 1.184.763 364.723 203.797 -86.138 3.892 133.024 1.530.229 1.049.960 748.498 1.798.458

6007 Fredericia og Kolding Sygehuse 1.004.767 257.187 188.113 -49.341 4.147 64.737 1.331.842 969.980 617.505 1.587.485 6008 Vejle og Give sygehuse 1.025.653 487.961 180.146 -172.294 27.493 241.109 1.252.864 735.762 987.095 1.722.857 Region Syddanmark 8.543.216 2.879.426 1.446.369 -819.610 238.801 972.298 10.838.301 7.467.851 5.685.177 13.153.028 Regionshospitalet Hor- 6006 sens/Brædstrup/Odder 625.158 120.684 92.273 12.111 2.528 21.335 826.363 640.238 411.068 1.051.306 Regionshospitalerne i Hospi- 6650 talsenheden Vest 1.531.796 383.129 167.588 -132.666 10.137 151.267 1.788.443 1.252.381 806.925 2.059.306 6620 Århus Universitetshospital 4.208.249 1.987.062 546.563 -542.511 185.000 751.815 5.262.547 3.882.754 2.058.714 5.941.468

7005 Regionshospitalet Randers/Grenå 798.505 123.448 85.223 16.654 2.000 22.245 999.585 762.202 477.864 1.240.066 7601 Hospitalsenhed Midt 1.646.461 414.777 190.234 -161.689 2.357 125.284 1.962.142 1.399.763 851.683 2.251.446 Region Midtjylland 8.810.169 3.029.100 1.081.881 -808.101 202.022 1.071.946 10.839.080 7.937.337 4.606.254 12.543.591 7603 Sygehus Thy - Mors 333.265 49.526 42.893 -23.273 0 5.871 396.540 242.591 134.336 376.927 8001 Aalborg sygehus 2.800.407 894.661 373.153 -197.669 94.775 270.917 3.504.859 2.409.176 1.498.873 3.908.049 8003 Sygehus Vendsyssel 771.214 145.640 86.672 -122.801 1.380 35.467 843.877 665.219 300.417 965.636 8005 Sygehus Himmerland 188.963 23.965 24.306 -27.748 0 560 208.926 211.350 51.078 262.428 Region Nordjylland 4.093.849 1.113.792 527.024 -371.492 96.156 312.816 4.954.201 3.528.336 1.984.704 5.513.040

Total 39.896.766 13.400.976 3.718.299 -3.880.888 1.119.828 4.737.897 50.081.939 36.883.245 21.555.125 58.438.370 ! ! ! 81! ! !

Data Sample 2 Input Output 2011/2012 No. Hospital Salaries Purchase of Goods Services Others Research Drug Correction Total Input DRG inpatient DRG outpatient Total Output 1301 Rigshospitalet 3.900.620 2.145.382 1.272.446 -846.503 175.460 925.781 5.370.703 4.257.551 1.675.544 5.933.095 1309 Bispebjerg Hospital 1.444.059 330.281 112.487 -214.173 53.972 61.237 1.557.445 1.233.016 526.268 1.759.284 1330 Hvidovre Hospital 1.573.090 449.912 220.940 -132.733 62.787 132.362 1.916.060 1.609.988 637.867 2.247.855 1351 Amager Hospital 259.708 28.139 80.963 1.872 605 1.742 368.336 264.622 89.479 354.101 1401 Frederiksberg Hospital 460.158 150.405 111.376 -9.623 1.330 58.993 651.992 460.830 251.040 711.870 1501 Gentofte Hospital 836.583 368.463 143.844 -91.649 31.656 66.724 1.158.860 743.851 483.977 1.227.828 1502 Glostrup Hospital 1.061.054 392.256 124.823 -54.542 59.185 206.619 1.257.788 851.104 533.581 1.384.685 1516 Herlev Hospital 2.083.002 763.808 401.185 -264.093 121.911 300.695 2.561.295 1.988.962 1.214.763 3.203.725 2000 Nordsjællands Hospital 1.790.015 400.089 256.212 -167.101 32.824 108.176 2.138.215 1.606.048 699.211 2.305.259 4001 Bornholms Hospital 264.682 65.828 80.235 -38.476 0 22.150 350.119 194.241 109.451 303.692 Region Hovedstaden 13.672.970 5.094.563 -1.817.019 539.730 1.884.482 17.330.814 13.210.213 6.221.181 19.431.394 2500 Sygehus Syd 2.415.107 604.762 305.035 -148.369 7.399 188.036 2.981.099 2.141.598 992.155 3.133.753 2501 Sygehus Nord 2.361.455 679.333 357.990 83.703 35.720 308.319 3.138.442 2.440.232 1.205.950 3.646.182 Region Sjælland 4.776.562 1.284.095 663.025 -64.667 43.119 496.355 6.119.541 4.581.830 2.198.105 6.779.935 4202 Odense Universitetshospital 3.228.548 1.292.410 472.920 -428.212 194.758 413.060 3.957.847 3.562.601 2.210.896 5.773.497 4212 OUH Svendborg Sygehus 824.178 114.157 137.614 -3.016 6.523 21.744 1.044.666 0 0 0 5000 Sygehus Sønderjylland 1.222.396 346.830 241.743 -81.624 1.988 98.371 1.628.986 1.001.622 759.764 1.761.386 5501 Sydvestjysk Sygehus 1.184.763 364.723 203.797 -86.138 3.892 133.024 1.530.229 1.055.944 683.852 1.739.796

6007 Fredericia og Kolding Sygehuse 1.004.767 257.187 188.113 -49.341 4.147 64.737 1.331.842 973.024 572.534 1.545.558 6008 Vejle og Give sygehuse 1.025.653 487.961 180.146 -172.294 27.493 241.109 1.252.864 743.051 899.085 1.642.136 Region Syddanmark 8.543.216 2.879.426 1.446.369 -819.610 238.801 972.298 10.838.301 7.403.166 5.215.753 12.618.919 Regionshospitalet Hor- 6006 sens/Brædstrup/Odder 625.158 120.684 92.273 12.111 2.528 21.335 826.363 633.221 379.574 1.012.795 Regionshospitalerne i Hospi- 6650 talsenheden Vest 1.531.796 383.129 167.588 -132.666 10.137 151.267 1.788.443 1.212.905 748.847 1.961.752 6620 Århus Universitetshospital 4.208.249 1.987.062 546.563 -542.511 185.000 751.815 5.262.547 3.786.441 1.954.157 5.740.598

7005 Regionshospitalet Randers/Grenå 798.505 123.448 85.223 16.654 2.000 22.245 999.585 765.377 450.720 1.216.097 7601 Hospitalsenhed Midt 1.646.461 414.777 190.234 -161.689 2.357 125.284 1.962.142 1.387.745 789.214 2.176.959 Region Midtjylland 8.810.169 3.029.100 1.081.881 -808.101 202.022 1.071.946 10.839.080 7.785.689 4.322.512 12.108.201 7603 Sygehus Thy - Mors 333.265 49.526 42.893 -23.273 0 5.871 396.540 246.497 123.561 370.058 8001 Aalborg sygehus 2.800.407 894.661 373.153 -197.669 94.775 270.917 3.504.859 2.365.060 1.389.113 3.754.173 8003 Sygehus Vendsyssel 771.214 145.640 86.672 -122.801 1.380 35.467 843.877 668.159 283.190 951.349 8005 Sygehus Himmerland 188.963 23.965 24.306 -27.748 0 560 208.926 214.648 46.863 261.511 Region Nordjylland 4.093.849 1.113.792 527.024 -371.492 96.156 312.816 4.954.201 3.494.364 1.842.727 5.337.091

Total 39.896.766 13.400.976 3.718.299 -3.880.888 1.119.828 4.737.897 50.081.939 36.475.262 19.800.278 56.275.540 ! ! 82! ! $

Data Sample 3 Input Output 2012/2012 No. Hospital Salaries Purchase of Goods Services Others Research Drug Correction Total Input DRG inpatient DRG outpatient Total Output 1301 Rigshospitalet 3.986.843 2.310.850 1.195.790 -963.351 168.088 912.154 5.449.889 4.387.531 1.751.721 6.139.252 1309 Bispebjerg Hospital 1.511.207 370.397 35.823 -185.381 55.788 70.604 1.605.655 1.289.019 558.299 1.847.318 1330 Hvidovre Hospital 1.605.098 491.750 188.472 -109.723 74.610 130.100 1.970.887 1.663.864 634.836 2.298.700 1351 Amager Hospital 220.985 28.888 70.485 49.377 0 1.076 368.659 302.629 83.624 386.253 1401 Frederiksberg Hospital 385.424 152.075 89.954 78.284 3.477 56.935 645.324 457.561 261.352 718.913 1501 Gentofte Hospital 831.660 378.164 100.118 -18.257 19.574 78.668 1.193.442 736.373 501.285 1.237.658 1502 Glostrup Hospital 1.117.974 564.351 20.297 23.498 44.758 251.777 1.429.586 972.386 612.539 1.584.925 1516 Herlev Hospital 2.124.766 1.167.468 -172.889 59.832 86.199 324.481 2.768.497 2.133.023 1.274.355 3.407.378 2000 Nordsjællands Hospital 1.727.066 427.131 240.850 -31.679 27.613 114.303 2.221.451 1.655.044 735.069 2.390.113 4001 Bornholms Hospital 260.883 71.784 71.493 -19.539 0 22.918 361.702 206.791 115.243 322.034 Region Hovedstaden 13.771.906 5.962.858 1.840.393 -1.116.941 480.107 1.963.017 18.015.092 13.804.221 6.528.323 20.332.544 2500 Sygehus Syd 2.479.506 662.013 303.089 -170.561 13.737 197.057 3.063.253 2.426.695 1.267.794 3.694.489 2501 Sygehus Nord 2.452.606 725.793 466.544 47.753 21.404 360.051 3.311.242 2.269.271 1.037.414 3.306.685 Region Sjælland 4.932.112 1.387.806 769.632 -122.808 35.141 557.108 6.374.494 4.695.966 2.305.208 7.001.174 4202 Odense Universitetshospital 4.249.485 1.548.731 680.505 -479.793 186.602 482.083 5.330.243 3.656.610 2.395.846 6.052.456 5000 Sygehus Sønderjylland 1.261.005 363.167 264.006 -109.350 3.323 101.195 1.674.310 978.441 795.125 1.773.566 5501 Sydvestjysk Sygehus 1.219.037 380.517 213.649 -82.532 8.495 137.713 1.584.463 1.034.779 724.106 1.758.885

6007 Fredericia og Kolding Sygehuse 1.020.323 290.744 170.844 -81.315 8.803 64.772 1.327.020 938.195 582.104 1.520.299 6008 Vejle og Give sygehuse 1.056.743 471.572 263.230 -99.509 58.362 230.839 1.402.835 730.467 942.736 1.673.203 Region Syddanmark 8.879.085 3.069.404 1.613.517 -851.259 265.585 1.016.946 11.428.216 7.381.408 5.568.730 12.950.138 Regionshospitalet Hor- 6006 sens/Brædstrup/Odder 665.663 130.937 98.251 42.146 5.980 25.751 905.266 648.140 400.616 1.048.756 Regionshospitalerne i Hospi- 6650 talsenheden Vest 1.483.606 417.682 193.670 -194.697 21.384 164.521 1.714.356 1.306.653 789.855 2.096.508 6620 Århus Universitetshospital 4.384.725 2.158.225 1.011.456 -867.603 248.987 840.703 5.597.113 3.956.030 2.011.487 5.967.517

7005 Regionshospitalet Randers/Grenå 770.914 130.200 82.743 8.162 537 28.250 963.232 716.901 445.459 1.162.360 7601 Hospitalsenhed Midt 1.618.750 499.427 254.218 -204.245 16.565 128.858 2.022.727 1.390.175 836.118 2.226.293 Region Midtjylland 8.923.658 3.336.471 1.640.338 -1.216.237 293.453 1.188.082 11.202.695 8.017.899 4.483.535 12.501.434 7603 Sygehus Thy - Mors 339.860 51.980 44.998 -40.426 0 4.952 391.461 256.305 131.572 387.877 8001 Aalborg sygehus 2.825.291 945.710 383.232 -122.793 109.477 305.023 3.616.940 2.360.085 1.411.878 3.771.963 8003 Sygehus Vendsyssel 785.299 152.447 99.819 -105.027 2.914 34.211 895.414 688.808 311.030 999.838 8005 Sygehus Himmerland 191.852 27.166 28.932 2.559 0 349 250.160 220.414 48.930 269.344 Region Nordjylland 4.142.302 1.177.304 556.981 -265.686 112.391 344.536 5.153.974 3.525.612 1.903.410 5.429.022

Total 40.649.063 14.933.843 6.420.861 -3.572.930 1.186.677 5.069.688 52.174.472 37.425.106 20.789.206 58.214.312 !

! 83! !

9.3$Results$from$R$software$ ! Data$Sample$1!

>!library(Benchmarking)! >!xobs!<9!matrix(c(5370703.460,!1557444.828,!1916060.331,!368335.520,!651992.394,!1158860.373,!1257787.919,!2561295.208,! 2138215.347,!350119.001,!2981099.417,!3138441.980,!3957847.233,!1044665.580,!1628985.912,!1530228.946,!1331841.557,! 1252863.882,!826362.572,!1788442.761,!5262547.384,!999585.045,!1962142.198,!396539.588,!3504858.722,!843877.227,!208925.920),! ncol=1)! >!yobs!<9!matrix(c(4194984.000,!1270234.000,!1628580.000,!291717.000,!491086.379,!763704.000,!858642.000,!1998617.768,! 1610852.692,!195740.167,!2171922.000,!2473641.000,!2885422.000,!756601.000,!1000829.000,!1049960.000,!969980.000,!735762.000,! 640238.000,!1252380.504,!3882753.510,!762202.463,!1399763.000,!242591.000,!2409175.858,!665219.000,!211350.000,!1790612.000,! 577626.000,!705293.000,!101800.000,!267276.000,!509845.000,!733960.000,!1281288.000,!761941.000,!119279.000,!1065855.000,! 1364215.000,!1949127.000,!443673.000,!843043.000,!748498.000,!617505.000,!987095.000,!411068.000,!806925.000,!2058714.000,! 477864.000,!851683.000,!134336.000,!1498873.000,!300417.000,!51078.000),!ncol=2)! >!cbind(xobs,yobs)! !!!!!!!!!!![,1]!!!!!![,2]!!!![,3]! ![1,]!5370703.5!4194984.0!1790612! ![2,]!1557444.8!1270234.0!!577626! ![3,]!1916060.3!1628580.0!!705293! ![4,]!!368335.5!!291717.0!!101800! ![5,]!!651992.4!!491086.4!!267276! ![6,]!1158860.4!!763704.0!!509845! ![7,]!1257787.9!!858642.0!!733960! ![8,]!2561295.2!1998617.8!1281288! ![9,]!2138215.3!1610852.7!!761941! [10,]!!350119.0!!195740.2!!119279! [11,]!2981099.4!2171922.0!1065855! [12,]!3138442.0!2473641.0!1364215! [13,]!3957847.2!2885422.0!1949127! [14,]!1044665.6!!756601.0!!443673! [15,]!1628985.9!1000829.0!!843043! [16,]!1530228.9!1049960.0!!748498! [17,]!1331841.6!!969980.0!!617505! [18,]!1252863.9!!735762.0!!987095! [19,]!!826362.6!!640238.0!!411068! [20,]!1788442.8!1252380.5!!806925! [21,]!5262547.4!3882753.5!2058714! [22,]!!999585.0!!762202.5!!477864! [23,]!1962142.2!1399763.0!!851683! [24,]!!396539.6!!242591.0!!134336! [25,]!3504858.7!2409175.9!1498873! [26,]!!843877.2!!665219.0!!300417! [27,]!!208925.9!!211350.0!!!51078! $ $ >!dea.boot(xobs,yobs,NREP=5000,RTS="vrs",ORIENTATION="in")!

! 84! !

$eff! ![1]!1.0000000!0.9650422!1.0000000!0.8482496!0.9074601!0.8493288!0.9595156!1.0000000!0.9010451! [10]!0.8139814!0.9004234!1.0000000!1.0000000!0.8971383!0.8599879!0.9061503!0.9270155!1.0000000! [19]!0.9841512!0.8964649!1.0000000!0.9636413!0.8992850!0.7610423!0.8990016!0.9186724!1.0000000! ! $eff.bc! ![1]!0.9225298!0.9360538!0.9584469!0.8036196!0.8869839!0.8320862!0.9316263!0.9570325!0.8660678! [10]!0.7659988!0.8642282!0.9637448!0.9219944!0.8803735!0.8265800!0.8851444!0.9103238!0.9208659! [19]!0.9683340!0.8741388!0.9215725!0.9493249!0.8734205!0.6981023!0.8556652!0.8931124!0.9215259! ! $bias! ![1]!0.07747016!0.02898838!0.04155314!0.04463005!0.02047619!0.01724264!0.02788932!0.04296747! ![9]!0.03497735!0.04798259!0.03619524!0.03625516!0.07800559!0.01676482!0.03340797!0.02100598! [17]!0.01669169!0.07913409!0.01581719!0.02232611!0.07842751!0.01431635!0.02586446!0.06294000! [25]!0.04333644!0.02555997!0.07847406! ! $var! ![1]!5.319052e903!4.212558e904!6.409759e904!7.559815e904!1.154549e904!6.161319e905!3.748589e904! ![8]!6.452786e904!3.560300e904!6.846614e904!3.026407e904!4.706810e904!5.162916e903!5.843219e905! [15]!2.921040e904!1.115457e904!7.108387e905!5.393660e903!8.890643e905!1.138549e904!!!!!!!!!!NaN! [22]!6.658776e905!1.337899e904!7.236272e904!5.836364e904!1.980397e904!5.490061e903! ! $var0! ![1]!3.365014e903!3.899434e904!5.307012e904!8.380628e904!1.271983e904!7.901196e905!3.481777e904! ![8]!5.298208e904!3.750811e904!8.197343e904!3.196103e904!3.963415e904!3.311602e903!6.737931e905! [15]!3.378423e904!1.231669e904!7.664925e905!3.391124e903!8.465256e905!1.288182e904!3.857295e903! [22]!6.673398e905!1.487536e904!9.775477e904!5.903551e904!2.076596e904!3.459414e903! ! $conf.int! !!!!!!!!!!!2.5%!!!!!97.5%! ![1,]!0.8193370!0.9974498! ![2,]!0.8998865!0.9630507! ![3,]!0.9183162!0.9974029! ![4,]!0.7651053!0.8458000! ![5,]!0.8683743!0.9053253! ![6,]!0.8197846!0.8476025! ![7,]!0.8961575!0.9572957! ![8,]!0.9153884!0.9974083! ![9,]!0.8388268!0.8983678! [10,]!0.7339961!0.8120428! [11,]!0.8398499!0.8981048! [12,]!0.9268293!0.9972002! [13,]!0.8244587!0.9974443! [14,]!0.8674354!0.8949980! [15,]!0.8019875!0.8578739! [16,]!0.8671101!0.9040731! [17,]!0.8954829!0.9252815! [18,]!0.8188943!0.9970626!

! 85! !

[19,]!0.9487429!0.9821000! [20,]!0.8577249!0.8946354! [21,]!0.8175386!0.9970549! [22,]!0.9327257!0.9619772! [23,]!0.8569270!0.8966862! [24,]!0.6816889!0.7590825! [25,]!0.8220975!0.8962877! [26,]!0.8686513!0.9159554! [27,]!0.8188893!0.9966467! ! $eref! NULL! $ >!dea.boot(xobs,yobs,NREP=5000,RTS="irs",ORIENTATION="in")! $eff! ![1]!0.8660525!0.9190812!0.9458579!0.8380856!0.8925702!0.8337305!0.9466344!0.9737601!0.8578957! [10]!0.8139814!0.8380479!0.9377147!0.9260674!0.8780789!0.8469958!0.8882358!0.9067352!1.0000000! [19]!0.9673227!0.8753295!0.8675965!0.9445523!0.8751169!0.7610423!0.8493354!0.8867133!1.0000000! ! $eff.bc! ![1]!0.8326551!0.8924330!0.9162444!0.7687162!0.8586046!0.8040178!0.9010113!0.9565360!0.8323438! [10]!0.7361783!0.8139944!0.9198020!0.9048143!0.8543384!0.8005375!0.8595405!0.8853475!0.8952538! [19]!0.9394861!0.8546466!0.8473214!0.9214395!0.8561299!0.6653935!0.8303959!0.8538218!0.8967233! ! $bias! ![1]!0.03339747!0.02664817!0.02961344!0.06936945!0.03396552!0.02971273!0.04562310!0.01722414! ![9]!0.02555191!0.07780317!0.02405353!0.01791268!0.02125311!0.02374051!0.04645822!0.02869521! [17]!0.02138775!0.10474618!0.02783660!0.02068286!0.02027514!0.02311285!0.01898697!0.09564885! [25]!0.01893955!0.03289147!0.10327673! ! $var! ![1]!0.0003152042!0.0002686207!0.0003504901!0.0011462778!0.0002333751!0.0001582952!0.0006783127! ![8]!0.0001522282!0.0001931848!0.0011787742!0.0001535931!0.0001224221!0.0001625001!0.0001266909! [15]!0.0004996322!0.0002063971!0.0001395061!0.0053143345!0.0002204349!0.0001263830!0.0001169991! [22]!0.0001668056!0.0001069468!0.0010432075!0.0001060432!0.0002738465!0.0053765549! ! $var0! ![1]!0.0003608819!0.0002786517!0.0003377201!0.0012402793!0.0002545744!0.0002012326!0.0006157515! ![8]!0.0001457307!0.0002327924!0.0013212134!0.0001957478!0.0001268400!0.0001700377!0.0001478162! [15]!0.0005758641!0.0002300550!0.0001529347!0.0032706850!0.0002068876!0.0001491182!0.0001410106! [22]!0.0001673058!0.0001271147!0.0013127035!0.0001339032!0.0003015217!0.0033058857! ! $conf.int! !!!!!!!!!!!2.5%!!!!!97.5%! ![1,]!0.8072032!0.8633661! ![2,]!0.8635182!0.9173035! ![3,]!0.8830010!0.9430258! ![4,]!0.7433958!0.8342716!

! 86! !

![5,]!0.8380992!0.8887358! ![6,]!0.7880245!0.8308931! ![7,]!0.8632230!0.9422679! ![8,]!0.9305681!0.9723875! ![9,]!0.8107023!0.8562498! [10,]!0.7152742!0.8099371! [11,]!0.7954114!0.8364522! [12,]!0.8973556!0.9359881! [13,]!0.8812389!0.9241861! [14,]!0.8369286!0.8755642! [15,]!0.7761985!0.8442895! [16,]!0.8377023!0.8855536! [17,]!0.8639571!0.9047187! [18,]!0.8171121!0.9942127! [19,]!0.9122779!0.9630343! [20,]!0.8353847!0.8736931! [21,]!0.8287485!0.8658225! [22,]!0.8976944!0.9419309! [23,]!0.8376923!0.8733431! [24,]!0.6660755!0.7557073! [25,]!0.8129314!0.8480398! [26,]!0.8304515!0.8837315! [27,]!0.8169256!0.9938058! ! $eref! NULL! $ Data$Sample$2$

>!library(Benchmarking)! >!xobs!<9!matrix(c(5370703.460,!1557444.828,!1916060.331,!368335.520,!651992.394,!1158860.373,!1257787.919,!2561295.208,! 2138215.347,!350119.001,!2981099.417,!3138441.980,!5002512.813,!1628985.912,!1530228.946,!1331841.557,!1252863.882,! 826362.572,!1788442.761,!5262547.384,!999585.045,!1962142.198,!396539.588,!3504858.722,!843877.227,!208925.920),!ncol=1)! >!yobs!<9!matrix(c(4257551.000,!1233016.000,!1609988.000,!264622.000,!460830.000,!743851.000,!851104.000,!1988962.000,! 1606048.000,!194241.000,!2141598.000,!2440232.000,!3562601.000,!1001622.000,!1055944.000,!973024.000,!743051.000,!633221.000,! 1212905.000,!3786441.000,!765377.000,!1387745.000,!246497.000,!2365060.000,!668159.000,!214648.000,!1675544.000,!526268.000,! 637867.000,!89479.000,!251040.000,!483977.000,!533581.000,!1214763.000,!699211.000,!109451.000,!992155.000,!1205950.000,! 2210896.000,!759764.000,!683852.000,!572534.000,!899085.000,!379574.000,!748847.000,!1954157.000,!450720.000,!789214.000,! 123561.000,!1389113.000,!283190.000,!46863.000),ncol=2)! >!cbind(xobs,yobs)! !!!!!!!!!!![,1]!!!![,2]!!!![,3]! ![1,]!5370703.5!4257551!1675544! ![2,]!1557444.8!1233016!!526268! ![3,]!1916060.3!1609988!!637867! ![4,]!!368335.5!!264622!!!89479! ![5,]!!651992.4!!460830!!251040! ![6,]!1158860.4!!743851!!483977! ![7,]!1257787.9!!851104!!533581!

! 87! !

![8,]!2561295.2!1988962!1214763! ![9,]!2138215.3!1606048!!699211! [10,]!!350119.0!!194241!!109451! [11,]!2981099.4!2141598!!992155! [12,]!3138442.0!2440232!1205950! [13,]!5002512.8!3562601!2210896! [14,]!1628985.9!1001622!!759764! [15,]!1530228.9!1055944!!683852! [16,]!1331841.6!!973024!!572534! [17,]!1252863.9!!743051!!899085! [18,]!!826362.6!!633221!!379574! [19,]!1788442.8!1212905!!748847! [20,]!5262547.4!3786441!1954157! [21,]!!999585.0!!765377!!450720! [22,]!1962142.2!1387745!!789214! [23,]!!396539.6!!246497!!123561! [24,]!3504858.7!2365060!1389113! [25,]!!843877.2!!668159!!283190! [26,]!!208925.9!!214648!!!46863! >$ >!dea.boot(xobs,yobs,NREP=5000,RTS="vrs",ORIENTATION="in")! $eff! ![1]!1.0000000!0.9475873!1.0000000!0.7650613!0.8650327!0.8378712!0.8736605!1.0000000!0.9066996! [10]!0.8157047!0.8926494!0.9829051!1.0000000!0.8502011!0.9024569!0.9253398!1.0000000!0.9714896! [19]!0.8739310!0.9614620!0.9676303!0.8924972!0.7638025!0.8840180!0.9279410!1.0000000! ! $eff.bc! ![1]!0.9112710!0.9172006!0.9582607!0.7052885!0.8375371!0.8125288!0.8522719!0.9477306!0.8697432! [10]!0.7618959!0.8557020!0.9454178!0.9103380!0.8085559!0.8761247!0.9036469!0.9097312!0.9518051! [19]!0.8450717!0.9018668!0.9493143!0.8614457!0.6956169!0.8336495!0.8986671!0.9099553! ! $bias! ![1]!0.08872901!0.03038667!0.04173931!0.05977275!0.02749561!0.02534234!0.02138868!0.05226939! ![9]!0.03695635!0.05380881!0.03694739!0.03748735!0.08966202!0.04164519!0.02633214!0.02169283! [17]!0.09026881!0.01968451!0.02885939!0.05959523!0.01831605!0.03105152!0.06818557!0.05036847! [25]!0.02927381!0.09004472! ! $var! ![1]!0.0069044205!0.0003616875!0.0005983949!0.0009291476!0.0001616169!0.0001322294!0.0001128406! ![8]!0.0010288294!0.0003546166!0.0007710904!0.0003186733!0.0004658320!0.0072439631!0.0004659182! [15]!0.0001722390!0.0001203523!0.0072773546!0.0001332399!0.0001755732!0.0019316572!0.0001117818! [22]!0.0001927798!0.0008089964!0.0006736225!0.0002332816!0.0069995961! ! $var0! ![1]!0.0041607615!0.0003482894!0.0004954971!0.0012084643!0.0001917329!0.0001681309!0.0001337368! ![8]!0.0008122218!0.0003668594!0.0009097252!0.0003398577!0.0004040022!0.0043213592!0.0005319962! [15]!0.0001875767!0.0001271948!0.0043676723!0.0001276987!0.0002035237!0.0015281425!0.0001087061! [22]!0.0002133736!0.0010722385!0.0006899807!0.0002367754!0.0042164871!

! 88! !

! $conf.int! !!!!!!!!!!!2.5%!!!!!97.5%! ![1,]!0.8066818!0.9964631! ![2,]!0.8858969!0.9449978! ![3,]!0.9196266!0.9968342! ![4,]!0.6773838!0.7626611! ![5,]!0.8193577!0.8626663! ![6,]!0.7968642!0.8357380! ![7,]!0.8348012!0.8715187! ![8,]!0.9009849!0.9970149! ![9,]!0.8431099!0.9038445! [10,]!0.7327224!0.8134942! [11,]!0.8314321!0.8895069! [12,]!0.9091085!0.9797182! [13,]!0.8034383!0.9965854! [14,]!0.7789358!0.8475041! [15,]!0.8552236!0.8996729! [16,]!0.8845478!0.9227925! [17,]!0.8066861!0.9971592! [18,]!0.9286448!0.9689140! [19,]!0.8268166!0.8715862! [20,]!0.8384386!0.9586143! [21,]!0.9274699!0.9649776! [22,]!0.8424655!0.8900492! [23,]!0.6821044!0.7614063! [24,]!0.8011988!0.8813707! [25,]!0.8726933!0.9250199! [26,]!0.8066007!0.9965740! ! $eref! NULL! ! >!dea.boot(xobs,yobs,NREP=5000,RTS="irs",ORIENTATION="in")! $eff! ![1]!0.8714418!0.8892236!0.9252822!0.7611435!0.8537939!0.8242200!0.8573564!0.9748762!0.8482640! [10]!0.8157047!0.8257222!0.9109733!0.8990825!0.8372256!0.8845840!0.9054441!1.0000000!0.9557489! [19]!0.8546416!0.8543176!0.9492203!0.8665195!0.7638025!0.8357868!0.8876204!1.0000000! ! $eff.bc! ![1]!0.8285944!0.8543138!0.8849909!0.6629074!0.8039055!0.7795229!0.8223852!0.9516881!0.8138928! [10]!0.7238552!0.7943956!0.8853001!0.8731076!0.7771044!0.8504530!0.8786500!0.8779453!0.9198610! [19]!0.8254173!0.8283969!0.9197750!0.8416229!0.6540337!0.8108494!0.8465402!0.8786514! ! $bias! ![1]!0.04284743!0.03490982!0.04029136!0.09823602!0.04988842!0.04469703!0.03497112!0.02318805! ![9]!0.03437124!0.09184956!0.03132660!0.02567328!0.02597495!0.06012113!0.03413095!0.02679412! [17]!0.12205472!0.03588782!0.02922435!0.02592068!0.02944534!0.02489657!0.10976878!0.02493736!

! 89! !

[25]!0.04108021!0.12134862! ! $var! ![1]!0.0005175019!0.0003894857!0.0005594510!0.0013072929!0.0003756975!0.0003259069!0.0002854031! ![8]!0.0002829085!0.0003285196!0.0013791349!0.0002353336!0.0002224400!0.0002555684!0.0006368579! [15]!0.0003173677!0.0002402883!0.0064844576!0.0003704759!0.0002340424!0.0001741332!0.0002981755! [22]!0.0001835536!0.0012319005!0.0001847679!0.0004001528!0.0066423985! ! $var0! ![1]!0.0005636269!0.0004183673!0.0005402671!0.0016176660!0.0004248307!0.0004010090!0.0003326843! ![8]!0.0002610690!0.0003908460!0.0014886209!0.0003002312!0.0002361390!0.0002764998!0.0007214221! [15]!0.0003469243!0.0002565500!0.0037384220!0.0003428248!0.0002790060!0.0002113381!0.0002861796! [22]!0.0002161773!0.0014885537!0.0002339176!0.0004257979!0.0038157749! ! $conf.int! !!!!!!!!!!!2.5%!!!!!97.5%! ![1,]!0.7993616!0.8685444! ![2,]!0.8252492!0.8866582! ![3,]!0.8493675!0.9213656! ![4,]!0.6606529!0.7553768! ![5,]!0.7866217!0.8486780! ![6,]!0.7621884!0.8197806! ![7,]!0.7997260!0.8544478! ![8,]!0.9175632!0.9728109! ![9,]!0.7893432!0.8461406! [10,]!0.7095167!0.8098377! [11,]!0.7740218!0.8235936! [12,]!0.8589969!0.9087139! [13,]!0.8453819!0.8973083! [14,]!0.7567933!0.8326224! [15,]!0.8239287!0.8815983! [16,]!0.8515095!0.9031688! [17,]!0.8046261!0.9919203! [18,]!0.8881988!0.9505463! [19,]!0.8021650!0.8526243! [20,]!0.8075352!0.8522987! [21,]!0.8893144!0.9456597! [22,]!0.8189452!0.8644231! [23,]!0.6613180!0.7582645! [24,]!0.7891946!0.8343103! [25,]!0.8208048!0.8834618! [26,]!0.8033251!0.9919888! ! $eref! NULL! $ $

! 90! !

Data$Sample$3$

>!library(Benchmarking)! >!xobs!<9!matrix(c(5449889.247,!1605655.062,!1970887.453,!368658.794,!645323.684,!1193441.984,!1429586.129,!2768496.683,! 2221451.019,361702.075,!3063252.645,!3311241.849,!5330243.477,!1674309.984,!1584462.978,!1327020.359,!1402834.886,!905265.676,! 1714356.222,!5597112.898,!963232.433,!2022727.296,!391461.071,!3616939.854,!895413.665,!250159.691),!ncol=1)! >!yobs!<9!matrix(c(4387531.000,!1289019.000,!1663864.000,!302629.000,!457561.000,!736373.000,!972386.000,!2133023.000,! 1655044.000,!206791.000,!2426695.000,!2269271.000,!3656610.000,!978441.000,!1034779.000,!938195.000,!730467.000,!648140.000,! 1306653.000,!3956030.000,!716901.000,!1390175.000,!256305.000,!2360085.000,!688808.000,!220414.000,!1751721.000,!558299.000,! 634836.000,!83624.000,!261352.000,!501285.000,!612539.000,!1274355.000,!735069.000,!115243.000,!1267794.000,!1037414.000,! 2395846.000,!795125.000,!724106.000,!582104.000,!942736.000,!400616.000,!789855.000,!2011487.000,!445459.000,!836118.000,! 131572.000,!1411878.000,!311030.000,!48930.000),!ncol=2)! >!cbind(xobs,yobs)! !!!!!!!!!!![,1]!!!![,2]!!!![,3]! ![1,]!5449889.2!4387531!1751721! ![2,]!1605655.1!1289019!!558299! ![3,]!1970887.5!1663864!!634836! ![4,]!!368658.8!!302629!!!83624! ![5,]!!645323.7!!457561!!261352! ![6,]!1193442.0!!736373!!501285! ![7,]!1429586.1!!972386!!612539! ![8,]!2768496.7!2133023!1274355! ![9,]!2221451.0!1655044!!735069! [10,]!!361702.1!!206791!!115243! [11,]!3063252.6!2426695!1267794! [12,]!3311241.8!2269271!1037414! [13,]!5330243.5!3656610!2395846! [14,]!1674310.0!!978441!!795125! [15,]!1584463.0!1034779!!724106! [16,]!1327020.4!!938195!!582104! [17,]!1402834.9!!730467!!942736! [18,]!!905265.7!!648140!!400616! [19,]!1714356.2!1306653!!789855! [20,]!5597112.9!3956030!2011487! [21,]!!963232.4!!716901!!445459! [22,]!2022727.3!1390175!!836118! [23,]!!391461.1!!256305!!131572! [24,]!3616939.9!2360085!1411878! [25,]!!895413.7!!688808!!311030! [26,]!!250159.7!!220414!!!48930! >! >!dea.boot(xobs,yobs,NREP=5000,!RTS="vrs",ORIENTATION="in")! $eff! ![1]!1.0000000!0.9741605!1.0000000!0.9463207!0.9462541!0.8600318!0.9121930!1.0000000! ![9]!0.9072748!0.9280528!1.0000000!0.8459242!1.0000000!0.8757605!0.9141038!0.9430733! [17]!1.0000000!0.9645523!1.0000000!0.9408752!1.0000000!0.8992099!0.9112961!0.8632953! [25]!0.9456262!1.0000000! !

! 91! !

$eff.bc! ![1]!0.9417030!0.9546404!0.9633299!0.9113388!0.9262252!0.8416067!0.8975027!0.9641547! ![9]!0.8831392!0.8969226!0.9689784!0.8142074!0.9410125!0.8491201!0.8960592!0.9289141! [17]!0.9405859!0.9493148!0.9833131!0.9011856!0.9853301!0.8789583!0.8727737!0.8267471! [25]!0.9270997!0.9406097! ! $bias! ![1]!0.05829695!0.01952016!0.03667008!0.03498193!0.02002884!0.01842512!0.01469027! ![8]!0.03584527!0.02413558!0.03113025!0.03102159!0.03171681!0.05898747!0.02664045! [15]!0.01804467!0.01415926!0.05941409!0.01523754!0.01668687!0.03968958!0.01466988! [22]!0.02025167!0.03852239!0.03654817!0.01852650!0.05939030! ! $var! ![1]!2.658357e903!1.801389e904!4.622618e904!6.724558e904!1.054502e904!6.700947e905! ![7]!5.494554e905!5.402416e904!1.709287e904!4.797312e904!3.428369e904!1.956156e904! [13]!2.611155e903!2.278354e904!9.077651e905!5.795377e905!2.741173e903!6.719897e905! [19]!1.229526e904!7.943751e904!6.785961e905!1.122982e904!5.976580e904!3.601543e904! [25]!8.535304e905!2.767148e903! ! $var0! ![1]!1.942916e903!1.706719e904!3.946237e904!6.176656e904!1.076027e904!8.355967e905! ![7]!6.165217e905!4.575463e904!1.851131e904!4.680397e904!2.981745e904!2.394387e904! [13]!1.906956e903!2.613410e904!9.983298e905!6.089909e905!1.992765e903!6.718695e905! [19]!1.131334e904!7.305783e904!6.316893e905!1.268791e904!5.985210e904!4.134879e904! [25]!8.770908e905!2.012013e903! ! $conf.int! !!!!!!!!!!!2.5%!!!!!97.5%! ![1,]!0.8674564!0.9978962! ![2,]!0.9264825!0.9726662! ![3,]!0.9291079!0.9979175! ![4,]!0.8649012!0.9443690! ![5,]!0.9079699!0.9446975! ![6,]!0.8287832!0.8583294! ![7,]!0.8837600!0.9103495! ![8,]!0.9264316!0.9980590! ![9,]!0.8605759!0.9055576! [10,]!0.8563392!0.9263694! [11,]!0.9383412!0.9980928! [12,]!0.7960970!0.8443841! [13,]!0.8662393!0.9981885! [14,]!0.8236306!0.8742966! [15,]!0.8789403!0.9123348! [16,]!0.9140792!0.9413329! [17,]!0.8645642!0.9978399! [18,]!0.9332704!0.9628274! [19,]!0.9601837!0.9984845! [20,]!0.8542135!0.9389074!

! 92! !

[21,]!0.9681797!0.9982050! [22,]!0.8610526!0.8976543! [23,]!0.8371418!0.9096829! [24,]!0.8021690!0.8617839! [25,]!0.9102186!0.9436994! [26,]!0.8652722!0.9983216! ! $eref! NULL! ! ! >!dea.boot(xobs,yobs,NREP=5000,RTS="irs",ORIENTATION="in")! $eff! ![1]!0.9611098!0.9741605!1.0000000!0.9463207!0.9462541!0.8600318!0.9121930!1.0000000! ![9]!0.9072748!0.9280528!0.9969991!0.8389999!0.9259825!0.8757605!0.9141038!0.9430733! [17]!1.0000000!0.9645523!1.0000000!0.8843363!1.0000000!0.8992099!0.9112961!0.8473688! [25]!0.9456262!1.0000000! ! $eff.bc! ![1]!0.9411029!0.9586763!0.9773093!0.9091147!0.9234891!0.8390396!0.8968936!0.9817219! ![9]!0.8912992!0.8924077!0.9828962!0.8226096!0.9074217!0.8469707!0.8956301!0.9281324! [17]!0.9346087!0.9473008!0.9851743!0.8691054!0.9836210!0.8823334!0.8675582!0.8262148! [25]!0.9270933!0.9347584! ! $bias! ![1]!0.02000690!0.01548418!0.02269066!0.03720603!0.02276492!0.02099219!0.01529942! ![8]!0.01827809!0.01597560!0.03564511!0.01410295!0.01639027!0.01856087!0.02878985! [15]!0.01847374!0.01494096!0.06539132!0.01725151!0.01482565!0.01523089!0.01637897! [22]!0.01687649!0.04373792!0.02115399!0.01853282!0.06524163! ! $var! ![1]!1.327688e904!8.756644e905!1.701349e904!7.964612e904!1.298096e904!8.222406e905! ![7]!5.766690e905!1.091527e904!7.235991e905!5.690312e904!6.598429e905!5.677140e905! [13]!7.837881e905!2.444558e904!8.899706e905!6.163591e905!2.995473e903!8.434363e905! [19]!8.144581e905!5.223873e905!8.376473e905!6.910583e905!6.817017e904!8.031637e905! [25]!8.815878e905!3.034947e903! ! $var0! ![1]!1.301198e904!8.493972e905!1.518734e904!7.258803e904!1.309298e904!1.014471e904! ![7]!6.438325e905!1.003204e904!8.113520e905!5.483723e904!6.192254e905!7.470220e905! [13]!8.410410e905!2.790575e904!9.763292e905!6.438155e905!2.134603e903!8.344657e905! [19]!7.559475e905!6.236657e905!7.722367e905!7.926636e905!6.733196e904!1.029748e904! [25]!9.054110e905!2.165453e903! ! $conf.int! !!!!!!!!!!!2.5%!!!!!97.5%! ![1,]!0.9185842!0.9595431! ![2,]!0.9390050!0.9723559!

! 93! !

![3,]!0.9509156!0.9973269! ![4,]!0.8604238!0.9441473! ![5,]!0.9036815!0.9442444! ![6,]!0.8256340!0.8580448! ![7,]!0.8831149!0.9102602! ![8,]!0.9615336!0.9980356! ![9,]!0.8754721!0.9054610! [10,]!0.8516755!0.9261915! [11,]!0.9662546!0.9951469! [12,]!0.8108786!0.8374807! [13,]!0.8918771!0.9241579! [14,]!0.8221082!0.8739059! [15,]!0.8787072!0.9120986! [16,]!0.9131205!0.9411172! [17,]!0.8594331!0.9974490! [18,]!0.9298193!0.9624066! [19,]!0.9661236!0.9983813! [20,]!0.8572503!0.8829737! [21,]!0.9647225!0.9978458! [22,]!0.8684541!0.8976137! [23,]!0.8318631!0.9092907! [24,]!0.8149331!0.8462830! [25,]!0.9103062!0.9434288! [26,]!0.8598799!0.9979348! ! $eref! NULL! $ $ $

! 94! !

Standard$Error$of$the$Median$! >!library(boot)! >!func!<9!function(d,i)!{!median(d[i])!}! >!treat!<9!matrix(c(5370703.460,!1557444.828,!1916060.331,!368335.520,!651992.394,!1158860.373,!1257787.919,!2561295.208,! 2138215.347,!350119.001,!2981099.417,!3138441.980,!3957847.233,!1044665.580,!1628985.912,!1530228.946,!1331841.557,! 1252863.882,!826362.572,!1788442.761,!5262547.384,!999585.045,!1962142.198,!396539.588,!3504858.722,!843877.227,!208925.920,! 4194984.000,!1270234.000,!1628580.000,!291717.000,!491086.379,!763704.000,!858642.000,!1998617.768,!1610852.692,!195740.167,! 2171922.000,!2473641.000,!2885422.000,!756601.000,!1000829.000,!1049960.000,!969980.000,!735762.000,!640238.000,!1252380.504,! 3882753.510,!762202.463,!1399763.000,!242591.000,!2409175.858,!665219.000,!211350.000,!1790612.000,!577626.000,!705293.000,! 101800.000,!267276.000,!509845.000,!733960.000,!1281288.000,!761941.000,!119279.000,!1065855.000,!1364215.000,!1949127.000,! 443673.000,!843043.000,!748498.000,!617505.000,!987095.000,!411068.000,!806925.000,!2058714.000,!477864.000,!851683.000,! 134336.000,!1498873.000,!300417.000,!51078.000),!ncol=3)! >!Ber!<9!c(25,50,100,250,500,1000,2500,5000,10000)! >!res!<9!NULL! >!for(B!in!Ber)!{! +!!!!!!boo!<9!boot(treat,func,B)! +!!!!!!res!<9!c(res,!format(sqrt(var(boo$t)),!digits=3))! ! rbind(Ber,!res)! ! [,1]!!!!![,2]!!!!![,3]!!!!![,4]!!!!![,5]!!!!![,6]!!!!![,7]!!!!![,8]!!!!![,9]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"221638"!"234851"!"239843"!"250814"!"250042"!"243929"!"240635"!"245288"!"247390"! ! !!!![,10]!!!![,11]!!!![,12]!!!![,13]!!!![,14]!!!![,15]!!!![,16]!!!![,17]!!!![,18]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"188664"!"280852"!"239103"!"242439"!"244562"!"239691"!"250002"!"242441"!"246911"! ! !!!![,19]!!!![,20]!!!![,21]!!!![,22]!!!![,23]!!!![,24]!!!![,25]!!!![,26]!!!![,27]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"253966"!"216107"!"247945"!"260370"!"246935"!"240405"!"245983"!"246309"!"241336"! ! !!!![,28]!!!![,29]!!!![,30]!!!![,31]!!!![,32]!!!![,33]!!!![,34]!!!![,35]!!!![,36]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"308167"!"240962"!"224850"!"230277"!"243288"!"256236"!"249552"!"242829"!"246783"! ! !!!![,37]!!!![,38]!!!![,39]!!!![,40]!!!![,41]!!!![,42]!!!![,43]!!!![,44]!!!![,45]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"203570"!"233136"!"276253"!"238735"!"275208"!"244611"!"245271"!"248675"!"239913"! ! !!!![,46]!!!![,47]!!!![,48]!!!![,49]!!!![,50]!!!![,51]!!!![,52]!!!![,53]!!!![,54]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"194873"!"232325"!"259902"!"256775"!"227190"!"249583"!"254675"!"245957"!"247944"! ! !!!![,55]!!!![,56]!!!![,57]!!!![,58]!!!![,59]!!!![,60]!!!![,61]!!!![,62]!!!![,63]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"281354"!"267723"!"229820"!"238893"!"240239"!"244048"!"247925"!"245112"!"245386"! ! !!!![,64]!!!![,65]!!!![,66]!!!![,67]!!!![,68]!!!![,69]!!!![,70]!!!![,71]!!!![,72]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"214323"!"238271"!"259773"!"242416"!"238649"!"250556"!"245055"!"243778"!"250014"! ! !!!![,73]!!!![,74]!!!![,75]!!!![,76]!!!![,77]!!!![,78]!!!![,79]!!!![,80]!!!![,81]!!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"309232"!"207962"!"236494"!"231010"!"234374"!"253141"!"243001"!"244331"!"244538"! ! !!!![,82]!!!![,83]!!!![,84]!!!![,85]!!!![,86]!!!![,87]!!!![,88]!!!![,89]!!!![,90]!!! ! Ber!"25"!!!!!"50"!!!!!"100"!!!!"250"!!!!"500"!!!!"1000"!!!"2500"!!!"5000"!!!"10000"!! ! res!"182291"!"233698"!"264340"!"249268"!"249633"!"248437"!"250769"!"241751"!"245097"!

! 95! !

9.4$Merger$Effects$ Data!Sample!1!

!! E#VRS! E#NDRS! Bias!E#VRS! Bias!E#NDRS! c(y1)! 1,503,000! 1,431,448! 1,457,852! 1,389,864! c(y2)! 591,657! 581,968! 578,307! 559,801! c(y1+y2)! 2,121,883! 2,013,367! 2,054,396! 1,959,849! x1! 1,557,445! 1,557,445! 1,557,445! 1,557,445! x2! 651,992! 651,992! 651,992! 651,992! x1+x2! 2,209,437! 2,209,437! 2,209,437! 2,209,437! DRG1+DRG2! 1,761,320! 1,761,320! 1,761,320! 1,761,320! DAGS1+DAGS2! 844,902! 844,902! 844,902! 844,902! c(0.5(y1+y2))! 1,045,877! 1,006,684! 1,018,560! 976,687! !! !! !! !! !! E! 0.9604! 0.9113! 0.9298! 0.8824! E*! 1.0130! 1.0000! 1.0090! 1.0000! LE! 0.9481! 0.9113! 0.9216! 0.8824! HA! 0.9986! 1.0000! 1.0005! 1.0000! SI! 1.0144! 1.0000! 1.0085! 1.0000! !

Bias E-VRS Bias E-VRS Bias E-NDRS Bias E-NDRS !! -2.5 +2.5 -2.5 +2.5 c(y1)! 1,401,524! 1,499,898! 1,344,882! 1,428,650! c(y2)! 566,173! 590,265! 546,434! 579,449! c(y1+y2)! 1,982,080! 2,115,279! 1,900,490! 2,009,357! x1! 1,557,445! 1,557,445! 1,557,445! 1,557,445! x2! 651,992! 651,992! 651,992! 651,992! x1+x2! 2,209,437! 2,209,437! 2,209,437! 2,209,437! DRG1+DRG2! 1,761,320! 1,761,320! 1,761,320! 1,761,320! DAGS1+DAGS2! 844,902! 844,902! 844,902! 844,902! c(0.5(y1+y2))! 990,557! 1,042,864! 948,869! 1,003,865! !! !! !! !! !! E! 0.8971! 0.9574! 0.8560! 0.9087! E*! 1.0073! 1.0120! 1.0000! 0.9998! LE! 0.8906! 0.9460! 0.8560! 0.9089! HA! 1.0068! 0.9979! 1.0000! 0.9998! SI! 1.0005! 1.0142! 1.0000! 1.0000! ! ! ! ! !

! 96! !

! Data!Sample!2!

E-VRS E-NDRS Bias E-VRS Bias E-NDRS !! c(y1)! 1,475,815! 1,384,917! 1,428,489! 1,330,547! c(y2)! 563,995! 556,667! 546,068! 524,140! c(y1+y2)! 2,063,976! 1,941,584! 1,993,223! 1,875,675! x1! 1,557,445! 1,557,445! 1,557,445! 1,557,445! x2! 651,992! 651,992! 651,992! 651,992! x1+x2! 2,209,437! 2,209,437! 2,209,437! 2,209,437! DRG1+DRG2! 1,693,846! 1,693,846! 1,693,846! 1,693,846! DAGS1+DAGS2! 777,308! 777,308! 777,308! 777,308! c(0.5(y1+y2))! 1,014,750! 970,792! 984,863! 933,383! !! !! !! !! !! E! 0.9342! 0.8788! 0.9021! 0.8394! E*! 1.0118! 1.0000! 1.0095! 1.0000! LE! 0.9232! 0.8788! 0.8937! 0.8394! HA! 0.9949! 1.0000! 0.9976! 1.0000! SI! 1.0170! 1.0000! 1.0119! 1.0000! !

Bias E-VRS Bias E-VRS Bias E-NDRS Bias E-NDRS !! -2.5 +2.5 -2.5 +2.5 c(y1)! 1,379,736! 1,471,782! 1,285,280! 1,380,921! c(y2)! 534,215! 562,452! 512,871! 553,332! c(y1+y2)! 1,927,504! 2,057,086! 1,815,059! 1,937,175! x1! 1,557,445! 1,557,445! 1,557,445! 1,557,445! x2! 651,992! 651,992! 651,992! 651,992! x1+x2! 2,209,437! 2,209,437! 2,209,437! 2,209,437! DRG1+DRG2! 1,693,846! 1,693,846! 1,693,846! 1,693,846! DAGS1+DAGS2! 777,308! 777,308! 777,308! 777,308! c(0.5(y1+y2))! 961,859! 1,011,604! 906,347! 967,454! !! !! !! !! !! E! 0.8724! 0.9310! 0.8139! 0.8755! E*! 1.0071! 1.0112! 1.0000! 1.0000! LE! 0.8663! 0.9207! 0.8139! 0.8755! HA! 1.0051! 0.9946! 1.0000! 1.0000! SI! 1.0020! 1.0167! 1.0000! 1.0000! ! ! ! ! !

! 97! !

Data!Sample!3! !

E-VRS E-NDRS Bias E-VRS Bias E-NDRS !! c(y1)! 1,564,166! 1,564,166! 1,532,823! 1,539,303! c(y2)! 610,640! 610,640! 597,715! 595,949! c(y1+y2)! 2,149,755! 2,149,755! 2,103,447! 2,116,356! x1! 1,605,655! 1,605,655! 1,605,655! 1,605,655! x2! 645,324! 645,324! 645,324! 645,324! x1+x2! 2,250,979! 2,250,979! 2,250,979! 2,250,979! DRG1+DRG2! 1,746,580! 1,746,580! 1,746,580! 1,746,580! DAGS1+DAGS2! 819,651! 819,651! 819,651! 819,651! c(0,5(y1+y2))! 1,079,337! 1,079,337! 1,059,853! 1,061,254! !! !! !! !! !! E! 0.9550! 0.9550! 0.9345! 0.9402! E*! 0.9885! 0.9885! 0.9873! 0.9912! LE! 0.9662! 0.9662! 0.9465! 0.9486! HA! 0.9926! 0.9926! 0.9949! 0.9940! SI! 0.9959! 0.9959! 0.9923! 0.9971! !

Bias E-VRS Bias E-VRS Bias E-NDRS Bias E-NDRS !! -2.5 +2.5 -2.5 +2.5 c(y1)! 1,487,611! 1,561,766! 1,507,718! 1,561,268! c(y2)! 585,934! 609,636! 583,167! 609,343! c(y1+y2)! 2,047,222! 2,145,685! 2,116,356! 2,145,532! x1! 1,605,655! 1,605,655! 1,605,655! 1,605,655! x2! 645,324! 645,324! 645,324! 645,324! x1+x2! 2,250,979! 2,250,979! 2,250,979! 2,250,979! DRG1+DRG2! 1,746,580! 1,746,580! 1,746,580! 1,746,580! DAGS1+DAGS2! 819,651! 819,651! 819,651! 819,651! c(0.5(y1+y2))! 1,039,600! 1,077,359! 1,042,541! 1,077,232! !! !! !! !! !! E! 0.9095! 0.9532! 0.9263! 0.9532! E*! 0.9873! 0.9882! 0.9972! 0.9884! LE! 0.9212! 0.9646! 0.9289! 0.9643! HA! 1.0027! 0.9923! 0.9972! 0.9926! SI! 0.9846! 0.9958! 1.0000! 0.9959! !

! 98!