Estimating  switching  costs  using  Shy’s  model

  Figure  10:  Switching  costs  of  consumers  calculated  using  Shy’s  model.  

The  blue  graph  shows  that  consumers  have  varying  switching  costs,  but  are  all  in  an  interval  of  10%.  

The  switching  costs  of  consumers  of  the  largest  banks  seem  to  vary  less  than  the  switching  costs  of   consumers  of  the  smaller  banks.  Generally  it  seems  as  the  largest  banks  serve  consumers  with  the   highest  switching  costs.  The  same  picture  can  be  seen  if  the  market  where  only  the  six  largest  banks   compete  is  considered.  So  according  to  the  model,  the  largest  banks  serve  the  consumers  with  the   highest  costs  of  switching;  similarly  does  the  smallest  banks  serve  the  consumers  with  the  lowest   costs  of  switching.    

From  Figure  10  it  is  obvious  that  the  two  definitions  of  the  market  on  which  the  banks  operates   yields  very  different  results.  Intuitively  this  seems  reasonable,  as  the  banks’  pricing  methods  should   depend  heavily  on  the  firm⁵  they  compete  with  or  in  the  model  framework,  the  one  firm  they  fear   will  undercut  them.  The  smallest  firm  in  the  market  with  the  six  largest  banks  have  retail  customer                                                                                                                  

5  Each  firm  only  fears  being  undercut  by  one  firm  according  to  Definition  3.  

deposits,  which  is  used  to  calculate  market  shares,  that  is  250  times  larger  than  the  smallest  firm  in   the  model  with  all  banks,  so  it  is  not  surprising  that  the  results  are  significantly  different.  The  most   obvious  difference  between  the  two  models  is  the  estimation  of  the  switching  costs  of  consumers  of   bank  five  and  six.  The  main  reason  is  that  they  go  from  being  large  banks  in  the  model  with  all  banks,   and  does  not  have  an  incentive  to  undercut  the  other  banks,  to  being  small  banks  in  the  model  with   only  six  banks  and  therefore  have  a  larger  incentive  to  undercut  the  other  banks.  The  overall  result   that  larger  banks  serve  the  customers  with  the  largest  switching  costs,  are  equivalent  for  both   market  definitions.    

Measuring  the  switching  costs,  as  an  interest  rate  can  be  hard  to  put  in  perspective,  since  the  actual   costs  also  depends  on  the  unobserved  principal  and  number  of  payments.  Using  an  interest  rate  as   the  unit  of  measure  can  also  be  misrepresentative  since  switching  costs  is  a  onetime  cost,  while  an   interest  rate  is  usually  associated  with  repeated  payments.  It  can  however  be  related  to  the  observed   price  of  the  bank.    If  the  switching  costs  are  measured  as  a  percentage  of  the  bank’s  price,  the  

switching  costs’  dependency  on  the  principal  and  number  of  payments  is  eliminated.  The  measure  is   also  independent  of  the  price  level  and  can  be  used  if  the  price  of  the  bank  is  not  measured  as  an   interest  rate.  The  graph  below  illustrates  the  result.  

  Figure  11:  Switching  costs  calculated  using  Shy’s  model  expressed  as  a  percentage  of  the  

price.  

Figure  11  shows  that  in  the  model  with  all  banks,  the  largest  banks  consumers’  switching  costs  are   essentially  the  prices  that  the  individual  banks  offer.  This  ratio  decreases  for  the  smaller  banks,  but   the  consumers’  switching  costs  are  still  above  50%  of  each  bank’s  price.  This  seems  very  high   compared  to  other  research,  as  well  as  general  knowledge  about  markets.  That  the  banks  with  the   largest  market  share  serve  the  costumers  with  the  largest  switching  costs  makes  sense,  as  having   consumers  with  high  switching  costs  will  for  obvious  reasons  often  result  in  a  high  market  share.  

Shy’s  definition  of  market  competition  is  not  appropriate  to  use  on  markets  where  there  are  large   differences  in  the  size  of  the  competitors,  and  therefore  large  differences  in  the  competition  between   the  individual  competitors.  The  results  of  the  model  are  highly  dependent  on  the  smallest  firm  in  the   market,  as  the  smallest  firm  is  the  one  most  likely  to  undercut  the  price  of  the  other  firms.  The  other   firms  in  the  market  are  therefore  essentially  setting  their  price  according  to  the  smallest  firm  in  the  

market.  If  the  smallest  firm  is  significantly  smaller  than  the  larger  firms,  it  is  unrealistic  that  the   larger  firms  will  price  according  to  the  smallest  firm,  and  the  assumption  is  not  suitable.  The  

problem  arises  because  of  the  utility  function  of  consumers  and  subsequently  the  demand  structure   of  firms.  The  market  shares  are  a  function  of  the  prices,  and  if  a  single  firm  undercuts  the  price  of  the   others,  and  compensate  the  consumer’s  switching  costs,  the  firm  will  capture  the  entire  market   share.  This  is  a  simplified  assumption,  and  is  not  in  line  with  empirical  observations.  Instead  of   modifying  the  market  assumptions,  the  demand  structure  of  the  model  could  be  modified  or  the   consumers  switching  costs  are  allowed  to  be  asymmetric.  For  example  could  construction  of  a  model   where  each  firm  face  downward-­‐sloping  demand  curves  be  constructed.  In  this  thesis  the  underlying   theoretical  assumption  of  the  model  are  intact,  while  the  market  assumptions  are  modified.  

Two  different  modifications  to  Shy’s  market  conditions  will  be  imposed.  The  purpose  is  to  examine,  if   a  more  suitable  assumption  for  the  Danish  banking  industry  can  be  found.  The  general  idea  is  that   the  firms  in  the  market  do  not  set  their  prices  according  to  the  smallest  firm  in  the  market,  but  rather   the  firms  with  market  shares  similar  to  themselves.  The  assumptions  are  meant  as  a  benchmark,  and   are  not  necessarily  an  improvement,  or  more  correct.  The  first  modification  is  that  each  bank  only   considers  undercutting  bank  𝑖+1,  still  using  an  index  where  banks  are  ranked  by  decreasing  market   share,  i.e.  each  bank  only  consider  undercutting  the  one  bank  with  higher  market  share  just  above   itself.  In  the  second  modification  a  moving  average  of  both  market  shares  and  prices  for  bank  

𝑖+3,𝑖+2,𝑖+1,𝑖−1,𝑖−2,𝑖−3,  i.e.  the  three  banks  with  market  share  just  above  or  below  bank  𝑖,   is  used  as  input  in  equation  (4.10).  For  the  three  largest  and  smallest  banks,  where  some  of  these  do   not  exist,  a  moving  average  of  the  available  banks  are  used.    Below  is  a  graphical  presentation  of  the   results.  

  Figure  12:  Switching  costs  calculated  using  Shy’s  model  with  modified  market  conditions.  

The  two  modified  estimations  of  switching  costs  are  quite  similar.  They  are  both  lower  than  the   estimations  using  Shy’s  assumption  of  undercutting  on  the  market  consisting  of  all  banks.  So  if   markets  are  defined  as  above,  with  different  competitors  for  each  bank,  the  switching  cost  of  the   consumers  they  serve  are  estimated  to  be  lower.  The  market  with  the  six  largest  banks  cross  both   the  new  lines,  implying  that  the  switching  cost  variation  of  consumers  is  higher  than  in  the  two   benchmark  cases.  Overall  it  seems  that  the  four  models  yield  estimated  consumer  switching  costs   with  similar  characteristics,  but  of  different  magnitude.  Below  is  the  switching  costs  given  as  a   percentage  of  the  each  banks  price  illustrated.  

  Figure  13:  Switching  costs  calculated  using  Shy’s  model  with  modified  market  conditions  

expressed  as  a  percentage  of  the  price.  

The  two  estimations  using  Shy’s  market  assumption  are  quite  different  than  the  estimations  with   modified  assumptions.  Shy  identify  one  bank  that  is  most  likely  to  undercut  the  others  and  the  rest   set  their  price  relative  to  that  bank,  which  usually  leads  to  continuously  decreasing  switching  costs  of   consumers.  In  the  benchmark  models  the  bank  or  banks  that  are  most  likely  to  undercut  are  different   for  each  bank,  which  leads  to  switching  costs  of  consumers  that  vary  for  each  bank,  and  there  is  no   uniform  trend  across  the  entire  market.  The  tendency  that  large  banks,  serve  consumers  with  high   switching  costs,  does  also  seem  to  be  existent  with  the  modified  market  conditions.  

The  model  is  very  simplified  as  it  only  considers  prices  and  market  shares,  and  makes  some  strong   assumptions  about  which  firms  that  potentially  undercut  each  other.  It  is  however  an  easy  method  to   assess  the  level  of  consumer  switching  costs  of  each  supplier  in  a  market.  Another  disadvantage  of   the  model  is  that  switching  costs  are  estimated  on  the  basis  of  observed  prices  and  market  shares.  

Prices  and  market  shares  will  always  be  historical,  and  so  will  the  consumer  switching  costs.  This   may  not  be  an  issue  if  switching  costs  of  consumers  are  fairly  constant  over  time,  which  is  an   interesting  topic  for  further  research.