Technical Background and Data Set

Z"$( ,E/0F&/0%1( /G,( $,&'0/=( ")( /G,( ."E/( *&'FJ#0E/( P$"+#./0L0/=( 0%+,M( 0%( /G,( H&0N&%( WOXOKY( 0%+#E/$=2( N,( &PP'=(&(/G$,,:E/&1,(F,/G"+A(HG,($,&'0/=(")(I*(N"#'+(V,("V/&0%,+(V=($,F"L0%1(/G,(,M"1,%"#E(,%L0$"%F,%/&'( %"0E,(V=(/G,(F,/G"+A(

Stage One: Estimate the Original Cost Malmquist Index

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e,( )#$/G,$(,M/,%+(/G,(+,."FP"E0/0"%(")(/G,(."E/(*&'FJ#0E/(P$"+#./0L0/=(0%+,M(#%+,$(/G,(L&$0&V',($,/#$%E(/"(E.&',A( HG,("L,$&''(/G,(+,."FP"E0/0"%(")(/G,(."E/(*&'FJ#0E/(P$"+#./0L0/=(0%+,M(0E(&E()"''"NE](

+, ' -./ u'u' . 0/ u' -/ u' +1/ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( W6Y(

NG,$,( '-./(i(P#$,(/,.G%0.&'(,))0.0,%.=(.G&%1,j('.(i(/,.G%0.&'(.G&%1,j('0/(i(&''".&/0L,(,))0.0,%.=(.G&%1,j( '-/( i( P$0.,(,)),./(.G&%1,j( &%+( '+1/( i( ."E/( E.&',(,))0.0,%.=(.G&%1,A( @&'#,E( ")( /G,(&V"L,( )0L,( ."FP"%,%/E( 1$,&/,$(/G&%(#%0/=(E#11,E/(+,/,$0"$&/0"%2(NG0',(L&'#,E(',EE(/G&%(6(E#11,E/(/G,(0FP$"L,F,%/A(

I"FP#/0%1(&%+(+,."FP"E0%1(/G,(."E/(*&'FJ#0E/(P$"+#./0L0/=(0%+,M(I*($,J#0$,E(/G,(."FP#/&/0"%(")(/G,( F0%0F#F(."E/()#%./0"%(#%+,$(V"/G(@\4(&%+(I\4(/,.G%"'"10,EA(Z"$(/G,(2/G(+,.0E0"%(F&h0%1(#%0/(Wd*UY("$(/G,(

3 3 OXOK()0$F( 3 +

4 W2 #$ Y ( 0E(."FP#/,+()$"F(/G,()"''"N0%1('0%,&$(P$"1$&FF0%1(P$"V',FE](

3 3 3 F0% 3 $6

2 5 5 + 4 W2 #$ Y (((((((((((((((((((((((((((((((( (

W>Y

(2 6 O

3 3 4#V^,./( 3 /"( ¦ O

9 # 9 7 t # 2 7 2 7 62 >2 AAA ,

¦ O 9 6 9 5 d 6 2 5 2 5 62 >2 AAA : j(

9 62 O 9 t ?2 6 5 t ? A(

3 3 Z"$( /G,( F0%0F#F( ."E/( )#%./0"%( 3 + + W2 #$ Y ( #%+,$( /G,( ."%E/&%/( $,/#$%E( /"( E.&',( /,.G%"'"1=2( 0/( .&%( V,(

.&'.#'&/,+( V=( $,'&M0%1( /G,( ."%E/$&0%/( 8 ¦ O

9 6 ( )$"F( DJ#&/0"%( W<YA( -E( )"$( /G,( F0M,+:P,$0"+( ."E/( )#%./0"%(

4 W # 2 $ Y 2(0/(.&%(V,(E0F0'&$'=(."FP#/,+(&E()"''"NE](

3 3 3 6 3 F0% 6 W

(2 6 O $6 2 5 5 + 4 # 2 $ Y ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( W<Y(

3 3 6 4#V^,./( 3 /"( ¦ O

9 # 9 7 t # 2 7 2 7 62 >2 AAA ,

¦ O 9 6 9 5 d 6 2 5 2 5 62 >2 AAA : j(

;9>( D4H3*-H35`(H[D(H[\DD:4H-`D(I_4H(*-R*fU34H(K\_dUIH3@3HT(35dDg(

9 62 O 9 t ?2 6 5 t ? A(

3 6 3 6 3 6 3 6 3 3 6 3 6 3 6 3 6 3 6 3 3 _/G,$( ."E/( )#%./0"%E2( 6 +

4 W # 2 $ Y 2( + 4 W2 #$ Y 2( + + W # 2 $ Y 2( &%+( + + W2 #$ Y ( &$,(

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9 6 A(

HG,(F,/G"+(")(T&%1(&%+([#&%1(W>??CY(0E(&%(,M.,'',%/(."%/$0V#/0"%2(V#/(0/(+0+(%"/(+,&'(N0/G(/G,(,M"1,%"#E( ,%L0$"%F,%/&'(L&$0&V',E(&%+(%"0E,EA(

Stage Two: Adjust the Original Input Variables by the Exogenous Environmental Variables

3%( /G,( E,."%+( E/&1,2( /G,( 0%P#/( E'&.hE2( /G,( "#/."F,E( )$"F( /G,( )0$E/( E/&1,2( &$,( $,1$,EE0%1( &1&0%E/( &( E,/( ")( ,%L0$"%F,%/&'( L&$0&V',EA( O,.&#E,( ")( /G,( $,1$,EE0"%2( /G,( "$010%&'( 0%P#/( L&$0&V',E( &$,( /G,%( &+^#E/,+( V=( /G,( ,M"1,%"#E(,%L0$"%F,%/&'(L&$0&V',EA(-.."#%/0%1()"$(,%L0$"%F,%/&'(,)),./E(&%+(E/&/0E/0.&'(%"0E,(0%(."E/(*&'FJ#0E/( P$"+#./0L0/=(0%+,M2(/G0E(E/&1,(0E(/G,(E&F,(&E(/G,(E/".G&E/0.()$"%/0,$(&%&'=E0E(W4Z-YA(3/(.&%(V,(EG"N%(&E](

I"E/(D))0.0,%.=(i(F&%&1,$0&'(,))0.0,%.=(k(%"%:+0E.$,/0"%&$=(0FP&./E(k($&%+"F(%"0E,(

+/ 0 +/ ;< WY = (

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DJ#&/0"%( W8Y( N,$,( "V/&0%,+( )$"F( /G,( I*( 0%( /G,( )0$E/( E/&1,A( HG,( E'&.h( L&$0&V',( ."#'+( V,( /G,( $,E#'/E( ")( ,%L0$"%F,%/&'()&./"$E2($&%+"F(,$$"$E2(&%+(F&%&1,F,%/(,$$"$EA(

1 >2 ? >2 ? >2 O t ? ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( W8Y(

NG,$,(? >2 (i(/G,(>/G(0%P#/(")(/G,(2/G(d*Uj(1 >2 (i(/G,(>/G(0%P#/(E'&.h(")(/G,(2/G(d*UA( HG,(."%.,P/E(&%+(0+,&E(")(E/".G&E/0.()$"%/0,$(P$"+#./0"%(&PP$"&.G(+,L,'"P,+(V=(O&//,E,(&%+(I",''0(W6C99Y( ."#'+(V,(0%/$"+#.,+A(

@A W 2 2 J Y / >2 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( W7Y( / >2 4 >2 B >2 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( W;Y(

NG,$,](

1 >2 (i(/G,(>/G(0%P#/(")(/G,(2/G(d*Uj(

A 2 (i(/G,(,M"1,%"#E(L&$0&V',Ej( J > (i(#%h%"N%(P&$&F,/,$Ej(

4 >2 (i(/G,($&%+"F(,$$"$(")(>/G(0%P#/("%("#/P#/(")(/G,(2/G(d*Uj(

B >2 (i(/G,(/,.G%0.&'(0%,))0.0,%.=2(%"%%,1&/0L,(,$$"$(")(>/G(0%P#/("%("#/P#/(")(/G,(2/G(d*Uj(

4 >2 (&%+(B >2 (&$,(0%+,P,%+,%/j(>(i(62(>2(<2(n2(C2(&%+(2(i(62(>2(n2(!A(

3%( DJ#&/0"%( W7Y2( /G,( > @A W

2 2 J Y A 2 J ( 0E( &( )$"%/0,$( P$"+#./0"%( )#%./0"%A( -EE#F,( 4 >2 o : W?2 V => Y (

&%+( > B >2 ( /"(V,(E,/(&E(/$#%.&/0"%E(&/(Q,$"(")( :D W2 V D> Y A(HG,(P&$&F,/,$E(")( J p 2( V p => 2( P p 2(&%+( V p D> ( &$,(/G,(

,E/0F&/"$E( ")( > J 2( V => 2( P 2( &%+( V D> ( WO&//,E,( X( O$".&2( 6CCBj( IG&$%,E2( I""P,$2( X( \G"+,E2( 6CB9j( K&$h( X( 40F&$2( 6CC8YA( d#,( /"( /G,( ,E/0F&/"$( ")( B >2 ( 0E( /B pl >2 q / >2 m 2( /G,( ,E/0F&/"$( ")( 4 >2 ( ."#'+( V,( +,/,$F0%,+( V=(

)"''"N0%1(DJ#&/0"%(WBY](

/4/ > p l

>2 m 1 >2 A 2 J p /B p l >2 / >2 m ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( WBY(

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2 p m lF&M W 2 4 p >2 Y 4 >2 m ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( W9Y( Z0%&''=2(/G,(/,.G%0.&'(,))0.0,%.=(N0''(V,("V/&0%,+()$"F(/G,(&+^#E/,+(0%P#/E( r ?

>2 ? >2 lF&M W 2 A 2 J p Y A J

>2 2(&%+("#/P#/(V=(0%/$"+#.0%1( /G,(/$&+0/0"%&'(I*A(

Stage Three: Estimate the Adjusted Cost Malmquist Index by Reusing the Adjusted Inputs

Z0%&''=2(&+^#E/,+(0%P#/(L&$0&V',E(P$"+#.,+(V=(/G,(E,."%+(E/&1,(&$,($,#E,+(0%(/G,(F,&E#$,F,%/(")(/G,(."E/( *&'FJ#0E/(0%+,M(WI*YA(HG,($,&'0/=(")(I*(N"#'+(V,("V/&0%,+(V=($,F"L0%1(/G,(,M"1,%"#E(,%L0$"%F,%/&'(%"0E,( 0%(/G,(/G0$+(E/&1,A(

The Source and Characteristics of Data Set

HG,(E/#+=(0E('0E/,+(0%(/G,(P,$0"+(")(5&/0"%&'(d,L,'"PF,%/(K'&%2(sIG&'',%10%1(>??9t2()$"F(>??8(/"(>??B2( &%+(/G,(E&FP',E(0%.'#+,(6<()0$FE(0%(/G,('0E/,+(E/".h(F&$h,/(&%+(67()0$FE(0%(/G,("L,$:/G,:."#%/,$(E/".h(F&$h,/A( -''($&N(+&/&(&$,()$"F(H&0N&%(D."%"F0.(!"#$%&'(d&/&(O&%h(WHD!YA(HN"("#/P#/E2(%,/($,L,%#,(WE 6 Y(&%+(F&$h,/( L&'#,(WE > Y2(&%+(/G$,,(0%P#/E2('&V"$E(W? 6 Y2(.&P0/&'(W? > Y2(&%+(F&/,$0&'E(&%+(P#$.G&E,(W? < Y(&$,(&+"P/,+(&%+(&.."#%/,+( V=(/G0E(E/#+=A(HG,(0%P#/(P$0.,E(")(? 6 2(? > 2(&%+(? < (&$,($,EP,./0L,'=(EG"N,+(&E(-F2(-!2(&%+(-,A(HG,(L&$0&V',E(")( "#/P#/E2(0%P#/E2(&%+(0%P#/(P$0.,E(&$,(EP,.0)0,+(&%+(+,E.$0V,+(V,'"NA( W6Y(_#/P#/E](5,/($,L,%#,(WE 6 Y(0E(+,)0%,+(&E(/G,(L&'#,(&..$#,+()$"F(&()0$FcE($,1#'&$(V#E0%,EE(&./0L0/0,E2(E#.G( &E(E,''0%1(/G,(1""+E(&%+(P$"L0+0%1(E,$L0.,EA(*&$h,/(L&'#,(WE > Y(")(&()0$F(0E(+,)0%,+(&E(/G,(/"/&'(L&'#,(")(."FF"%( E/".hE(/$&+,+(0%(/G,(E/".h(F&$h,/2(E#11,E/0%1(G"N(&(."FP&%=(0E(L&'#,+(V=(0/E(E/".hG"'+,$EA(

W>Y( 3%P#/E( &%+( 0%P#/( P$0.,E]( O,.&#E,( /G,( OXOK( 0%+#E/$=( 0%( H&0N&%( G&E( /G,( P$"P,$/0,E( ")( G01G( ,%/$&%.,( V&$$0,$E2(G01G(F&/,$0&'(L&'#,:&++,+(),&/#$,E("$('"N(F&/,$0&'(."E/E2(G01G(/,.G%"'"1=:"$0,%/,+(),&/#$,E(&%+(G01G( \Xd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h(L&'#,(")( /G,(PG=E0.&'(&EE,/E2("$()0M,+(&EE,/EA(

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Technical Background and Data Set