WATER  AND  FARM  EFFICIENCY:  INSIGHTS  FROM  THE  FRONTIER  LITERATURE        

Authors:      Boris   E.   Bravo-­‐Ureta:   Agricultural   and   Resource   Economics   University   of   Connecticut   and  Agricultural   and   Economics   Universidad   de   Talca,   Chile,   corresponding   author  boris.bravoureta@uconn.edu    Roberto  Jara-­‐Rojas:  Agricultural  Economics  Universidad  de  Talca,  Chile  rjara@utalca.cl    Michée   A.   Lachaud:   Agricultural   and   Resource   Economics   University   of   Connecticut  malchallenger007@yahoo.fr    Víctor   H.   Moreira   L.   Agricultural   Economist,   Universidad   Austral   de   Chile,   Chile  vmoreira@uach.cl    Susanne  M.  Scheierling:  Sr.  Irrigation  Water  Economist,  Water  Global  Practice,  The  World  Bank,  Washington  D.C.  sscheierling@worldbank.org    

 

       

Selected  Paper  prepared  for  presentation  at  the  2015  Agricultural  &  Applied  Economics  Association  and  Western  Agricultural  Economics  Association  Annual  Meeting,  San  Francisco,  CA,  

July  26-­‐28            

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WATER  AND  FARM  EFFICIENCY:  INSIGHTS  FROM  THE  FRONTIER  LITERATURE*      

Boris  E.  Bravo-­‐Ureta1,  Roberto  Jara-­‐Rojas2,  Michée  A.  Lachaud3,    Víctor  H.  Moreira  L.4,  Susanne  M.  Scheierling5  

   Abstract  This   paper   presents   an   overview   of   a   recently   completed   meta-­‐analysis   of   the   frontier  function  literature  focusing  on  the  technical  efficiency  (TE)  component  of  water  productivity  in  agriculture.    A  descriptive  analysis   is   first  performed   for  a   comprehensive  meta-­‐dataset  that  includes  409  farm  level  TE  studies,  published  between  1981  and  mid-­‐2014.    Of  this  total  of  409,  94  are  water  studies—defined  here  as  those  that  explicitly  include  irrigation  and/or  precipitation   in   the   analysis.     Some   studies   report   several   mean   TEs,   resulting   in   904  observations  or  cases.    The  Average  of  the  Mean  Technical  Efficiencies  (AMTE)  reported  for  all  studies  is  74.3%,  with  74.5%  for  non-­‐water  studies  vs.  73.4%  for  water  studies.        The  analysis  reveals  considerable  heterogeneity  in  the  methods  used  and  with  regard  to  how  water  is  defined  and  treated.    Some  studies  include  volumetric  measures  of  irrigation  water  and  combine  this  with  a  robust  methodology  that  provides  measures  of  irrigation  water  use  efficiency   (IWUE).    The   latter  quantifies   the  amount  of  water   that   could  be   saved  on-­‐farm  while   holding   output,   other   inputs   and   the   technology   constant.   This   methodology,  particularly   when   implemented   along   with   a   parametric   model,   can   provide   valuable  information   not   only   on   IWUE   but   also   on   other   key   economic   parameters   for   irrigation  water   (e.g.,   shadow   values,   production   elasticities).     Despite   the   importance   of   water   in  farming  and  the  continued  vibrancy  of  the  productivity  literature,  it  is  surprising  how  little  analytical  work  has  been  carried  out  in  this  critical  field.          Keywords:  Irrigation  Water  Use;  Technical  Efficiency;  Agriculture;  Meta-­‐Analysis.    JEL  Classification:  Q25,  Q12,  D24.  

     

 ••   This   study  was  partially   funded  by   the  Water  Partnership  Program   (WPP),   a  multi-­‐donor   trust   fund  at   the  World  Bank.      

 

1Agricultural   Economist,   University   of   Connecticut   and   Universidad   de   Talca,   Chile   corresponding   author  boris.bravoureta@uconn.edu  

2  Agricultural  Economist,  Universidad  de  Talca,  Chile  rjara@utalca.cl    3  Agricultural  Economist,  University  of  Connecticut,  USA  malchallenger007@yahoo.fr    4Agricultural  Economist,  Universidad  Austral  de  Chile,  Chile  vmoreira@uach.cl    5   Sr.   Irrigation   Water   Economist,   Water   Global   Practice,   The   World   Bank,   Washington   D.C.          sscheierling@worldbank.org    

   

   

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WATER  AND  FARM  EFFICIENCY:  INSIGHTS  FROM  THE  FRONTIER  LITERATURE      1.    INTRODUCTION  Irrigation  water  worldwide  accounts  for  approximately  70%  of  all  freshwater  withdrawals,  which   generate   low   returns   relative   to   other   water   using   sectors.     It   is   expected   that  increasing  water  scarcity  will  put  pressure  on  farming  to  reduce  consumption  so  that  water  can  be  diverted  elsewhere.    Therefore,   it  becomes  critical   to   improve   the  productivity  and  efficiency   of  water   use   in   agriculture.     However,   the   literature   that   deals  with   the   role   of  water   on   farm   productivity   provides   limited   insights   on   actions   that   could   be   taken   to  increase   agricultural   production   while   using   water   in   a   way   that   avoids   adding   to   the  scarcity  of  the  resource  (Scheierling  et  al.  2014).        The  objective  of  this  paper  is  to  provide  an  overview  of  the  frontier  function  literature  and  then  focus  on  water  productivity  and  Technical  Efficiency  (TE)  studies,  building  on  previous  meta-­‐analyses  work  by  Bravo  Ureta  et  al.  (2007)  and  Moreira  and  Bravo-­‐Ureta  (2009).    This  paper,  which   is   extracted   from   a  more   detailed   study,   contributes   to   the   existing   frontier  function  literature  by  providing  an  up  to  date  systematic  and  comprehensive  analysis  of  the  effects   that  different  methodologies  and  study-­‐specific   attributes  have  on  mean  TE  scores.    Moreover,  we  focus  on  water  studies,  defined  here  as  those  that  explicitly  include  irrigation  and/or  precipitation   in   the  analysis  of  TE.    This  detailed   focus  on  water  appears   to  be   the  first  of   its  kind.    A   comprehensive   literature   search  has  been  conducted  yielding  a   total  of  425   TE   studies,   409   or   which   reported   TE   at   the   farm   level,   our   main   focus.     The   total  number  of  studies  with  a  focus  on  water  is  110.      The   remainder   of   this   paper   is   structured   as   follows.   Section   2   contains   an   overview  discussion  of  the  alternative  methodologies  used  in  frontier  analysis.    Section  3  presents  the  approach  followed  to  generate  the  data  used  in  the  meta-­‐analysis,  and  presents  a  descriptive  analysis  of  the  data.    The  paper  continues  with  a  discussion  of  the  water  papers  in  Section  4,  and  Section  5  provides  some  concluding  remarks.        2.    OVERVIEW  OF  FRONTIER  METHODOLOGIES  Although  preceded  a  few  years  by  Debreu  (1951)  and  Koopmans  (1951),  the  1957  seminal  paper   by   Farrell   is  widely   credited   as   the   intellectual   impetus   that   has   propelled   frontier  function   research   (Fried,   Lovell   and   Schmidt   2008;   Greene   2008).     Farrell   relied   on   the  efficient   unit   isoquant   to   define   and  measure   TE,   allocative   efficiency   (AE),   and   economic  efficiency   (EE).     The   focus   in   this   study   is   farm   level   TE,   so   this  methodological   summary  favors   this   particular   efficiency   concept   as   opposed   to   a   number   of   other   related   notions.    Our  intention  is  not  to  provide  an  exhaustive  review  but  rather  to  point  out  some  of  the  key  features  that  appear  in  the  studies  included  in  our  meta-­‐analysis.    For  clarity  it   is   important  at  the  outset  to  differentiate  between  Technological  Change  (TC)  and  TE.    TC  measures  shifts  of  the  production  frontier  stemming  from  the  fruit  of  innovation  (Färe,  Grosskopf  and  Margaritis  2008).    By  contrast,  TE  has   to  do  with   the  distance  a   firm  operates  relative  to  its  frontier  and  such  distance  can  be  measured  with  input  or  an  output  orientation.     In   the   simple   single   input   production   frontier   case,   the   output   oriented  

   

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approach,  which  is  most  commonly  used  in  applied  work,  TE  is  given  by  the  ratio  between  the   observed   and   the   maximum   (frontier)   level   of   output   that   can   be   produced   given   a  quantity  of  input  and  the  technology.    By  contrast,  the  input  orientated  approach  is  given  by  the   ratio   of   the   quantity   of   input   needed   to   produce   a   given   level   of   output   if   the   farm  operates  on  the  frontier  relative  to  the  input  actually  used.    Therefore,  TE,  whether  input  or  output  oriented,  is  an  index  that  ranges  between  0%  and  100%  and  can  be  interpreted  as  a  proxy   measure   for   managerial   effort   or   performance   (Martin   and   Page   1983;   Triebs   and  Kumbhakar   2013).     Analogous   measures   can   be   defined   for   the   multiple   input-­‐multiple  output  technologies  (Coelli  et  al.  2005).    Frontier  function  methods  have  become  widely  used  in  applied  production  economics  given  their  consistency  with  the  neo-­‐classical  notion  of  maximization  or  minimization  imbedded  in  the  definitions  of  production,  revenue,  profit  and  cost  functions.    The  popularity  of  frontier  methods  is  substantiated  by  the  abundance  of  methodological  and  empirical  frontier  studies  over  the  last  three  decades.    Methodological  reviews  of  the  panoply  of  models  that  have  been  developed  can  be   found   in  Førsund,  Lovell  and  Schmidt  (1980);  Schmidt  (1985-­‐86);  Bauer  (1990);  Seiford  and  Thrall  (1990);  Kumbhakar  and  Lovell  (2000);  Fried,  Lovell  and  Schmidt  (2008);   Greene   (2008);   and   Thanassoulis,   Portela   and  Despić   (2008),   among   others.     The  popularity   of   applied   frontier   studies   in   agriculture   is   documented   in   several   reviews   and  meta-­‐analyses   including   Battese   (1992),   Bravo-­‐Ureta   and   Pinheiro   (1993),   Thiam,   Bravo-­‐Ureta  and  Rivas  (2001),  Gorton  and  Davidova  (2004),  Bravo-­‐Ureta  et  al.  (2007),  Moreira  and  Bravo-­‐Ureta   (2009),   Darku,   Malla   and   Tran   (2013),   Minviel   and   Latruffe   (2013),   and  Ogundari  (2014).    The   frontier   methodology   is   commonly   divided   into   parametric   and   non-­‐parametric  methods.     Parametric   methods   require   the   specification   of   a   functional   form   for   the  technology  (e.g.,  Cobb-­‐Douglas,  Translog)  whereas  non-­‐parametric  models  do  not  have  such  requirement  and  this  constitutes  a  major  advantage  of  the  latter.    Parametric  models  can  be  subdivided   into   deterministic   and   stochastic   frontier   analysis   (SFA)   where   the   former  assumes   that   any  deviations   from   the   frontier   stem   from   inefficiency,  while   the   stochastic  approach   incorporates   statistical   noise   (Coelli   et   al.   2005).     Hence,   a   key   limitation   of  deterministic   frontiers   is   that   measurement   errors,   as   well   as   other   sources   of   random  variation  are  captured  as  inefficiency  and  this  means  that  outliers  have  a  distorting  effect  on  TE  scores  (Fried,  Lovell  and  Schmidt,  2008).      The   stochastic   frontier  model,   developed   separately   but   around   the   same   time   by   Aigner,  Lovell   and   Schmidt   (1977)   and  Meeusen   and   van   den   Broeck   (1977),   copes  with   outliers  through   a   composed   error   structure   with   a   two-­‐sided   symmetric   term   and   a   one-­‐sided  component.     The   two-­‐sided   error   captures   random   shocks   outside   the   control   of   the   firm  whereas  the  one-­‐sided  component  takes  care  of  inefficiency.      Non-­‐parametric   frontiers   trace   their   origin   directly   to   Farrell   (1957);   however,   it   took  almost  20  years  for  non-­‐parametric  frontiers  to  get  a  firm  footing  in  the  literature  and  such  is  due  to  the  seminal  contribution  by  Charnes,  Cooper  and  Rhodes  (1978).    As  already  noted,  the  main  feature  of  non-­‐parametric  frontiers  is  that  they  do  not  require  the  specification  of  a  functional   form  while   a  major  drawback   is   that   these  methods   are  deterministic   and   thus  sensitive  to  extreme  observations.    In  addition,  the  TE  scores  generated  by  non-­‐parametric  

   

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methods   can   be   sensitive   to   the   number   of   observations   in   the   data   and   to   the  dimensionality   of   the   frontier.     Non-­‐parametric  measures   of   efficiency   are   obtained   using  mathematical  programming  techniques  widely  known  as  Data  Envelopment  Analysis  or  DEA  (Thanassoulis,  Portela  and  Despić  2008).    This  area  of   the   frontier   literature  gained  major  popularity  early  on  in  management  science  and  operations  research  but  now  is  also  firmly  established  in  economics  including  agricultural  economics  (Fried,  Lovell  and  Schmidt  2008).        Frontier  studies  can  also  be  separated  into  primal  and  dual.    The  primal  approach  has  been  more  common  in  frontier  estimation  since  it  does  not  require  price  data,  often  difficult  to  get  at  the  firm/farm  level,  nor  does  it  rely  on  maintained  hypothesis  regarding  behavior  such  as  cost  minimization  or  profit  maximization  (Coelli  et  al.  2005).  The  validity  of  dual  models  has  been  questioned,  particularly  when  profit  maximization  is  the  maintained  hypothesis  in  the  context  of  developing  country  agriculture  (e.g.,  Junankar  1980).    An  important  advantage  that  non-­‐parametric  models  enjoyed  for  a  number  of  years  is  their  ability   to   easily   accommodate   multi-­‐input   multi-­‐output   technologies   within   a   primal  specification.     By   contrast,   to   accommodate   such   technologies,   parametric   models   had   to  appeal  initially  to  dual  cost  or  profit  frontiers,  which  presented  data  challenges  as  well  as  the  need  to  make  stringent  behavioral  assumptions  (e.g.,  Ali  and  Flinn  1987;  Bailey  et  al.  1989).    More   recently,   developments   in   the   parametric   stochastic   literature   have   enabled   the  estimation   multi-­‐input   multi-­‐output   models   by   means   of   input   and   output   distance  functions.    The  main  advantage  of  using  a  distance  function  is  that  price  information  is  not  needed   and   these   models   can   be   estimated   without   assuming   input-­‐output   separability  (Coelli   2005).     A   further   extension   is   the   directional   distance   function,   which   is   a  generalization   of   the   input   and   output   distance   functions.     The   directional   distance  specification  simultaneously  allows  for  the  expansion  of  outputs  and  the  reduction  of  inputs  toward  all  points  that  are  on  the  frontier  and  dominate  the  observation  being  assessed  (Färe,  Grosskopf   and   Margaritis   2008).     Directional   distance   functions   have   also   been   used   to  incorporate  bad  outputs  and  examine  the  tradeoff  between  good  and  bad  outputs  (e.g.,  Njuki  and  Bravo-­‐Ureta  2015  and  papers  cited  therein).    Frontier   function   analyses   can   also   be   characterized   in   terms   of   the   type   of   data   used,   as  cross-­‐section  or  panel.    Frontier  estimation  with  panel  data  has  made  considerable  progress  in   both   the   non-­‐parametric   and   the   parametric   worlds   and   this   is   an   appealing   feature  because   it   can   significantly   enhance   the   analysis   particularly   in   decomposing   total   factor  productivity   change   in   terms   of   TC,   TE   change   (TEC)   and   scale   efficiency   change   (SEC)  (Kumbhakar  and  Lovell  2000;  Fried,  Lovell  and  Schmidt  2008).    In  the  stochastic  approach,  the  recent  work  by  Greene  (2005a;  2005b)  has  opened  up  useful  options  to  account  for  time  invariant  firm  heterogeneity  in  addition  to  time  variant  TE.      Very  recently,  several  authors  have  presented  and  applied  models  that  decompose  (overall)  efficiency   into   a   persistent   (long-­‐run)   and   a   transient   (short   run)   component   while   also  capturing   unobserved   time   invariant   heterogeneity   (Colombi   et   al.   2014;   Filippini   and  Greene  2014;  Kumbhakar,  Lien  and  Hardaker  2014;  Tsionas  and  Kumbhakar  2014;  Lachaud,  Bravo-­‐Ureta  and  Ludena  2014).    Panel  data  methodologies  clearly  offer  an  interesting  path  forward  but  the  challenge  is  to  develop  the  necessary  data  sets  to  take  full  advantage  of  the  emerging  methods.      

   

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 Another   strand   on   the   frontier   literature   has   to   do   with   efforts   geared   at   explaining   the  variability   of   TE   in   terms   of   exogenous   factors   that   typically   include   socioeconomic   and  environmental  variables.    The  original  approach  is  the  so  called  two-­‐step  model  where  TE  is  estimated   in   the   first  step,  using  any  of   the  models  we  have  discussed,  without  accounting  for   exogenous   and   environmental   factors   and   then   in   the   second-­‐step   TE   is   regressed   on  such  factors  (Greene  2008;  Bravo-­‐Ureta  and  Pinheiro  1993).    Examination  of  the  validity  of  the  two-­‐step  procedure  indicates  that  this  approach  leads  to  biased  or  invalid  results  in  both  parametric  and  non-­‐parametric  models  (Wang  and  Schmidt  2002;  Simar  and  Wilson  2007).    Taking  a  forceful  position  on  this  matter,  Fried,  Lovell  and  Schmidt  (2008)  state:  “We  hope  to  see  no  more  two-­‐stage  SFA  models”  (p.  39).      These  objections  of  the  validity  of  two-­‐step  models  have  motivated  the  development  of  one-­‐step  procedures  in  the  stochastic  frontier  literature,  where  the  most  widely  applied  model  is  the   one   presented   by   Battese   and   Coelli   (1995).     Progress   has   also   been   made   in   the  explanation  of  TE   in   the  non-­‐parametric   literature  using  bootstrapping   techniques.     Simar  and  Wilson  (2007;  2008)  argue  that  the  results  of  many  studies  that  have  estimated  second-­‐step   regressions   to   explain   the   variation   in   TE   scores,   derived   from   DEA   models,   have  produced   invalid   results.     The   first   problem   they   pinpoint   is   that   a   large   volume   of   these  studies  do  not   describe   the   associated  data   generating  process   (DGP)   “that  would  make   a  second-­‐stage   regression   sensible”   (Simar   and  Wilson   2008,   p   501).     A   second   and   “more  serious  problem   in  all  of   the   two  stage  studies”   found  by  Simar  and  Wilson  (2007)  “arises  from  the  fact  DEA  efficiency  estimates  are  serially  correlated”  (p.  33).    The  latter  invalidates  any  inferences  regarding  the  parameters  of  the  second-­‐step  regression.    These  authors  then  present  a  DGP  that  affords  the  foundation  for  the  second-­‐step  regression  of  TE  scores  from  DEA  models.     The   authors   also  present   a   truncated   regression  model   along  with   a   double  bootstrap  approach  and  argue  that  this  framework  makes  it  possible  to  obtain  unbiased  TE  scores  (first  bootstrap)  and  valid  estimates  of  confidence  intervals  for  the  coefficients  of  the  second-­‐step   regression   (second   bootstrap)   while   increasing   statistical   efficiency   in   the  estimation.     Examples   of   applications   of   this   procedure   in   agriculture   include   Latruffe,  Davidova  and  Balcombe  (2008),  Balcombe  et  al.  (2008),  and  Keramidou  and  Mimis  (2011).    An   additional   and   emerging   strand   of   the   literature  we  want   to  mention   concerns   recent  efforts  in  stochastic  frontier  models  to  correct  for  selectivity  bias  (Kumbhakar,  Tsionas  and  Sipiläinen  2009;  Lai,  Polachek  and  Wang  2009;  Greene  2010).    Bravo-­‐Ureta,  Greene  and  Solís  (2012)  have  combined  the  Greene  (2010)  model  with  Propensity  Score  Matching  (PSM)  to  account   for  biases   from  observable  and  unobservable  variables   in  order   to  decompose   the  impact   of   development   projects   into   output   growth   (i.e.,   upwards   shifts   in   the  production  frontier   due   to   TC)   and   management   improvements   (i.e.,   narrowing   the   gap   from   the  frontier)   when   only   cross   sectional   data   are   available   (Bravo-­‐Ureta   2014).     The  model   is  applied  to  data  generated  from  the  MARENA  Project  in  Honduras.    Additional  applications  of  the  Bravo-­‐Ureta,  Greene  and  Solís  (2012)  model  include  the  work  by  González-­‐Flores  et  al.  (2014)  for  a  sample  of  small-­‐scale  potato  farmers  from  Ecuador  and  by  Villano  et  al.  (2014)  who   investigate   the   impact   of   adopting   certified   seed   varieties   on   the   productivity   of   rice  farmers  in  the  Philippines.    Another   area   that   is   receiving   attention   in   the   recent   literature   concerns   the   possible  

   

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endogeneity  of   inputs   in   stochastic   frontiers.     Zellner,  Kmenta   and  Drèze   (1966)  provided  what   has   become   the   classical   justification   for   valid   econometric   estimates   of   production  functions.     These   authors   assumed   that   firms   maximize   the   mathematical   expectation   of  profits   rather   than  deterministic  profits.    More   recently,   several   authors   such  as  Tran  and  Tsionas   (2013),   and   Shee   and   Stefanou   (2014)   have   proposed   alternative   approaches   to  tackle   endogeneity   in   stochastic   frontier   models   building   on   previous   work   by   Olley   and  Pakes  (1996),  Levinsohn  and  Petrin  (2003),  and  Kutlu  (2010),  among  others.        Is   useful   to   underscore   that   major   methodological   advances   have   been   made   in   both  parametric  (econometric)  and  non-­‐parametric  (programming)  frontiers.    Paraphrasing  from  Fried,   Lovell   and   Schmidt   (2008),   SFA   and   DEA   have   important   similarities   as   well   as  differences.    Both  approaches  are  rigorous  analytical  tools  to  measure  efficiency  relative  to  a  frontier.    “At  the  risk  of  oversimplification,  the  differences  between  the  two  approaches  boil  down  to  two  essential  features:  [1]  The  econometric  approach  is  stochastic.    This  enables  it  to  attempt  to  distinguish  the  effects  of  noise  from  those  of  inefficiency,  thereby  providing  the  basis   for   statistical   inference.   [2]   The   programming   approach   is   nonparametric.     This  enables  it  to  avoid  confounding  the  effects  of  misspecification  of  the  functional  form  (of  both  technology  and  inefficiency)  with  those  of  inefficiency”  (p.  32-­‐33).    Despite   the   ‘conciliatory’   remarks   in   the  preceding  paragraph,   in  a   recent  paper  O’Donnell  (2014)  argues  that  the  core  assumptions  on  which  the  DEA  machinery  stands  “…  are  rarely,  if   ever   true   (e.g.,   output,   input   and   environmental   variables   are   almost   always  measured  with   error,   if   not   unobserved).     It   follows   that   most,   if   not   all,   DEA   estimators   are  inconsistent”   (p.   22).     O’Donnell   goes   on   to   quote   Simar   and   Wilson   (2000)   who   wrote:  “Consistency   is  an  essential  property  of  any  estimator   [p.  56].….   If   the  data  contains  noise,  DEA  …  estimators  will  be   inconsistent,  and   there  seems   little  choice  but   to  rely  on  SFA  [p.  76].”    One  is  left  with  the  distinct  impression  that  the  SFA-­‐DEA  controversy  will  go  on  for  a  few  more  rounds.        3.      GENERATION  OF  THE  DATASET  AND  DESCRIPTIVE  ANALYSIS  A   key   aspect   in   a   meta-­‐analysis   is   to   conduct   a   thorough   and   systematic   review   of   the  literature  to  develop  the  list  of  papers  to  be  included  in  the  investigation.    We  performed  a  comprehensive   search   of   the   literature   using   the   following   databases:   EBSCOhost,   Econlit,  Academic  Search  Premier,  Agricola,  Scopus  and  ISI  Web  of  Knowledge  which  includes  Agris  International,   Science   Direct   and   Social   Science   Citation   Index.     An   additional   search  was  done  for  specific  journals  that  overtime  have  published  a  good  number  of  applied  TE  studies  and/or   are   major   outlets   of   agricultural   economics   work.     The   journals   included   are   the  American   Journal   of   Agricultural   Economics,   the   Journal   of   Agricultural   Economics,  Agricultural   Economics,   the   European   Review   of   Agricultural   Economics,   the   Australian  Review   of   Agricultural   and   Resources   Economics,   the   Canadian   Journal   of   Agricultural  Economics,  the  Journal  of  Productivity  Analysis,  Empirical  Economics,  the  European  Journal  of  Operations  Research  and  Applied  Economics.    

 A  complementary  search  was  conducted  for  water  related  TE  papers  using  the  following  key  words:   Irrigation,   Technical   Efficiency,   Farming,   Agriculture,   Productivity   and   Frontier,  water,  water  use,  groundwater,  water  flows,  return  flows,  water  quality,  and  leaching  which  

   

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were  combined  in  different  ways  to  expand  the  search.    It  is  important  to  emphasize  that  the  two   critical   and   necessary   key   words   in   all   searches   were   Technical   Efficiency   and  Agriculture.     In  other  words,  we  keep  only   the  papers   related   to  TE  and  Agriculture.     The  combined   searches,   limited   to   papers  written   in   English,   yielded   a   total   of   409   farm   level  papers  that  contain  all  the  data  required  for  our  analysis.1    Descriptive  Analysis  As  indicated,  the  total  number  of  studies  with  a  water  focus  is  110.    Of  this  110,  16  are  only  partially   included   in   the   study   due   to   the   following   reasons:   missing   data   [5];   use   of  aggregate  data  [10],  considering  that  our  main  focus  is  on  farm  level  studies;  and  [1]  is  in  the  grey  literature  and  thus  outside  the  criteria  used  for  selecting  the  studies.    The  latter  study,  however,   is   incorporated   in   the   longer   version   of   this   paper   because   it   brings   a   novel  dimension   to   the   discussion.     In   sum,   for   the   primary   analysis   presented   here,  we   have   a  total  of  409  farm-­‐level  studies,  315  without  a  water  focus  and  94  with.    The  key  variable  in  our  analyses   is   the  mean   technical   efficiency   (MTE)   reported   in  each  paper.     Some  papers  present  more   than  one  MTE  due   to   the  use  of  alternative  methods,   so   the   total  number  of  MTEs,  or  cases,  from  the  409  studies  is  904,  of  which  193  come  from  the  water  studies.      Table   1   shows   that   of   the   904   total   cases,   623   come   from  parametric   and   281   from  non-­‐parametric   models;   in   addition,   552   observations   come   from   stochastic   and   352   from  deterministic  frontiers.    The  AMTE  for  all  papers  is  74.3%,  which  is  slightly  lower  than  the  76.6%  reported  by  Bravo-­‐Ureta  et  al.  (2007).    For  the  193  water  cases,  Table  1  indicates  that  120  come  from  parametric  and  73  from  non-­‐parametric  models,  and  120  are  from  stochastic  and   73   from   deterministic   frontiers.     The   AMTE   for   all   water   papers   is   73.4%,   which   is  slightly   lower   that   the   value   of   74.5%   for   non-­‐water   papers   but   this   difference   is   not  statistically  significant.    Table  1  also  reports  statistical   tests   for  the  null  hypothesis  that  AMTE  for  each  category   is  the  same  and,  overall,  we  observe  only  a  few  differences.    For  the  non-­‐water  papers,  there  is  a   significant   difference   between   the   stochastic   and   deterministic   approaches   (75.4%   vs.  73.3%,  respectively).    Another  significant  difference  is  for  the  data  structure  category  in  both  the   non-­‐water   and   all   cases,   where   panel   data   is   higher   than   cross   sectional   (77.7%   vs.  72.6%  for  non-­‐water,  and  77.3%  vs.  73.5%  for  water).    The  last  difference  is  for   functional  form  where  TL  is  higher  than  CD  (78.3%  vs.  72.0%  for  non-­‐water,  and  77.3%  vs.  72.4%  for  water).    Looking  at  the  highest  AMTE  for  each  of  the  three  groups,  we  see  that  the  top  value  for   the   water   papers   is   for   panel   data   (76.3%),   while   the   TL   is   at   the   top   for   non-­‐water  (78.3%).    For  all  papers  combined,  the  panel  data  and  TL  groups  exhibit  the  highest  AMTE,  both  at  77.3%.    Table   2   contains   a   summary   of   AMTE   for   various   groupings   according   to   geographical  region,   income   category   and   product   type.     The   following   six   geographical   regions   are  included:  Africa,  Asia,  Latin  America,  North  America,  Eastern  Europe,  and  Western  Europe  and  Oceania.    In  terms  of  country  income,  we  use  the  following  four  categories  based  on  the  World   Bank   (2014):   LICs   (Lower   Income   Countries);   LMICs   (Lower   Middle   Income  Countries);  UMICs  (Upper  Middle   Income  Countries);  and  HICs  (Higher   Income  Countries).                                                                                                                    1  The  list  of  all  409  papers,  including  those  reviewed  in  Section  4,  is  available  from  the  authors  upon  request.  

   

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The  product  groups  are  as  follows:  Rice;  Maize;  Wheat;  Mixed  Grains;  Crops  and  Livestock;  Dairy;   Other   Animals;   and  Whole   Farm.     As   is   the   case  with   Table   1,   we   note   only   a   few  significant  AMTE  differences.    The  data  shows   that  AMTE   for  water  papers   is  higher   in  W.  Europe  and  Oceania  (83.9%)  and  lowest  for  Latin  America  (55.1%).    For  the  country  income  category,   there   is   no  difference   for   the  water   studies,   but   the  non-­‐water   studies   show   the  highest  values  for  LIC  (78.7%)  and  HIC  (77.7%)  and  the  same  pattern  for  all  studies  (74.1%  LIC  and  77.6%  HIC)  and  the  lowest  for  UMIC  (65.3%  for  non  water  and  67.2%  for  all).  The  last   point  we  want   to  make   in   this   comparison   is   that   Dairy   farming   exhibits   the   highest  AMTE  across  products  for  all  three  study  groups  -­‐-­‐  84%  water,  80.7%  non-­‐water  and  80.9%  all-­‐-­‐  and  is  statistically  significant  in  the  last  two.      Taking  a  broader   look  at   the  data   in  Table  2  we  see   that   the   lowest  AMTE  values   for  both  water  and  non-­‐water  papers  and  thus  for  all  papers  combined  is  for  Latin  America  (55.1%,  62.0%   and   61.7%)   and   Africa   (65.7%,   70.0%   and   68.3%).     By   contrast,   North   America  (81.0%   water;   78.7%   non-­‐water;   78.9%   all),   and   W.   Europe   and   Oceania   (83.9%   water;  76.4%  non-­‐water;   77.0%   all)   have   the   highest   AMTEs.     By   comparison,   Bravo-­‐Ureta   et   al.  (2007)   find   that   the   lowest   AMTE   for   all   cases   analyzed   by   them   is   for   Eastern   Europe  (70.0%)  followed  by  Africa  (73.7%)  while  the  highest  is  for  W.  Europe  and  Oceania  (82.0%)  followed   by   Latin   America   (77.9%).   Aggregating   the   countries   by   income   leads   to   a   fairly  irregular  pattern  although  the  HICs  have  the  highest  AMTE  for  all  papers  at  77.6%  and  the  UMICs   the   lowest   at   67.2%.     This   latter   pattern   is   consistent  with   Bravo-­‐Ureta   et   al.  who  report  an  AMTE  of  78.8%  for  HICs  (their  highest)  and  68.3%  for  UMICs  (their  lowest).        Turning  to  the  Product  grouping  we  see  that  the  lowest  AMTE  for  all  three  types  of  papers  in  Table  2  is  for  Crops  and  Livestock  (69.8%  water;  69.6%  non-­‐water;  69.6%  all).    By  contrast  the  highest  AMTE  is  uniformly  for  dairy  papers  at  84.0%  for  water,  80.7%  for  non-­‐water  and  80.9%  for  all  papers.    It  is  interesting  to  note  that  this  is  very  close  to  the  results  of  Bravo-­‐Ureta  et  al.  (2007)  who  reported  an  AMTE  for  dairy  and  cattle  of  80.6%  which  is  the  second  highest  average  in  their  paper  following  Other  Animals  at  84.5%  but  the  latter  only  has  six  observations.    In   sum,   this   section   presented   a   descriptive   analysis   of   409   farm   level   studies,   315   non-­‐water   and   94  with   some   type   of  water   focus.     The   respective  AMTE   is   74.3%,   74.5%   and  73.4%.     The   AMTE   across   methodological   attributes   tend   to   be   quite   similar   for   the   two  groups   of   studies   but   several   significant   differences   are   observed   when   comparisons   are  made  across  geographical   regions,   income   levels,   and   type  of  product.     Some  comparisons  are  made  with  the  previous  comprehensive  meta-­‐analysis  by  Bravo-­‐Ureta  et  al.  (2007).      

   

4.    ANALYSIS  OF  WATER  STUDIES  Now  we   classify   all   110  water   studies,  which   includes   94   at   the   farm   level   plus   16   other  studies,  10  of  which  use  aggregate  data,   five  do  not  report  TE  and  one   is  a  working  paper.    We  have  classified   these  110  papers   into   five  groups,  A   through  E,  and   in  some  cases   into  additional  subgroups.    The  studies  in  Groups  A  through  D  use  farm  level  data  while  those  in  Group  E  use  aggregate  data.    The  five  groups  (A-­‐E)  are:    

   

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A. Irrigation:  76  studies  and  is  further  subdivided  into  three  sub-­‐groups  (A1,  A2  and  A3),  depending  on  how  the  water  variable  used  to  capture  irrigation  is  measured.    A1.   Quantity:   56   studies   further   subdivided   into   the   following   five   classes   (1-­‐5)  

depending  on  how  the  continuous  variable  used  to  quantify  irrigation  is  reported:  1)   Quantity  of  Water  used  =  19  2)    Hours  of  Irrigation  =  5  3)   Number  of  Irrigations,  Index,  or  Irrigation  Expenses  =  22  4)   Percent  of  Land  Irrigated  =  7  5)   Land  Area  Irrigated=  3  

A2.  Dummy:  9  studies  that  capture  irrigation  with  a  binary  Yes/No  indicator.  A3.  Mixed:  11  papers  that  combine  a  continuous  measure  of  irrigation  and  a  dummy.  

 B.  Precipitation:  6  papers,  5  use  a  continuous  measure  of  precipitation  and  one  uses  a  

dummy  variable.      

C.     Irrigation   and   Precipitation   (Combines   A   and   B):   13   papers   that   use   various  measures  of  both  irrigation  and  precipitation.  

 D.   Distance  Functions:  5  articles.    E.    Aggregate:  10  papers  that  use  data  at  a  level  of  aggregation  higher  than  a  farm.  

 Key  Features  Table  3  presents  a  summary  of  the  AMTE  for  each  of  the  groups  and  sub-­‐groups  mentioned  above.  The  data  clearly  shows  a  great  deal  of  variability  in  the  AMTEs  which  reveals  that  the  way   water   is   defined   in   the   various   studies   has   a   considerable   effect   on   TE   scores.     The  lowest  AMTE  is  61.6%  for  Group  E  (studies  that  use  aggregate  data)  while  the  next  lowest,  is  66.2%  for  Group  C  (Groups  A  and  B  combined).    By  contrast,  the  highest  AMTE  is  91.4%  for  Group   A1.2   (hours   of   irrigation)   followed   by   81.1%   for   Group   A1.5   (land   area   irrigated).    However,  we  should  note  that  these  last  two  groups  contain  very  few  studies.    The  next  value  is  79.9%  for  Group  A1.3  (number  of  irrigations,  index  measures  or  irrigation  expenses).    The  overall  AMTE  for  Group  A  is  76.3%  and  is  the  highest  compared  to  the  other  four  groups.        Moreover,  we  note  that  four  papers  used  a  meta-­‐frontier  approach,  i.e.,  estimated  a  frontier  of   frontiers   (Battese,  Rao,  O’Donnell,  2004;  O’Donnell,  Rao  and  Battese,  2008;  Moreira  and  Bravo-­‐Ureta,   2010).   Given   this   small   number,   we   did   not   define   a   separate  meta-­‐frontier  group   and   these  papers   are   classified   according   to  how   the   variable   “water”   enters   in   the  estimation   procedure.   Specifically,   one   is   classified   in   group   A1.3   as   water   enters   as   a  component   in   a   Divisia   Index   (Boshrabadi   et   al.,   2008);   another   one   is   in   group   C   as   it  compares  irrigated  versus  rainfed  farming  systems  (Mariano  et  al.,  2010);  another  one  in  A2  as   it  uses  a  dummy  variable   to  compare   the  difference   in  having  access   to   irrigation  using  public  service  or  private-­‐owned  water  pumps  (Mariano  et  al.,  2011);  and  the  last  one  is  also  an  A2  study  where  a  dummy  variable   is  used  to  compare  the   impact  of  different   irrigation  technologies  on  TE  (Rao  et  al.,  2012).      In  addition,  we  conduct  AMTE  mean  difference  tests  across  each  of  the  five  groups.    We  first  test  whether  or  not  each  group  has  equal  or  unequal  variance  and  then  we  proceed  with  the  

   

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testing   of   mean   differences.     The   findings   show   that   there   is   no   statistically   significant  difference  in  AMTE  across  Groups  except  for  Group  A  and  C  and  Group  A  and  E.    The  AMTEs  across   the   other   groups   are   statistically   the   same.     Is   important   to   underscore   that   TE  provides  a  measure  of  the  gap  between  what  is  produced  and  what  could  be  produced  given  inputs,  the  environment,  and  the  technology,  but  it  does  not  give  any  insight  about  water  use  efficiency  per  se.      Irrigation  Water  Use  Efficiency  (IWUE)  Studies  Here   we   provide   a   more   detailed   analysis   of   11   studies   that,   in   addition   to   providing   a  conventional   analysis   of   TE,   examine   irrigation  water   use   efficiency   (IWUE).     The   general  unifying  theme   in   these  studies   is   the  use  of  a  methodology   introduced  by  Reinhardt  et  al.  (1999)   that   makes   it   possible   to   derive   non-­‐radial   measures   of   efficiency   for   an   input   of  interest,   which   in   our   case   is   irrigation   water.   Reinhardt   et   al.   (2002)   extended   this  methodology  in  order  to  estimate  a  second  step  model  to  explain  IWUE  in  a  manner  that  is  compatible   with   econometric   assumptions.     Another   analysis   that   can   be   done,   following  Akridge  (1989),  is  to  evaluate  the  feasible  cost  savings  that  could  be  achieved  by  managing  water  more  efficiently.    This  has  been   termed   in   this   literature   Irrigation  Water  Technical  Cost  Efficiency  or  IWTCE.    This  term  can  be  defined  as  the  cost  savings  that  are  possible  by  holding   irrigation   water   use   at   its   technically   efficient   level   while   other   inputs   are   held  constant  at  their  observed  levels.        To  illustrate  this  methodology,  we  cast  our  discussion  assuming  a  deterministic  parametric  model;   however,   it   should   be   understood   that   similar   analyses   can   be   performed   using   a  stochastic  production  frontier  (e.g.,  Karagiannis,  Tzouvelekas  and  Xepapadeas,  2003)  as  well  as   a   sub-­‐vector   DEA   approach   (e.g.,   Lilienfeld   and   Asmild,   2007).     We   highlight   this  methodology   because   it   appears   as   a   promising   area   for   further   empirical   work   and  methodological  refinements.    Figure  1  presents  a  graphical  illustration  of  an  output  measure  of  efficiency  assuming  for  simplicity  that  water   is  the  only  variable   input.    A  firm  (point  C)  that  uses  IW1  to  produce  Y0  units  of  output  operates  considerably  below  the  maximum  level  of  output  Ym  that  could  be  attained  by  operating  on  the  frontier  (point  B).    Thus,  the  level  of  TE  for  this  firm  is  equal  to  the  ratio  OY0/OYM.    Alternatively,  we  could  compare  the  amount  of  water   actually   used  with   the   amount   that   would   be   used   by   operating   on   the   frontier   to  attain   Y0   output.     Based   on   the   graph,   the   input   oriented   measure   of   TE   is   given   by  OIW0/OIW1,  for  output  Y0  while  holding  other  inputs  and  the  level  of  technology  constant.      In  Figure  2  we  can  observe  that  a  hypothetical  inefficient  firm  operates  at  point  A  using  OW1  units  of  water   and  OX1  units  of   all   other   inputs   to  produce  Y0  output.     The   input  oriented  measure  of  TE   in   this   case   is  OB/OA.    Again,   if  we   focus  on   the   input   savings   side  we   can  observe  that  a  non-­‐radial  measure  of  efficiency  can  be  expressed  as  X1C/X1A  or  alternatively  as  OW2/OW1.    These  measures,  which  are  equivalent  to  each  other,  represent  the  amount  of  water  that  could  be  reduced  if  the  firm  was  to  move  to  the  frontier  holding  X  constant  at  X1  and  still  produce  Y0.    This  measure  has  become  known  in  the  literature  as  Irrigation  Water  Efficiency   (IWE),   Irrigation   Water   Technical   Efficiency   (IWTE)   or   Irrigation   Water   Use  Efficiency  (IWUE).    Here  we  adopt  the  term  IWUE.    Finally,  it  is  useful  to  note  the  difference  between  IWUE  and  the  water  savings  that  is  achieved,  OW1-­‐OW3,  by  the  radial  contraction  of  both  inputs  to  get  to  the  technically  efficient  point  B.    OW1-­‐OW3  is  an  input  oriented  measure  of  TE.  

   

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 Before   turning   to   a   review   of   the   11   IWUE   papers,   we   present   in   Table   4,   without  much  discussion,  key  features  of  48  Non-­‐IWUE  studies  that  report  a  number  of   informative  farm  output   responses   to   water,   including   partial   elasticities   of   production   with   respect   to:  volume  of  irrigated  water  applied;  irrigation  expenditures;  hours  a  plot  is  irrigated;  number  of  times  a  plot  is  irrigated  during  a  particular  season;  and  the  amount  or  percent  of  irrigated  land.    As  the  data  in  Table  4  shows,  these  response  indicators  clearly  show  that  irrigation  has  a  positive  and  significant  effect  on  output.    Now  we  highlight  the  key  aspects  of  the  11  IWUE  studies,  which  are  shown  in  Table  5.  First,  AMTE  is  70.4%  ranging  from  61.5%  to  81%.    Three  papers  show  Irrigation  Water  Technical  Cost  Efficiency  (ITCE)  with  an  average  of  84.4%.    All  11  papers  report  IWUE  with  an  average  of  47.2%  ranging  from  15.7%  to  69.9%.    We  now  present  a  few  remarks  for  each  of  the  11  IWUE  papers.      We  start  with  Dhehibi,  Lachaal  and  Elloumi  (2007)  (A1.  1-­‐6)  who  used  data  for  a  sample  of  144  citrus  farms  from  the  area  of  Nabeul  in  Tunisia.    They  used  a  Translog  functional  form  along  with  a  Battese  and  Coelli  (1995)  model  to  explain  the  variation  in  TE  and   the   Reinhartd   et   al.   (2002)   two-­‐stage   approach   to   investigate   the   variables   that  influence  IWUE.  Irrigation  water  exhibited  the   largest  partial  elasticity  of  production  equal  to  0.298  and  returns  to  scale  equal  to  1.106  (at  the  mean  of  the  data).    The  authors  report  Mean  IWUE  and  output  oriented  TE  at  53.0%  and  67.7%,  respectively  while  mean  IWTCE  is  70.8.  The  value  for  IWUE  suggests  that  the  average  farmer  could  produce  the  same  level  of  output  with  47%  less  water.  This  study  also  reports  that  both  TE  and  IWUE  are  associated  with  farmer’s  age,  education  level,  agricultural  training,  farm  size,  share  of  productive  trees  and  water  availability.    Frija  et  al.,  (2009)    (A1.1-­‐9)  examined  data  collected  in  2005  for  a  sample  of  47  small-­‐scale  greenhouse  producers  of  (primarily)  tomatoes,  melons  and  peppers  located    in  the  region  of  Teboulba   in   east-­‐central   Tunisia.   The   authors   used   the   DEA   sub-­‐vector   efficiency  methodology   to   calculate   IWUE  and  a   second   stage   tobit  model   to   analyze   the   association  between  TE  and  IWUE  with  various  explanatory  variables.  The  analysis  showed  that  farmers  in   the   samples   in   the   farmer   are   overall   producing   at   the   right   scale.     Results   obtained  assuming  constant  returns  to  scale  reveal  an  average  TE  equal  to  67.3%  while  average  IWUE  is  reported  at  42%.  The  authors  conclude  that  providing  framers  with  training  in  greenhouse  management,   investments   in  water  saving  technologies  and  fertigation  techniques  (i.e.,   the  mixing  of  irrigation  water  with  fertilizers  can  be  expected  to  enhance  IWUE.  In  contrast,  the  authors  find  that  the  proportion  of  total  farmland  assigned  to  greenhouses  had  a  significant  negative  association  with  IWUE.      Wang  (2010),  which  is  paper  A1.1-­‐18,  uses  DEA  along  with  data  collected  for  the  2006  crop  year  from  a  sample  of  432  wheat  producers  located  in  11  villages  in  Northwestern  China  to  examine  TE  and  IWUE.    Water  measured  in  m3,  along  with  several  other  inputs  is  introduced  into  the  model.    An  average  TE  of  61.5%  is  reported  using  an  output  oriented  measure  and  a  CRS   model.     By   contrasts   the   average   input-­‐oriented   IWUE   is   30.7%.     The   author   also  calculated  the  more  traditional  single  factor  efficiency  and  found  that  on  average  0.61  kg  of  wheat   is   produced   per   m3   of   water   used.     The   author   then   applied   a   second   step   Tobit  regression  model   to  examine   the  determinants  of   IWUE.    The   results   show   that  additional  experience   and   financial   strength   are   associated   with   higher   irrigation   water   efficiency,  

   

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while   an   inverted   u-­‐shaped   association   between   IWUE   and   water   flow   is   reported.     The  author  also  argues   that  a  gradual   introduction  of  water  prices  would   likely   lead   to  a  more  efficient  use  of  water.      Another  paper  using  data  from  Tunisia  is  by  Mahdhi,  Sghaier  and  Bachta  (2011)    (A1.1-­‐12)  who  used  data   collected  between  April   2005   and  August   2009   for   a   sample   of   100   small-­‐scale  private  irrigated  farms  in  the  region  of  Zeuss-­‐  Koutine  in  south-­‐eastern  Tunisia.    This  study  evaluates  TE  and   IWUE  and,  under  variable   returns   to   scale,   the   average  TE   for   the  sample  was  80.3%  while  average  IWUE  was  60%.    Yet  another  study  for  Tunisia  using  the  DEA  sub-­‐vector  efficiency  methodology  is  by  Chemak  (2012)    (A1.1-­‐4)  who  used  2007,  2008  and  2009  data  for  47  farms  that  grew  olive  trees,  cereal  crops,  forage  crops  and  horticulture  crops.    The  results  showed  an  average  TE,  IWUE  and  scale  equal  to  81%,  68%  and  88%.      Njiraini  and  Guthiga  (2013),  paper  A1-­‐14,  focus  on  TE  and  IWUE,  while  also  examining  the  variables   associated   with   the   latter.     A   cross   sectional   data   set,   collected   in   March-­‐April  2010,   including  201  small  scale   irrigation  farmers  located  in  the  lake  Naivasha  basin  along  with   a   variable   returns   to   scale   DEA  model   are   used   to   estimate   input   oriented   TE.     The  model  incorporates  a  single  output  in  value  terms  and  several  inputs  including  the  quantity  of  water  used  for  irrigation  measured  in  m3.    Once  TE  is  calculated  the  authors  implement  a  sub-­‐vector   efficiency   analysis   to   calculate   IWUE  while   holding   output   and   all   other   inputs  constant.     The   results   show  an   average  TE   equal   to   63.3%  and   an   average   IWUE  equal   to  31.9%  with  a  Pearson  correlation  coefficient  for  these  two  efficiency  vectors  of  0.68.    They  then   proceed   with   a   second   step   Tobit   model   to   examine   the   variables   that   might   be  associated   with   IWUE.     The   Tobit   model   includes   various   socioeconomic   variables,   crop  choice   as   an   indicator   of   profitability,   a   land   fragmentation   index,   a   dummy   variable   to  capture  membership  in  a  water  use  group,  and  dummies  to  capture  the  irrigation  technology  used   (sprinkler,   drip   or   bucket).     The   key   results   are   as   follows:   farm   profits,   which   are  associated  with  the  choice  of  particular  crops,  has  a  positive  and  significant  effect  on  IWUE  while   land   fragmentation   exhibits   a   negative   effect;   the   use   of   sprinkler   technology   has   a  negative   effect   on   IWUE  while   the   drip   technology   has   a   positive   effect   relative   to   bucket  technology;  and  membership  on  water  use  groups  has  no  effect.    The  key  implications  drawn  are  that  the  low  levels  of  IWUE  is  likely  due  to  the  fact  that  water  is  available  free  of  charge.    In  addition,  the  choice  of  irrigation  technology  is  important,  as  is  the  choice  of  crops,  which  provides   important   lessons   for   extension   programming.     The   results   concerning   land  fragmentation  suggest  that  irrigation  might  be  better  managed  on  larger  plots  and  this  has  implications  for  policies  regarding  farm  size.    The  final  paper  (A1.1-­‐16)  that  we  review  in  the  A1.1  subgroup  is  by  Tang  et  al.  (2014)  who  argue  that  a  substantial  share  of  the  food  produced  in  China  relies  on  irrigated  land  and  that  water  use  efficiency  in  the  country,  measured  as  the  quantity  of  water  absorbed  by  irrigated  plants  relative  to  the  amount  of  water  used,  is  very  low  at  around  40%  compared  with  80%  in  developed  countries  such  as  Israel,  the  US  and  Japan.    Moreover,  the  authors  indicate  that,  on  average,  one  m3  of  water  is  used  to  produce  0.85  kg  of  output  and  this  is  about  half  of  the  water   productivity   achieved   in   developed   countries.     Therefore,   the   authors   set   out   to  investigate  the  efficiency  of  irrigation  water  at  both  the  farm  and  the  canal  levels,  and  then  examine  the  key  variables  associated  with  efficiency  focusing  on  the  various  types  of  water  management  systems  that  emerged  from  the  reforms  initiated  in  1998.    The  authors  use  an  

   

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unbalanced   panel   data   set   for   the   period   2000-­‐2005   for   a   sample   including   800   farmers  distributed  along  80  different  irrigation  canals  in  the  primary  irrigation  districts  in  Shaanxi  Province   in   Northwestern   China.     A   TL   SPF   model   is   estimated   where   the   dependent  variable,   total   value   of   farm  output,   is   expressed   as   a   function   of   various   inputs   including  irrigation  water  measured  in  m3.    An  interesting  feature  of  the  estimation  is  the  application  of   the   ‘true   fixed   effects   model’   introduced   by   Greene   (2005a   and   b),   which   captures  unobserved  time  invariant  farm  specific  heterogeneity  in  addition  to  time  variant  efficiency.    Another  feature  is  that  farm  and  canal  level  data  are  used  to  estimate  separate  SPF  models.    The  results  show  low  irrigation  water  TE  averaging  15.5%  for  the  farm  data  and  48.8%  for  the   canal   data.     In   both   cases,   however,   performance   improves   over   the   time   period  analyzed.    The  results  of  a  second-­‐step  fixed  effects  Tobit  regression  indicate  water  price  has  a  significant  positive  effect  on  irrigation  water  TE  for  both  canals  and  farmers.    In  addition,  the  disclosure  of  management  procedures  as  well  as  management  reforms  in  general  tends  to  have  a  positive  effect  on  TE.    When  compared  to  the  unreformed  case,  the  implementation  of   water   user   associations   has   the   largest   efficiency   effect   followed   by   joint-­‐stock  cooperatives  and  private  companies.    Karagiannis,   Tzouvelekas   and   Xepapadeas   (2003),   paper   A3-­‐6,  who   present   a  measure   of  irrigation  water   efficiency   relying   on   an   input-­‐specific   TE  measure.     This  measure   is   non-­‐radial,   input  oriented,   and  has  an  economic   instead  of   an  engineering   interpretation.     It   is  equal  to  the  ratio  of  the  minimum  amount  of  water  required  to  the  observed  water  used  to  produce   a   given   level   of   output   conditional   on   the   technology   and   the   quantity   of   other  inputs.     Thus,   this  measure   gives   the   amount   of  water   that   could   be   saved  while   keeping  output   and   other   inputs   constant,   which   implies   that   any   irrigation   technology   could   be  operated  inefficiently.    The  model  is  implemented  using  a  small  random  sample  of  50  out-­‐of  season  vegetable  farms  located  in  four  regions  of  Crete,  Greece  for  the  1998-­‐1999  harvesting  period.     A   stochastic   production   TL   frontier   is   fitted   using   the   Battese   and   Coelli   (1995)  approach.    The  dependent  variable  is  the  total  value  of  vegetables  produced  expressed  as  a  function   of   conventional   inputs   and   irrigation  water,  measured   in  m3.     In   addition   to   the  inefficiency  effects,  the  authors  also  implement  a  second  stage  equation  to  explain  irrigation  water  efficiency  and  both  of  these  models  include  the  same  variables  and  among  them  is  a  dummy  for  farms  using  modern  greenhouse  technology,  and  another  dummy  for  farms  using  irrigation  water   from   their   own  well.     The   results   indicate   that   water   has   a   positive   and  significant   partial   elasticity  with   an   average   equal   to   0.053;   this   value   is   the   lowest   of   all  partial   elasticities.     In   addition,   returns   to   scale   are   increasing   with   an   average   equal   to  1.126.    The  shadow  price  of  water  is  found  to  be  significantly  higher  than  the  market  price  but  the  authors  caution  that  the  former  should  be  considered  an  upper  bound  given  that  all  other  inputs  are  assumed  constant.    The  reported  mean  output  oriented  TE  is  70.2%  ranging  from   36.3%   to   89.1%.     By   comparison,   mean   irrigation   water   efficiency   is   47.2%   and  exhibits  considerable  variation  going   from  23.1%  to  98.6%.    The   implication   is   that,  at   the  mean,   the   observed   level   of   output   could   have   been   achieved   using   52.8%   less   irrigation  water   holding   other   inputs   at   their   observed   levels.     Overall,   TE   and   irrigation   water  efficiency  are  negatively  correlated.    Finally,  the  authors  indicate  that  the  “cost  savings  that  could  be  attained  by  adjusting  irrigation  water  to  its  efficient  level  would  be  small  since  its  outlays  constitute  a  small  proportion  of  total  cost”  (p.  68).    Speelman,   Buysse,   and   D’Haese   (2008)   (A3-­‐9)   set   out   to   examine   efficiency   in   the   use   of  

   

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irrigation  water  in  small-­‐scale  irrigation  schemes  using  data  collected  for  only  60  vegetable  farmers  from  July  to  September  2005  in  North-­‐West  Province,  South  Africa.    These  farmers  grew  mainly   butternuts,   cabbages   and   tomatoes,   using   simple   irrigation   techniques.     The  authors   note   a   high   degree   in   landholding   fragmentation   since   farmers   divide   their   fields  into  many  plots  to  plant  a  number  of  different  crops.    They  also  note  high  variation  in  input  use,  output  produced  and  in  farm  size  ranging  from  less  than  100  squared  meters  to  2.8  ha.  In  particular,  water  use  per  ha  varies  widely  from  3,872  m3  to  10,030  m3.  Average  TE  and  for  CRS  and  VRS  are  51%  and  84%,  respectively.    The  respective  numbers  for  AWUE  are  43%  and   67%.   Farmers   characteristics   (gender,   age,   education,   household   size)   were   not  significant   in   explaining   TE   and   IWUE,   while   cultivated   area   had   a   negative   effect,   and  landownership,  a  dummy  for  food  gardens  and  the  crop  choice  had  significant  and  positive  effects   in   both   efficiency  models.   The   authors   conclude   that   there   is   potential   to   ease   the  rising  pressure  on  water  resources  by  reallocating  some  water  away  from  irrigation.      Yigezu   et   al.,   (2013)     (A3.11)   attempted   to   investigate   differences   in   irrigation  water   use,  adoption   of   modern   irrigation   technologies   and   water   use   efficiency,   and   the   major  determinants  of   irrigation  water  use  efficiency.    To  address  these   issues  the  authors  relied  on  a   sample  of  385  wheat   farms   located   in   six  districts   in   the  Aleppo  province   in  Syria   to  estimate   a   Translog   production   frontier   using   the   Battese   and   Coelli   (1992)   model.    Somewhat   surprisingly,   the  authors  estimate   the  model  on  a  per  ha  basis   and   then   report  sharply   decreasing   returns   to   scale   (0.41).     This   low   level   is   due   to   a   highly   negative  elasticity  for  labor  while  the  average  elasticity  for  irrigation  water  is  0.11.    We  should  point  out  that  these  results  do  not  agree  with  the  reported  linear  terms  for  the  translog  and  this  incongruence  is  not  apparently  clear  from  reading  the  discussion.    Nevertheless,  the  average  TE,   IWUE  and   IWTCE  are  reported  at  78.2%,  69.9%  and  89.8%,  respectively.    The  authors  concluded  that  switching  from  traditional  surface  canal  irrigation  to  modern  irrigation  methods,  in  particular  sprinklers,  could  lead  to  19%  and  9%  higher  output  oriented  TE  and  IWUE,  respectively    Lilienfeld   and   Asmild   (2007)   motivated   by   the   well-­‐documented   over-­‐pumping   of   the  Ogallala  aquifer,  in  paper  C-­‐10  they  set  out  to  examine  the  effect  that  irrigation  system  type  has  on   irrigation  water  use  efficiency   for  a   sample  of   farmers   from  western  Kansas.    They  formulate  an   input-­‐oriented  DEA  model  and  use  data   for  the  8-­‐year  period  between  1992-­‐1999  from  43  farms,  which  yielded  a  total  of  339  observations  given  that  data  was  missing  for  five  farms.    The  sub-­‐vector  variation  of  DEA  is  implemented  since  the  interest  is  to  focus  on  efficiency  gains  for  only  the  water  input.    All  farmers  in  the  sample  produced  crops  under  irrigation  using  water  pumped  from  the  Ogallala  aquifer.    A  major  shift  is  observed  between  1992,  when  just  over  50%  of  the  farmers  used  flood  irrigation  systems,  and  1999,  when  85%  relied  on  center  pivot  sprinklers.    The  model  incorporates  output  for  six  crops,  non-­‐irrigated  and  irrigated  area  for  each  crop,  irrigation  water  (m3),  available  water  supply  (AWS)  in  the  soil  based  on  average  water  capacity  (cm  water/100  cm  soil),  average  annual  precipitation  (mm)   and   other   conventional   inputs.     The   results   show   average   water   excess   per   year  ranging  from  349  to  1,216  m3.    An  average  of  1,540  m3/ha  per  year  is  used  per  farm  while  the  calculated  average  excess  water  applied  per  farm  is  692  m3/ha.    These  figures  reveal  that  roughly  half  of   the  water  applied   is   in  excess.    The  authors  point  out   that  one  of   their  key  findings   is   “…   that   no   single   irrigation   system   seems   to   be   associated  with   high   levels   of  water  use  efficiency,   or   zero  …  water   excess”   (p.  80).    They  go  on   to   indicate   that  moving  toward  center  pivot  sprinkler  systems  may  not  be  warranted  and  that  assigning  public  funds  

   

15  

to  improve  management  might  be  a  desirable  policy  option.    Kaneko  et  al.,  (2004)    (E-­‐5)  estimated  a  Cobb-­‐Douglas  SPF  model  using  a  panel  data  set  for  30   Chinese   provinces   for   the   period   1999-­‐2002   (120   observations)   to   investigate   TE   and  IWUE.    The  dependent  variable  in  the  production  frontier   is  the  value  of  total  grain  output  per   ha   encompassing   rice,  wheat,   corn,   and   other   grains.   The   partial   elasticity   of  water   is  estimated  at  0.35  and  is  highly  significant.    Mean  TE  is  79%  while  mean  IWUE  is  54%.        5.    CONCLUDING  REMARKS      This   paper   provides   an   up   to   date   comprehensive   analysis   of   the   effects   that   different  methodologies   and   study-­‐specific   attributes  have  on  Mean  Technical  Efficiency   (MTE).    As  far  as  we  know,   this   focus  on  TE  and  water   is   the   first   study  on   this  particular   topic.    The  results  reveal  an  overall  AMTE  of  73.4%  for  all  farm  level  water  studies  examined.    The  data  also   shows   significant   variability   on   how  water   is   defined   in   the   various   studies.     In   our  judgment,  the  category  of  studies  that  provides  the  most  information  corresponds  to  those  that   focus   on   Irrigation   Water   Use   Efficiency   (IWUE).     This   group   includes   a   total   of   11  studies,  which  present  an  overall  mean  value  of  IWUE  equal  to  47.2%.    These  results  suggest  significant  scope   to   improve   farm  productivity  by  using  water  more  efficiently.    Moreover,  several  studies  provide  various  farm  output  responses  to  water,  including  partial  elasticities  of   production  with   respect   to:   volume   of   irrigated  water   applied;   irrigation   expenditures;  hours/number   of   times   a   plot   or   field   is   irrigated   during   the   season;   and   the   amount   or  percent  of  irrigated  land.    The  evidence  for  all  these  response  indicators  clearly  shows  that  irrigation  has  a  positive  and  significant  effect  on  output.    Technical   Efficiency   measures   provide   useful   information   regarding   productivity   gaps.    These   TE   measures   are   more   comprehensive   than   simple   single   factor   productivity  measures  (“crop  per  drop”)  since  they  account  for  the  fact  that  production  technologies  are  multi-­‐input,  and  there  is  also  the  potential  for  including  multiple  outputs.    However,  as  part  of  a  future  research  agenda,  it  is  desirable  to  go  further  by  incorporating  irrigation  in  Total  Factor  Productivity  analyses.    In  this  way,  it  would  be  possible  to  analyze  the  contribution  of  water  to  TFP  growth,  which  would  be  useful  information  for  policy  analysis.      One  shortcoming  of  the  studies  examined  is  the  dearth  of  comparative  evidence  concerning  the   efficiency   of   different   irrigation   systems.   Furthermore,   no   evidence   is   found   of  applications   of   efficiency   measures   in   cost   benefit   analysis   for   irrigation   investments.    Another   shortcoming   is   the   lack   of   evidence   regarding   the   interaction   between   climatic  variability,  especially  precipitation,  and  irrigation  and  this  also  deserves  attention.      Most  of   the   literature  on   irrigation  and  TE   focuses  on   intra-­‐farm  considerations.     The   few  studies  that  use  more  aggregate  data  tend  to  focus  on  TE  comparisons  across  geographical  regions.   We   found   no   studies   examining   efficiency   tradeoffs   associated   with   irrigation  between  farms  and  the  respective  basin  or  sub-­‐basin.  A  specific  issue  concerns  productivity  interactions   between   modern   irrigation   techniques   and   effects   on   return   flows   going   to  neighboring  farms  that  might  no  longer  receive  such  flows.  There  is  considerable  scope  for  research  on  this  topic,  which  is  complex  and  highly  site  specific.    

   

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Another  important  issue  has  to  do  with  the  potential  use  of  Production  Frontier  methods  in  project   evaluation,   particularly   for   projects   focusing   on   irrigation.     A   clear   area   where  production  frontiers  can  be  applied  in  water  projects  has  to  do  with  evaluating  the  efficiency  of   farmers   that   use   irrigation.     This   could   be   done   by   focusing   on   conventional   output  oriented   technical   efficiency  measures   at   the   farm   or   plot   levels,   and/or   using   non-­‐radial  measures  of  IWUE.    These  alternatives  provide  the  basis  to  benchmark  farmers  that  irrigate  and   then   to   develop   farm   groups   and   extension   programs   that   can   utilize   these   data   to  evaluate   farmer   performance   and   to   try   to   identify  ways   to   improve   efficiency   relative   to  peers.        Efficiency   measures   can   also   be   used   in   project   preparation   to   calibrate   anticipated  productivity  effects  with  and  without  irrigation.    Common  practice  in  project  preparation  is  to   use   economic-­‐engineering   procedures   to   project   cash   outflows   and   inflows   in   order   to  develop   ex-­‐ante   rates   of   returns   and   net   present   values.   TE   measures   for   relevant  countries/regions/farm   types   from   the   literature   could   be   used   to   adjust   the   economic  engineering   projections   with   the   intention   of   generating   cash   flows   that   reflect   more  realistic  productivity  outcomes  and  to  obtain  ultimately  more  relevant  ex-­‐ante  results.          Many   agricultural   projects   are   designed   to   increase   output   growth   while   also   improving  managerial   performance   (e.g.,   Cavatassi   et   al.,   2011;   Bravo-­‐Ureta,   Greene   and   Solís   2012;  Maffioli   et   al.,   2011).   In   this   context,   irrigation   projects   are   very   relevant   where   one  component  would  be  promoting   the   adoption  of  modern   irrigation   technology   to   increase  output  and  a  companion  component  would  be  to  provide  extension  support  to  augment  farm  management   capabilities   of   project   beneficiaries,   often   by   enhancing   the   institutional  capacity  of  water  user  associations  (e.g.,  Bandyopadhyay,  Shyamsundar  and  Xie  2007;  World  Bank  2008;  Gebregziabher,  Namara  and  Holden  2012).      Conceptually,  Stochastic  Production  Frontiers  (SPF)  are  well  suited  to  evaluate  the  impact  of  projects   designed   to   promote   improved   technologies   to   increase   output   while   also  attempting   to   enhance   productivity   by   promoting   managerial   performance   (Bravo-­‐Ureta  2014).     Nevertheless,   very   few   studies   have   used   SPF  models   in   impact   evaluation  work.    Early   exceptions   are   the   work   by   Taylor   and   Shonkwiler   (1986),   Taylor,   Drummond   and  Gomes   (1986)   and   Dinar,   Karagiannis   and   Tzouvelekas   (2007).   These   three   papers,  however,   did   not   consider   selectivity   bias,   a   critical   challenge   in   impact   evaluation  work.    One   avenue   to   incorporate   SPF  models   that   address   selectivity   bias   in   impact   evaluation  applications   is   based   on   Greene   (2010),   as   extended   by   Bravo-­‐Ureta,   Greene   and   Solís  (2012),  and  recent  applications  have  been  reported  by  González-­‐Flores  et  al.  (2014)  and  by  Villano   et   al.   (2014).     In   closing,   if   only   endline   cross   sectional   data   is   available,   not   an  uncommon   occurrence,   these   methods   make   it   possible   to   decompose   the   impact   of  irrigation  projects  on  the  shift  of  the  frontier  (e.g.,  output,  income,  value  of  production)  and  the  managerial  effects  of  the  intervention.        

   

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 Table 1. Overview of Empirical Studies of Technical Efficiency in Farming Category   Water  papers   Non-­‐water  papers   All  papers  

  No.  of  Cases  

AMTE*   No.  of  Cases  

AMTE   No.  of  Cases  

AMTE  

Approach              Parametric   120   73.0   503   74.9   623   74.5  Non-­‐Parametric   73   74.0   208   73.7   281   73.8  

             Stochastic   120   73.0   432   75.4   552   74.9  Deterministic   73   74.0   279   73.3   352   73.4  

             Data              Panel   47   76.3   270   77.7   317   77.3  Cross  Sectional   146   72.5   414   72.6   560   73.5                Functional  Form**          Cobb-­‐Douglas   78   73.6   269   72.0   347   72.4  Translog   42   72.1   211   78.3   253   77.3  Others   0   -­‐-­‐-­‐   24   73.7   24   73.7                Technology  Representation      Primal   191   73.5   663   74.5   854   74.2  Dual   0   -­‐-­‐-­‐   32   73.8   32   73.8  

             AMTE   73.4   74.5   74.3  Number  of  Cases   193   711   904  Number  of  Studies***   94   315   409  

*  Numbers  underlined  denote  statistical  differences  for  each  category  with  each  column.    **  Valid  for  Parametric  approach  studies  ***  Excludes  16  papers  as  follows:  10  aggregate  level;  5  due  to  missing  data;  and  1unpublished.  

   

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Table 2. Average Mean Technical Efficiency (AMTE) by Methodological Characteristics

Category   Water  papers   Non-­‐water   All  papers  

  No.   AMTE*   No.   AMTE   No.   AMTE  

Geographical  Region          Africa   40   65.7   63   70.0   103   68.3  Asia   118   74.0   138   75.4   256   74.8  L.  America   3   55.1   69   62.0   72   61.7  N.  America**   8   81.0   130   78.7   138   78.9  E.  Europe   1   69.0   29   72.9   30   72.7  W.  Europe  &  Oceania   23   83.9   282   76.4   305   77.0              Country  Income            LIC***   50   69.8   47   78.7   97   74.1  LMIC   64   74.7   138   71.4   202   72.4  UMIC   39   73.1   116   65.3   155   67.2  HIC   40   76.2   410   77.7   450   77.6  

             Product              Rice   63   76.1   57   73.3   120   74.7  Maize   2   74.5   27   76.3   29   76.2  Wheat   23   74.0   14   75.2   37   74.4  Mixed  Grains   0   -­‐-­‐-­‐   38   73.7   38   73.7  Crops  and  Livestock   91   69.8   285   69.6   376   69.6  Dairy   13   84.0   198   80.7   211   80.9  Other  Animals   1   81.0   72   78.3   73   78.3  Whole  Farm   0   -­‐-­‐-­‐   20   72.5   20   72.5  

             AMTE   73.4   74.5   74.3  Number  of  Cases   193   711   904  Number  of  Studies***   94   315   409  

*  Numbers  underlined  denote  statistical  differences  for  each  category  with  each  column.  **  North  America  includes  the  United  States  and  Canada.  *** LICs: Lower Income Countries, LMICs: Lower Middle Income Countries, UMICs: Upper Middle Income Countries,

and HICs: Higher Income Countries (World Bank, 2014). ****  Excludes  16  papers  as  follows:  10  aggregate  level;  5  due  to  missing  data;  and  1unpublished.                      

   

19  

    Table  3.  AMTE*  by  Group  for  110  Water  of  Studies  

    Group  ID  Nº  of  studies   MTE       Min       Max  

    A1.1    19   71.9       13.5       99       A1.2    5   91.4       75       99       A1.3    22   79.9       25.5       99       A1.4    7   68.7       36.7       87.4       A1.5    3   81.1       65       97       A2    9   69.0       36       89.6       A3    11   72.2       51       90.2       A    76   76.3       13.5       99       B    6   70.8       51       98.4       C    13   66.2       15.6       90.4       D    5   67.4       47       83.1  

    E    10   61.6       45       79.7  

   *  Average  Mean  Technical  Efficiencies  (AMTE)  differences  are  statistically  significant  only  for  Group  A  and  C,  and  A  and  D.  

     

         

                                               

   

20  

Table  4:    TE  and  Output  Response  to  Different  Variables  in  Farm  level  Studies    

Group   TE   Variable  Output  

Group   TE   Variable  Output  

Response   Response  A1.1-­‐1   73.8   VWater   0.115   A1.3-­‐15   63.0   VWater   0.350  A1.1-­‐2   72.4   VWater   0.223   A1.3-­‐18   58.8    #Irrig.   0.000  A1.1-­‐3   NA   VWater   -­‐0.590   A1.4-­‐1   83.9   %Irrig.L   0.300  A1.1-­‐5   79.0   VWater   0.297   A1.4-­‐2   86.7   %Irrig.L   0.500  A1.1-­‐6   43.5   VWater   -­‐-­‐   A1.4-­‐4   68.9   %Irrig.L   0.000  A1.1-­‐7   90.0   VWater   -­‐-­‐   A1.4-­‐5   61.0   %Irrig.L   0.310  A1.1-­‐8   84.0   VWater   -­‐-­‐   A1.4-­‐8   43.3   %Irrig.L   0.210  A1.1-­‐9   68.0   VWater   -­‐-­‐   A1.5-­‐1   77.0   %Irrig.L   0.130  A1.1-­‐10   82.0   VWater   -­‐-­‐   A.2-­‐6   75.8   Irrig.A_D   0.150  A1.1-­‐11   68.0   VWater   -­‐-­‐   A.2-­‐7   61.0   AIrrigT_D     0.000  A1.1-­‐13   96.0   VWater   -­‐-­‐   A3.3   80.0    #Irrig.   0.314  A1.1-­‐15   51.0   VWater   -­‐-­‐   A3.5   72.0   VWater   0.320  A1.1-­‐17   65.0   VWater   0.500   A3.6   72.0    #Irrig.   0.060  A1.1-­‐19   58.3   VWater   0.660   A3.7   66.0    #Irrig.   0.350  A1.2-­‐1   91.0   Irrig  H.   0.190   A3.8   76.4   Irrig.L/L   0.078  A1.2-­‐15   90.2   IrrigEx.   0.080   A3-­‐10   82.0   VWater   0.080  A1.2-­‐16   25.5   IrrigEx.   0.000   A3.11   78.2   VWater   -­‐0.013  A1.3-­‐2   91.0    #Irrig.   -­‐0.325   C-­‐4   89.3   Irrig.L_D   0.268  A1.3-­‐4   79.0   IrrigEx.   0.020   C-­‐5   90.4   Irrig.L_D   0.267  

A1.3-­‐6   76.6   IrrigEx.   0.127   C-­‐6   63.5  MVP  IL-­‐RFL     175  Birr  

A1.3-­‐8   89.0    #Irrig.   0.113   C-­‐11   NA  MVP  IL-­‐RFL     1450  Birr  

A1.3-­‐9   91.0   IrrigEx.   0.000   C-­‐13   81.0   VWater   0.086  A1.3-­‐10   95.4   IrrigEx.   0.070   D-­‐1   48.0   Irrig.  Land   0.200  A1.3-­‐13   69.0   IrrigEx.   0.910   D-­‐3   66.0   IrrigEx.   0.068  

Avg.   71.6   VWater                      TE:  Technical  Efficiency       Irrig  H.:  irrig.  in  hours  VWater:  Volumetric  water       IrrigEx:  Irrig.  expenses  #Irrig:  Number  of  times  a  field  is  Irrigated   Irrig.A_D:  Irrig.  acces  dummy  %Irrig.L.:  %  Irrig.  land           Irrig.L/L:  Irrig.  land/total  land  AIrrigT_D:  Advanced  irrigation  Technology   Irrig.  Land:  Irrig.  Land  Irrig.L_D;  Irrig.  land  dummy                      MVP  IL-­‐RFL:  Marg.  Value  Product  irrig.  land  minus  rain-­‐fed  land                

     

   

21  

Table  5:    TE,  IWUE,  and  Output  Response  to  Different  Variables  in  Farm  level  Studies  

Group   TE   ITCE   IWUE   Variable   SFA=1,  DEA=2  Output  Response  

A1.1-­‐4   81.0       68.0   VWater   2   -­‐-­‐  A1.1-­‐6   67.7   70.8   53.0   VWater   1   -­‐-­‐  A1.1-­‐9   71.5       47.3   VWater   2   -­‐-­‐  A1.1-­‐12   64.0       47.8   VWater   2   -­‐-­‐  A1.1-­‐14   63.0       31.0   VWater   2   -­‐-­‐  A1.1-­‐16   NA       15.7   VWater   1   0.735  A1.1-­‐18   61.5       30.6   VWater   2   -­‐-­‐  A3-­‐6   70.2   92.5   47.2   Mixed   1   0.053  A3-­‐9   67.5       55.0   Mixed   2   -­‐-­‐  A3-­‐11   78.2   89.8   69.9   Mixed   1   0.240  

E-­‐5   79.0     54.0   Aggregate   1    

0.350    

Average   70.4   84.4   47.2        

TE:  Technical  Efficiency       IWUE:  Irrig.  Water  Use  Efficiency  VWater:  Volumetric  water       Irrig  H.:  irrig.  in  hours  #Irrig:  Number  of  times  a  field  is  Irrigated       IrrigEx:  Irrig.  expenses  %Irrig.L.:  %  Irrig.  land       Irrig.A_D:  Irrig.  access  dummy  AIrrigT_D:  Advanced  Irrig.  Technology       Irrig.L/L:  Irrig.  land/total  land  Irrig.L_D;  Irrig.  land  dummy       Irrig.  Land:  Irrig.  Land  

MVP  IL-­‐RFL:  Marg.  Value  Product  irrig.  land  minus  rain-­‐fed  land    ITCE:   Irrigation   Water   Technical   Cost  Efficiency  

   

 

 

 

 

 

 

 

     

   

22  

   

       

           

     

           

   

           

     

   Figure  1.    Output  Oriented  TE  &  IWTE  (Karagiannis,  Tzouvelekas  and  Xepapadeas,  2003)            

Y Output

Irrigation    Water  (m3) O

YM

Max/Frontier  Y

Observed  Y

IW0 IW1

Y0

Output  Oriented   Inefficiency

A  

B  

C  

   

23  

     

   

             

 

                             

     

 Figure  2.    Input  Oriented  TE  &  IWTE  (Karagiannis,  Tzouvelekas  and  Xepapadeas,  2003)            

Input  X

Irrigation    Water  (m3) O

X1 C

B

A

Y0

W2 W3 W1

TE              =  OB/OA IWTE  =  X

1C/X

1A

                         =  0W2/  0W

1

   

24  

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