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Large countries are better off in a closed economy and small countries are better off in an open economy - with empirical evidence

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     Ca’  Foscari  University  of  Venice  

 

                                                           

 

 

                                                       M.Sc  programme  in  Economics  

                                                                                 

(A.Y.  2011-­‐2013)  

 

 

               

Large  countries  are  better  off  in  an  open  economy  and  small  countries   are  better  off  in  a  closed  economy  -­‐  with  empirical  evidence  

 

Candidate:  Mumu  Ayesha  Sugandhi   Student  ID:  823742  

Supervisor:  Prof.  Federico  Etro   Assistant  Supervisor:  Elisabetta  Lodigiani  

                           

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Abstract  

 

Two   of   the   fundamental   political   and   economic   phenomena   of   the   last   century   have   been   the   break   up   of   nations   into   smaller   states   and   the   increased  economic  integration  of  international  markets.  This  dissertation   reviews   the   theoretical   literature   on   these   topics.   The   purpose   of   this   dissertation   is   to   study   the   relationship   between   size,   government   consumption  and  trade  openness.  We  present  empirical  results  that  show   that   of   open   economy   are   positively   and   statistically   significant   and   are   economically   sizable   for   small   countries,   and   country   size   is   negatively   related  to  the  government  spending  and  most  of  the  government  spending   items.  The  results  are  robust  to  different  time  periods  and  country  samples,   different  econometric  techniques  and  to  several  sets  of  control  variables.                                                

 

 

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Contents  

 

Abstract                                                                                                                                                                                                                                                            2     Contents                                                                                                                                                                                                                                                          3    

List  Of  Tables                                                                                                                                                                                                                                      5  

 

Executive  Summary                                                                                                                                                                                                                                              6    

Chapter  One:  Introduction                                                                                                                                                                                8      

1.1.  Determinant  of  borders  .  .  .  ..  8    

1.2.  Determinant  of  Size  of  countries  .  .  .  10    

1.3.  The  benefits  of  size  .  .  .    .  .  .  .13    

1.4.  The  cost  of  size  .  .  .  14  

 

Chapter  Two:  Theoretical  Presentation  Of  The  Models                                                          15  

 

2.1.  Alesina,  Spolaore  and  Wacziarg(2000)  :  basic  structure.  .  .  ..  .  .  15    

 

                           2.1.1.  Production  and  trade  .  .  .    .  .  .  15  

 

                           2.1.2.  Capital  accumulation  and  growth  .  .  .  17    

                           2.1.3  Steady  state  income/output  .  .  .  .18    

 

2.2.    Equilibrium  analysis  .  .  .  19    

 

                           2.2.1.  Equilibrium  analysis  part  1:  The  main  Alesina  and  Spolaore                                                  

(1997,2003)  Trade,  growth  and  openness  theory  .  .  .  ..  .  .  19    

 

                           2.2.2.    Equilibrium  analysis  part  2:  Etro  (2006)  theory  .  .  .  21    

 

• Equilibrium  welfare    

• Equilibrium  government  spending  and  public  spending  provision    

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2.3.            Summary  and  Conclusions  .  .  .    .  .  .  .    .29    

Chapter  Three:  Empirical  Evidence                                                                                                                                        31  

 

3.1.  The  relationship  between  size  and  openness.  .  .    .  .  .    .  .  .  .31    

3.2  The  relationship  between  government  consumption  and  size.  .  .    .  .  .    .39    

3.3.  Summary  and  Conclusions  .  .  .  .52    

Chapter  Four:  Summary  And  Concluding  Remarks                                                                          53  

  REFERENCES                                                                                                                                                                                                                                    55     • Theoretical  part       • Empirical  part                                                        

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List  of  Tables  

 

 

2.1.  Comparison  between  the  utility  function  of  endogenous  and  exogenous  government   spending  models  .  .  .    .  .  .    .  .  .  ..  .  .    ..  .  .    23    

 

2.2.  Comparison  between  the  optimal  size  of  our  distinct  models.  .  .    .  .  .  .  ..  .  .  28    

 

3.1.1.  Descriptive  statistics  (1970-­‐2011  averages)  .  .  .  .35    

 

3.1.2.  Pairwise  correlations  for  the  main  variables  of  interest  (1970-­‐2011  averages)  .  .  35    

 

3.1.3.  Conditional  correlation  (1970-­‐2011)  .  .  .  .36    

 

3.1.4.  Constrained  SUR  estimate  (size  =log  pop,  openness=N.  openness).  .  .  ..  .  .  .  .37    

 

3.2.1.  Descriptive  statistics  (1970-­‐2011  averages)  .  .  .  .41    

 

3.2.2.  Pairwise  correlations  for  the  main  variables  of  interest  (1970-­‐2011  averages)  .  ..42    

 

3.2.3.a   Table   3.2.3(b)   OLS   regression   for   various   control   variables   of   government   consumption  (size=log  of  population)-­‐Demographic  size.  .  .    .  .  .  .44    

 

3.2.3.b.   Table   3.2.3(b)   OLS   regression   for   various   control   variables   of   government   consumption  (size=log  of  total  GDP)-­‐Economic  size  .  .  .    .  .  .45    

 

3.2.4.  Cross-­‐sectional  time-­‐series  FGLS  regression.  .  .    .  .  .    .  .  .  50    

 

3.2.5.  1  tail  p-­‐value  test  for  sasabuchi  test.  .  .    .  .  .    .    .  .  .  .  51  

     

 

 

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Executive  summary  

 

 

A   large   body   of   literature   deals   with   the   economic   determinants   of   government  size,  the  relationship  of  government  consumption  with  size  of   country   and   the   determinants   of   trade   openness.   Recent   studies   of   the   economics  of  country  formation,  by  Alesina,  Spolaore  and  Wacziarg  (2003);   Etro  (2006)  suggest  that  country  size,  government  size  and  trade  openness   are   interconnected   and   Rodrik   (1996)   suggest   that,   size   is   negatively  

correlated  with  government  spending.

 

Normally   size   of   countries   has   always   been   considered   an   exogenous   variable.   Nevertheless,   the   borders   of   countries   and   therefore   their   size   change  in  response  to  economic  factors  such  as  the  pattern  of  international   trade.   For   instance   smaller   countries   have   a   greater   stake   in   maintaining   free  trade  because  of  the  larger  market  space  it  gets  through  open  economy   while   for   a   close   economy,   being   large   is   considered   as   a   benefit.   There   exists   a   trade-­‐off   between   heterogeneity   costs   and   benefits   from   scale   economies,  and  both  increase  in  the  size  of  a  country.  Trough  these  trade-­‐ off,  size  effects  the  share  of  its  public  spending,  which  is  maximized  at  an   intermediate  size  and  the  higher  the  heterogeneity  cost  the  larger  are  the   size.    

 

The  main  inspiration  of  my  research  is  the  theoretical  work  of  Alesina  and   Spolaore   (1997,2005),   who   have   introduced   that;   there   is   a   trade-­‐off   between   heterogeneity   (in   preferences)   and   scale   economies   (in   public   good  provision).  And  this  trade-­‐off  works  as  the  determinant  of  the  political   geography.  Their  implications  of  openness  and  heterogeneity  cost  pointed   out  towards  political  secessions  and  lots  of  small  countries.    

 

My   second,   paper   of   references   are   Rodrik   (1996),   who   determined   a  

negative  relationship  between  government  consumption  and  size  and  Etro1  

who   has   reconstructed   and   renovated   the   AS2  theory.   Etro,   in   his   paper,  

pointed  out  the  limits  of  the  Alesina  and  Spolaore  (1997,2005)  model,  that   is   considering   public   spending   per   nation   as   an   exogenous   and   fixed   variable.  Which  limited  the  countries  from  choosing  the  size  of  their  public   spending  and  constrained  the  countries  to  provide  same  amount  of  public   goods   independently   from   their   dimension.   Considering   size   of   countries  

                                                                                                               

1    Etro  refers  to  Etro(2006)  

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and  public  spending  as  endogenous  variables,  he  explained  the  relationship   between   government   consumption   and   size.   And   argued   that,   the   optimal  

geography3  might   not   be   a   stable   equilibrium   because   it   may   imply   too  

large  countries  from  which  citizens  at  the  borders  would  prefer  to  escape.     In  particular,  these  papers  have  put  forward  two  hypotheses:  

   

• Large   countries   are   better   off   in   a   closed   economy   and   small   countries  are  better  off  in  an  open  economy  

 

• Smaller  countries  have  a  larger  share  of  public  consumption  in  GDP    

We  will  be  reviewing  both  of  the  above-­‐discussed  hypotheses  empirically.   The  empirical  relationship  of  size  and  openness  has  already  been  proved  by   Alesina,  Spolaore  and  Wacziarg  (2003). Notwithstanding,  to  the  best  of  my   knowledge,   the   impact   of   the   size   of   nations   upon   the   determination   of   government   spending   has   not   yet   been   empirically   discussed   in   the   literature  after  Rodrik(1996).  These  two  facts,  taken  together,  may  account   for  the  observation  that  open  countries  have  larger  governments.    

 

This  paper  is  organized  as  follows;  

In   the   first   chapter,   we   discuss   some   of   the   stylized   facts   concerning   the   determinants  of  size  of  a  country.  Chapter  2  presents  the  theoretical  models   specifying  our  targeted  relationship.  And  chapter  3  empirically  checks  and   confirms   the   results   of   both   AS   and   relationship   between   government   consumption  and  size.  Basically  we  show  that,  small  countries  are  better  off   in  an  open  economy  and  larger  countries  are  better  off  in  a  closed  economy.   Chapter  four  concludes  the  findings  of  overall  discussion.  

                                                                                                                                                                                                                                   

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                                                                                                                               Chapter  1         Introduction    

Countries   come   in   all   size,   some   are   large   and   some   are   small.   The   five   largest   countries   (by   population)   in   the   world   are   China,   India,   the   USA,   Indonesia,  and  Brazil.  Among  them  only  the  USA  is  a  rich  country.  Basically,   many   of   the   richest   countries   in   the   world   are   small. In   fact   the   richest   country   in   the   world   in   2010,   in   terms   of   income   per   capita,   was   Luxembourg  that  had  518252  inhabitants.  According  to  World  Bank,  of  the   ten  richest  countries  in  the  world  in  terms  of  GDP  per  capita  (indicator  of  a   country’s  standard  of  living),  six  have  population  above  one  million.  They   are   the   United   States   (313.9   million   people),   Australia   (22.32   million),   Austria   (8.424   million),   Switzerland   (7.912   million),   Norway   (4.953   million),  and  Singapore  (5.184  million).    And  of  these  six  countries,  two  are   below  average  in  terms  of  population.  The  largest  increase  in  the  number  of   independent  countries  in  the  post  II  world  war  has  been  accompanied  by   an   expansion   of   world   trade   and   by   a   sharp   increase   in   economic   integration.   Basically   today’s   countries   are   smaller   in   size   than   the   countries  that  got  independence  decades  back.  This  independence  depends   on  various  facts  such  as  regional  separatism  and  ethnic  conflicts.  Some  big   countries   are   getting   divided   like   Quebec   or   Catalonia   and   some   are   reuniting   like   Germany   and   Yemen.   Actually,   economic   integration   works   better  with  political  disintegration.  Quebec’s  separatism  is  a  good  example.     These  results  gives  arise  to  the  following  questions:  Why  is  this  difference?   Why   do   country   size   varies?   What   are   the   determinants   of   country   size?   What  are  the  cost  and  benefit  of  size?  Well  in  the  following  subsections,  we   will  be  exploring  the  solution  of  these  questions.  

 

 

     1.1.Determinant  of  borders      

 

Size   is   a   relative   concept;   land   area,   population   and   GDP   can   derive   it.   Based   on   AS,   we   have   pointed   out   the   trade-­‐off   between   size   and   heterogeneity,   majority   voting   and   trade   regime   as   the   determinant   of   border   (namely   cause   of   political   disintegration),   across   countries.   The   following  part  describes  briefly  these  factors:  

 

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Trade-­‐off  between  size  and  heterogeneity    

Trade-­‐off   between   size   and   heterogeneity   of   certain   public   goods   determine   the   borders   of   countries.   Usually   public   goods   are   a   basic   financial  system,  tax  collection  and  fiscal  institutions,  legal  juridical  system,   government  infrastructure,  public  libraries,  national  parks  and  embassies.   In  most  instances  the  provision  of  these  public  goods  include  fixed  costs.  In   this   world,   everyone   pays   certain   amount   of   taxes   to   the   government   for   enjoying   the   facilities   of   these   public   goods.   And   different   people   have   different   views   about   how   the   policy   should   spend   their   tax   money.   In   general,   public   good   have   both   ideological   and   political   dimension,   which   means   cost,   is   negatively   correlated   with   the   distance.   (Ex:   public   school)   for   example:   in   Italy   concerning   the   location   of   hub   of   the   main   national   airline   had   substantial   implications   for   the   distribution   of   travel   costs   in   different  parts  of  Italy.  

 

There  exist  two  dimensions  of  heterogeneity:    

• Geography   (how   distant   an   individual   is   from   a   public   good):   jurisdictions   are   generally   geographically   compact   because   there   is   administrative  cost  in  disjoint  countries.  

 

• Ideology   (how   close   are   public   good   and   policies   to   the   individual   preference):   individuals   who   are   close   together   in   a   space   are   also   more  alike  in  preference  because  of  the  following  reasons:  

 

1. Sorting:   individuals   of   same   attitudes,   ideology,   preference,   income  and  religion  attempts  to  live  close  to  each  other.  

 

2. Uniformity:   hundreds   of   years   of   proximity   generate   more   uniformity  of  beliefs  and  preferences.  (Ex:  a  common  language   that  evolves  from  geographical  proximity)  

 

3. Degree   of   heterogeneity:   which   itself   do   explicit   policy   decisions  influence.              

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Majority  voting:    

Apart   from   the   fact   of   tradeoff   between   heterogeneity   and   size,   the   formation  of  democratic  institutions  within  countries  of  borders  can  also  be   decided   by   majority   voting.   The   formation   is   also   defined   between   the   evolution  of  optimal  country  size  and  the  country  that  results  from  majority   vote   on   its   borders.   Basically   in   an   one   person   vote,   everyone   equally   contributes  to  the  decision  on  borders  however  in  that  case  individual  will   have  the  authority  to  vote  to  break  up  of  a  country  just  because  they  were   not  experiencing  the  benefits  of  public  goods  as  much  as  closer  regions  in   preference   to   government   policy   making.   While   in   majority   voting   it   is   everyone’s   mutual   duty   to   compensate   the   distant   region   with   favorable   interests  through  fiscal  policy  in  order  to  avoid  inefficient  secessions.  

 

Trade  regime    

The  size  of  the  market  (or  the  border)  for  any  country  also  depends  on  the   trade  regime  and  on  the  state  of  its  international  economic  relations.  

 

• When   all   borders   are   close   each   country’s   market   is   determined   equivalent  to  its  size⟹  two  extremes:  

 

1. (All   country)   without   international   trade   ⟹ size   of   the   market  economy ↑  large  country  advantage  

 

2. (All  country)  open  to  trade  in  goods⟹small  and  large  countries   compete  in  the  same  market  through  factors  of  production  and   financial  instruments.  

   

1.2.Determinant  of  Size  of  countries    

This  subsection  of  chapter  one  describes  the  trade-­‐off  of  economies  of  scale   and   scale   trade-­‐off   of   political   and   market   size   as   the   determinants   of   country  size  (namely-­‐economic  integration).    

           

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Trade-­‐off  of  economies  of  scale    

If   there   are   economies   of   scale   to   the   size   of   the   market,   larger   countries   can   be   expected   to   do   better   economically   than   smaller   countries   (considering   all   other   things   being   equal   such   as   natural   resources,   geographical   size,   population   etc).   Political   size   becomes   less   relevant   as   economic   integration   increases,   because   it   reduces   the   limit   of   certain   country.   In   other   words,   the   “stable”   size   of   country   reduces   economic   integration.  If  we  see  the  evidence,  it  is  clear  that  even  in  world  of  free  trade   national  borders  do  not  turn  into  inappropriate.  The  evidence  on  Canadian   and  U.S.  trade  is  striking.  In  spite  of  distance  being  strong  determinant  of   trade   flows,   U.S.   states   and   Canadian   provinces   trade   much   less   than   two   distant   Canadian   provinces.   Which   enlightens   the   fact   that   free   trade   just   makes  borders  more  fact  that  free  trade  just  makes  borders  more  open  in   return  of  huge  cost  in  terms  of  trade  flows  cost  in  terms  of  trade  flows.  The   bottom  line  is  that  small  countries  can  prosper  as  long  as  they  are  open  to   international   trade.   Conversely,   small   countries   are   more   open   towards   free   world   trade   regime.   The   empirical   evidence   gathered   by   Alesina,   Spolaore,  and  Wacziarg  (2000)  is  consistent  with  implications.    

   

The  substitution  effect  of  public  and  private  goods    

The  historical  process  of  the  last  century  toward  smaller  size  nations  may   be   a   consequence   of   the   increased   substitutability   between   private   and   public   goods.   One   may   view   publicly   provided   private   goods,   as   close   substitutes   with   private   goods   while   pure   public   goods   are   less   substitutable  with  private  goods.  It  is  a  well  known  fact  that  the  diffusion  of   Communism  around  the  world  since  the  first  half  of  the  twentieth  century   and   the   diffusion   of   the   welfare   state   in   western   countries   in   the   second   half   of   the   twentieth   century   have   extended   government   activity   toward   publicly   provided   private   goods   as   education,   health   and   social   security.   Since  scale  economies  are  much  less  powerful  and  heterogeneity  of  views  is   more  accurate  for  these  kinds  of  activities  a  tendency  toward  a  decreasing   size   of   nations   emerged   during   the   twentieth   century.   The   other   crucial   factor   in   the   secular   decline   of   the   size   of   nations   is   the   increase   in   openness.  Openness  plays  a  very  crucial  role  in  determining  both  the  size   and  growth  of  countries.    

 

   

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Scale  tradeoff  of  political  and  market  size    

Basically  a  country’s  market  size  coincides  with  its  domestic  size  only  if  the   country’s   economy   is   perfectly   integrated   domestically   but   completely   closed   to   the   rest   of   the   world.   In   short   in   a   world   of   complete   autarky,   political  size  and  market  size  of  a  country  coincide.  That  is  a  world  without   any   economic   relationships   among   the   countries   has   a   small   market   and   thus  low  demand  for  output  and  low  production.  It  follows  that  if  a  country   is   small   it   has   a   small   market.   But   we   have   to   keep   in   mind   that   what   matters   is   the   total   income   not   the   population   size.   Whereas   there   exists   also  economically  integrated  world,  where  the  market  size  of  a  country  is   larger  than  its  political  size.  In  this  economically  integrated  world  borders   are  totally  irrelevant  for  economic  interactions,  the  market  size  defines  the   world,   where   free   trade,   political   borders   are   irrelevant.   But   true   fact   is   that,   people   have   contrived   ways   to   deprive   themselves   and   one   another;   and  prefer  agglomerated  animosities  to  singular  happiness.  

 

Market   size=political   size   has   the   following   intuitions   in   different   situations:  

 

• Autarkic   world:   small   country ⇒ smaller   market ⇒ low   demand ⇒ low production   (from   the   point   of   view   of   market   size  where  income  matters  not  population)  

 

• Economically   integrated   world:   larger   market   size   than   its   political   size.   (A   country’s   economic   prosperity   completely   depends   on   its   economic  integration  with  rest  of  the  world)  

 

• Extreme  case:  the  market  size  of  the  country  is  whole  world  (borders   are  completely  irrelevant)  

 

• Free  trade  world:  political  borders  are  irrelevant.    

After   discussing   the   formal   reason   of   economic   integration   (1.2)   and   political  disintegration  (1.1)  we  can  summarize  our  findings  as  follows:   Two  configurations  of  trade  and  size  are;  

 

1. Large   and   closed   economy ⇒ little   interest   in   promoting   trade   liberalization  (free  trade)  

 

2. Small  countries  promote  free  trade    

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Both   democratization   and   opening   of   international   trade   accompany   political   separatism   and   the   breakups   of   large   countries.   According   to   functional  theory:  

↑Economic  integration  ⇒↑in  political  integration  (both  regional  and  global   levels)  

     

1.3.The  benefits  of  size  

 

This  section  of  chapter  one  emphasizes  the  benefits  of  size.  According  to  AS   the  benefits  of  size  are  the  followings:  

 

1. The   first   motivation   is   the   importance   of   Economies   of   scale   in   running  the  public  sector.    

 

2. The   second   one   is   defense   against   foreign   aggression.   If   we   neglect   the  term  peaceful  world,  than  it  is  notable  that  the  larger  the  country   the   more   valuable   it   is.   In   fact,   being   large   is   especially   valuable   if   much  has  to  be  spent  on  defense  and  economies  of  scale.  Obviously   small   county   size   has   coincided   with   an   explosion   of   political  

separatism.   In   short,   Political   borders   and   political   size   are   very  

important  for  the  growth  of  a  country  as  they  are  incorporated  with   obstacles  to  economic  exchange  and  political  barriers  to  trade.  

 

3. The   size   of   a   country   affects   the   size   of   its   economy.   So   larger   countries   have   larger   markets   hence   larger   economy   and   smaller   countries   have   the   smallest   economy.   Which   effects   in   the   productivity   of   the   countries,   the   number   of   individuals   and   the   amount  of  spending  in  an  economy  depends  on  the  trade  openness  of   a   country.   An   economically   integrated   country   has   the   whole   world   as  its  market,  which  reflects  in  its  economic  success.  So,  the  economic   benefits  of  size  depend  on  the  openness  of  country.  

 

4. Large   countries   have   the   redistribution   scheme   advantage,   which   allows   them   to   redistribute   schemes   from   richer   to   poorer   individuals   and   regions,   thereby   achieving   distributions   of   after-­‐tax   income   that   wouldn’t   have   been   possible   in   independent   economy   acting  at  its  own.  

 

5. And  the  last  one  deals  with  the  creation  of  a  common  market,      

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1.4.The  cost  of  size      

If   there   were   only   benefits   from   size,   then   the   whole   world   should   have   been  organized  in  a  single  country.    Well  here  comes  the  cost  of  size.  

 

In   principal,   larger   countries   entails   administrative   and   congestion   costs   which  offsets  the  benefits  of  size  pointed  in  the  previous  section.  But  these   costs   are   not   same   for   all   large   countries.   Actually   larger   countries   have   diverse   preferences,   cultures   and   languages   within   the   population.   A   country’s   heterogeneity   of   preference   increases   as   it   becomes   larger   because   more   people   gets   added   to   the   country   and   more   people   means   more  preference.  Basically,  belonging  to  a  country  implies  agreeing  to  a  set   of   policies   and   these   policies   could   be   any   kind   of   redistributive   scheme,   public   goods   or   foreign   trade.   Heterogeneity   implies   every   individual   of   that   specific   country   comes   to   an   agreement   on   these   matters.   Of   course   certain   policies   can   be   delegated   to   localities,   in   order   to   allow   local   preference   but   the   same   does   not   work   for   every   policy.   Because   with   increased  heterogeneity  their  increases  number  of  individuals  who  are  less   satisfied  by  the  central  government  policies.  Indeed,  many  violent  domestic   conflicts  around  the  world  are  associated  with  this  type  of  racial,  religious,   and  linguistic  heterogeneity,  which  have  literally  threatened  the  stability  of   national   governments.   Apparently,   in   a   large   republic   the   common   good   gets  sacrificed  to  a  thousand  of  considerations  while  in  a  small  republic  the   presence   of   public   good   is   more   recognized,   better   known   and   are   more   closer  to  each  citizen.  

   

Summary    

In  summary,  at  one  extreme,  market  size  coincides  with  political  size  in  an   autarky   world   whereas   at   other   extreme   political   size   is   smaller   than   the   market  size  in  a  world  of  free  trade.  In  general,  the  viable  size  of  country   decreases  with  international  openness  because  country’s  market  is  defined  

by   its   domestic   market   and   foreign   market4.   In   presence   of   economies   of  

scale   to   the   size   of   market,   larger   countries   can   be   expected   to   do   better   economically   than   smaller   countries   (all   other   things   being   equal)   when  

international  openness  is  low  and  vice  versa.    

 

                                                                                                                       

                                                                                                               

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                                                                                                                       Chapter  2  

   

Theoretical  presentation  of  the  models    

The   theories   of   this   chapter   linking   country   size,   international   trade   and   economic   growth   is   built   upon   AS,   Alesina,   spolaore   and   Wacziarg(2000)   and  Spolaore  and  Wacziarg(2005).  

 

2.1.  Alesina,  spolaore  and  Wacziarg  (2000):  Basic  static  model    

Alesina,Spolaore  and  Wacziarg  constructed  a  simple  static  model  of  a  world   economy  with  a  large  number  N  of  identical  countries  and  a  continuum  [0,   1]   agents   and   N   “economic   units”   which   are   basic   entities(countries)   carrying   out   economic   activities.   Each   country   produces   differentiated   goods,  and  countries  are  specialized  in  different  varieties.  Consumers  enjoy   utility  from  the  consumption  of  differentiated  goods  and  a  country-­‐specific   public  good.  Governments  set  policies  unilaterally  so  as  to  maximize  utility   of  domestic  citizens.    

 

2.1.1.  Production  and  trade    

If   we   consider   the   following   utility   function,   where   the   world   population   N=1,  and  each  population  is  living  at  location  i  ϵ 0,1 :  

       U  (  c!")=   !!"!!! !!! ! !  e!!!dt…  ………(1)    

Where  c!"  denotes   the   consumption   at   time   t,   with  σ > 0  and  ρ > 0,  K!(t)  

and  L!(t)  denotes  aggregate  capital  and  labor  at  location  i.  And  both  inputs  

are   elastically   supplied   and   are   not   mobile.   At   each   location   i   a   specific  

intermediate   input  X!(t)  is   produced   using   the   location-­‐specific   capital  

according  to  the  linear  production  function    

     X!(t)  =  K!(t)………(2)    

If   each   location   i   produces   Y! t units  of  the  same  final  good  Y  (t) ,   then  

according  to  the  production  function  we  can  write;    

     Y! t = !!X!"! t dj L!!!! (t)………..  (3)    

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Assuming,  0<α < 1, X!" t denotes  the  amount  of  intermediate  input   j  used   in  location  i  at  time  t.    

 

Intermediate   inputs   can   be   traded   across   different   locations   in   perfectly   competitive   markets   by   profit-­‐maximizing   firms   without   any   cost   (assuming  open  economy).  Conversely  if  one  unit  of  intermediate  good  i’  is   shipped  to  a  location  i’’  of  a  different  country  then  (1-­‐  β)  units  of  the  good  i   will   arrive   due   to   the   extensive   political   borders   that   entail   trading   cost.   (Assuming  0≤β≤1)  This  trading  costs  varies  as  following:  

 

1)  Open  economy,  where  intermediate  goods  can  be  traded  across  locations   without  inducing  any  cost.  

 

2)   Closed   economy,   the   transfer   of   intermediate   goods   across   different   location  incurs  cost.  

 

If  we  consider,      

D!(t)=The   intermediate   inputs   produced   in   either   at   location   i   or   another  

location  that  belongs  to  the  same  country  as  location  i.    

F!(t)=  The  units  of  input  i  shipped  to  a  location  that  doesn’t  belong  to  the  

same  country  as  location  i.    

Then  due  to  the  border  cost  assumption,  only  (1-­‐  β)  F!(t)  units  will  be  used  

for  production5.  Therefore,  

 

     Pi t =αDiα-­‐1 t =α(1-­‐β)    α  F

iα-­‐1(t)…………(4)  

   

Where  P! t  is   the   market   price   of   input   i   at   time   t.   at   each   time   t   the   resource  constraint  for  each  input  i  is  given  by,  

   

siDi(t)+ W-­‐si Fi(t)=Ki(t)  

   

Where,  si  denotes  size  of  country  at  location  i  that  it  belongs  to;    

                                                                                                               

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The   intuition   of   these   equation   states   that   barriers   to   trade   increases   the   domestic   use   of   the   intermediate   output   to   discourage   foreign   trade.   For   the  simplicity  of  analysis  we  will  assume  uniform  barriers  to  trade  across   countries.    

 

Let’s   now   introduce   openness  "ω"  to   our   model,   Assuming   0<  ω < 1,  and   the  lower  the  barriers  to  trade  the  higher  is  the  openness,  we  can  define  it   as  following;  

 

     ω ≡ (1 − β)!!!! ………….  (4)  

   

• ω = 1  when  there  are  no  barriers  to  trade β = 0 -­‐Open  economy    

• ω = 0  when  there  are  barriers  to  trade, complete  autarchy β = 1 − closed  economy  

 

Thus  our  domestic  D! t and  foreign  F! t  inputs  simplifies  as  follows:  

    Di t = Ki t ω+(1-­‐ω)si                                                                                        And        Fi t

=

Ki t ω+(1-­‐ω)si        

2.1.2.  Capital  accumulation  and  growth  

 

Lets   now   assume,   in   each   location   i,   consumers   net   household   assets   are  

identical   to   the   stock   of   capital  K!(t).   Since   each   unit   of   capital   yields   one  

unit   of   intermediate   input  X!(t),   the   net   return   to   capital   is   equal   to   the  

market  price  P!".            

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From  intertemporal  optimization6  we  get,          dCdtit  C1 it  =  Pi t -­‐ρ                  = α   ω+(1-­‐ω)si 1-­‐α K i α-­‐1 t -­‐ρ      

The   Solow’s   model   steady   state   level   of   capital   at   each   location   i   of   a  

country  size  S!, will  be;  

      Kiss=K i ss 1-­‐ρ +  α ω+(1-­‐ω)s i 1-­‐α Kiss(α-­‐1)      

     ⇒

Kiss= α ρ α 1-­‐α ω+(1-­‐ω)si ………  (5)        

2.1.3.  Steady  state  income/output:    

 

.  With  N  number  of  identical  countries  of  size  s:    

The  steady-­‐state  level  of  output  in  each  unit  of  a  country  size  𝑠!  is  given  by;  

    Y!!! = s!(D!!!)!+ s !(1 − β)!(F!!!)! !!!    

by   substituting   D!!!   and   Fiss  into   the   equation   above,   we   obtain   the  

following;        Y!!! = α ρ α 1-­‐α ω+(1-­‐ω)si … … … (6)                                                                                                                     6  ct ct= πt-­‐ρ γ(ct),  γ(ct)= -­‐u''c c

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PROPOSITION  1  :  By  far,  we  can  say  that  steady-­‐state  output  per  capita  is   increasing  in  openness  and  size,  which  means  they  both  have  positive  effect   in  economic  growth  of  a  country.  But  openness  is  less  important  for  large   countries.  Which  summarizes  as  follows:  

   

• The   smaller   the   effect   of   country   size   s!  is,   the   larger   is  

the  openness  ω      

 

Apparently,   the   growth   rate   of   output   around   the   steady   state   can   be   approximated  by;  

dY

dt .

1

Y=ξe-­‐ξ(lnYss-­‐lnY 0 )  

    Where,  ξ = ! ! 1+ 4 1-­‐α α 1 2

-­‐1  And  Y  (0)  is  initial  income7  

   

PROPOSITION   2:   Around   the   steady   sate,   the   growth   rate   of   income   per   capita  increases  in  size  and  openness  and  decreases  in  size  time’s  openness.   These  results,  how  ever  are  the  evidence  of  the  fact  that,  economic  benefits   from   size   decreases   in   openness   and   economic   benefits   from   openness   decreases  in  size.    

 

     

2.2.  Equilibrium  analysis    

 

2.2.1.Equilibrium  analysis  part  1,  AS  

 

Based  on  the  same  normalization  assumption,  lets  consider  the  world  has   at  least  one  government,  thus  N≥ 1,  N  denoting  number  of  countries  in  the   world.  And  to  avoid  complexity  a  country’s  government  cost  is  assumed  to   be  k,  regardless  of  the  size  of  the  country.  If  every  individual  has  the  same  

                                                                                                               

7The  derivation  of  this  result  can  be  found  in  appendix  2B,  Barro  and  Sala-­‐i-­‐Martin  (1995,   Chapter  2)  

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exogenous   income   y   and   pays   taxes  ti = ks,  (where   i   stand   for   individual   identity)  than  the  utility  of  individual  “i”  is:  

 

U! = g − al!+ y −k

s    

 

Where   “g”   and   “a”   are   two   positive   parameters   and  li  is   the   distance   from  

individual  i  to  his/her  government.  The  utility  function  is  linear  to  private   consumption.    

g=  measures  the  maximum  utility  of  the  public  good  at  l!=0.  

a=   measures   the   loss   in   utility   due   to   the   distance   of   his/her   preferred   government.  

 

Based  on  the  above  assumptions,  the  social  planner  maximizing  the  sum  of  

individual  utilities  would  choose  the  number  of  countries  N∗;  

 

N∗ = a

4k  

 

If   public   good   is   located   in   the   middle   of   each   country   and   if   each   citizen   pays   same   taxes   in   its   own   country   and   enjoys   the   benefits   from   public  

spending  according  to  his  or  her  distance  from  the  public  good  than  s*=!!  

is  the  size  of  each  country.  Hence  the  utility  in  steady  state  for  an  individual   living  at  location  i  become:  

         ui=g-­‐ali+ α ρ α 1-­‐α ω+(1-­‐ω)si -­‐k s……(7)        

Therefore,   the   number   of   equally   sized   countries   that   maximizes   average   utility  is;     dW ds * =-­‐a 4+ α ρ α 1-­‐α (1-­‐ω)-­‐s2k=0    

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⇒N*= a-­‐4(1-­‐ω) α ρ α 1-­‐α 4k ……  (8)    

And  the  equilibrium  size8  of  countries:  

 

     s∗ = !

!∗  ………  (9)  

 

Optimizing  the  welfare  on  openness  gives  us  the  following:     dW dω = α ρ α 1-­‐α (1 − s)    

We  can  summarize  the  findings  of  this  theory  as  following:  

This   theory   explained   the   relationship   of   country   size,   openness,   and   income  per  capita  through  a  model  that  benefits  of  country  size  decrease  by   an  increasing  economic  integration  between  different  political  borders.  But   this   benefits   gets   bigger   by   the   increasing   trade   openness   and   economic   integration   in   smaller   countries.   The   theory   also   argued   a   positive   relationship  between  economic  and  political  integration.  It  proved  that  as   the  economy  becomes  more  integrated,  scale  effect  of  large  country  starts   to   vanish   due   to   the   shift   of   increasing   trade-­‐off   between   size   and   heterogeneity   of   smaller   countries.   So   overall   summary   of   this   theory   reflects   the   fact   of   two   possible   worlds;   one   world   of   large   and   relatively   closed  economies,  and  another  of  many  smaller  and  open  economies.  

   

2.2.2.Equilibrium  analysis  part  2,  ETRO  

 

After   the   basic   theoretical   part   of   AS,   let’s   begin   by   finding   the   social   planner   equilibrium   solution   in   an   integrated   economy   as   stated   by   Etro,   where   the   number   and   sizes   of   countries   and   location   of   the   public   good   can  be  individually  chosen.  Assuming  that  the  social  planner  maximizes  the   sum  of  individual  utilities,  the  social  planner  problem  is:  

 

     Max   U01 idi  s. t. 01tidi=Nk…….….(9)  

 

                                                                                                               

(22)

Where,  a  social  planner  maximizing  the  sum  of  individual  utilities  locate  the   government  in  the  middle  of  each  country,  chose  N*  countries  of  equal  size,   such  that;  In  the  world  there  are  many  countries  each  one  with  a  “capital   city”  set  in  the  middle  of  the  country.  So  utility  for  agent  i  in  country  j  have   the  following  functional  form:  

 

     Uij=u CjijH gj ,    given    αij=λ-­‐ali    

Here  H  (g!)  =  utility  from  public  spending  g!  in  country  j  and  

 

     u(Cj)=   utility   from   private   consumption,   which   is   income   net   of  

effective  taxation,      

     αij  =  Heterogeneity  cost  across  citizens  in  a  way  discussed  below.  

 

Any  assumption  on  the  utility  from  public  goods  is  not  necessary  as  we  are   going  to  focus  on  the  necessary  taxation  of  each  agent  to  finance  the  latter.   Since  this  part  is  going  to  endogenize  public  spending,  we  need  to  be  more   precise.  Although  the  following  results  will  also  hold  within  a  general  well-­‐ behaved  utility  function,  but  for  the  sake  of  closed  form  solutions,  we  will   focus  on  linear  utility  from  consumption  and  iso-­‐elastic  utility  from  public   spending.  Finally,  some  assumptions  on  technology  of  production  of  public  

goods  and  on  the  distortions  induced  by  the  corresponding  individual  tax  t!  

in   country   j   are   needed.   Later   on   we   will   follow,   David.   Ricardo’s   growth   model   of   diminishing   marginal   returns   in   the   production   process   and   a   distortion   of   taxes   that   is   increasing   and   convex   in   the   taxation   level.   For   simplicity  issue,  in  our  model  we  will  be  summarizing  both  these  elements   with  a  convex  cost  function  of  taxation,  and  in  particular  a  quadratic  one.     In  conclusion,  utility  is  the  following:  

         Uij=gj 1-­‐Θ 1-­‐Θ λ-­‐alij +yj-­‐ tj2 2 ……….  (10)        

Θ∈ 0,1 =the  elasticity  of  marginal  utility  of  public  expenditure9  

                                                                                                               

9  The  lower  it  is,  the  more  substitutable  are  public  and  private  consumption.  If  publicly  provided   goods  belong  to  a  wide  range  which  starts  with  purely  private  goods  (drugs  or  school’s  books)   and  arrives  to  purely  public  goods  (defense),  the  former  typology  corresponds  to  goods  with  

(23)

Here,  lij=distance  from  the  public  good10  

 

     a=  cost  of  heterogeneity  and    λ=utility  provided  by  the  public  good11    

In  this  section,  the  tax  independent  output  yj=  y  is  assumed  constant  across  

countries.   Let   us   define   the   size   of   country   j   as  s!  and   the   per   capita  

provision  of  public  goods  as  given  by  the  revenue  constraint.         Summary      

From  the  model  suggested  by  Etro  it  is  clear  that,  there  are  some  specific   assumptions   on   the   technology   of   production   of   public   goods.   The   increasing  cost  function  of  taxation  causes  diminishing  marginal  returns  in   the  production  process  of  pubic  goods,  which  is  by  the  way  useful  because   of  the  tractability  of  the  first  order  conditions.  Whereas  AS’s  model  didn’t   made  any  assumption  on  technology  of  production  of  public  goods  because   their  utility  from  the  exogenous  public  spending  is  a  given  parameter  g,  and   the  costs  of  taxation  is  exogenous  parameter.  

 

Table  2.1  

Comparison  between  the  utility  function  of  endogenous  and  exogenous  government   spending  models  

 

  AS  (exogenous  

government  spending)   Etro  (endogenous  government  spending)  

Utility   from   public  

spending   g   g! !!! 1 − Θ   Heterogeniety   of   preferences   −al!"   λ − al!"   Costs  of  taxation/public  

good  

/   t!!

2  

                                                                                                                                                                                                                                                                                                                                                          perfect  substitutability  with  the  private  goods  and  the  latter  one  with  those  that  are  less  

substitutable  for  the  private  goods  

10    l

!"=!!if  the  good  is  situated  at  the  capital;   It   is   typically   recognized   that   regions   far   away   from  the  capital  of  a  country  are  the  most  likely  to  have  at  least  different  preferences  from  the   regions  close  to  the  capital,  and  at  most  a  separatist  tendency  (the  experience  of  many  European   countries  is  quite  clear  in  this  direction).  

   

(24)

 

Equilibrium  welfare  

 

Here   we   define   the   optimal   organization   of   the   worlds   as   the   equilibrium   welfare;  as  we  have  assumed  uniform  distribution  of  citizens,  the  optimal   equilibrium   would   contain   countries   of   equal   size   s   and   the   public   good   would   be   situated   at   the   center   of   each   country.   So,   the   optimal   welfare   choosing   the   size   of   nations   and   the   provision   of   national   public   goods   would  be  as  following;    

    W = gj 1-­‐Θ 1-­‐Θ   λ-­‐alij  +y  -­‐   tj2 2 di    s.t.    tjs=gj 1 0          =  gj1-­‐Θ 1-­‐Θ   λ-­‐ ! !s  -­‐ 1 2  ( ! !) 2+y    

Applying  AS  optimal  size  of  the  nation  rule,  that  is  maximizing  welfare  w.r.t   s,  we  obtain  the  following;  

    dW ds =    -­‐a   g1-­‐Θ 4 1-­‐Θ + g2 s3=0     ⟹s*=  g1+Θ3 4(1-­‐Θ) a 3   Comparitive  statics:      

• The  ↑ g ⇒ s∗ ↑  for  exploiting  economies  of  scale  and  ↑ a ⇒ s∗ ↓  

 

• The  optimal  size  of  a  given  amount  of  public  good  remains  unaffected   by  the  absolute  utility  from  the  public  good.  

 

We   get   our   very   first   relationship   between   optimal   size   and   optimal   per   capita  provision  of  public  goods  from  this  optimality  condition;  

t=g/s    

   

(25)

s  =  g1+Θ3 4 1-­‐Θ a 3          ⇒ s s1+Θ3  =  g 1+Θ 3 s1+Θ3 .   4 1-­‐Θ a 3         ⇒ t*=  s1+Θ2-­‐Θ  . a 4 1-­‐Θ 1 1+Θ =ψ*(s)      

PROPOSITION   1:   Optimal   size   of   nations   is   an   increasing   and   concave   function  of  the  provision  of  public  good  (government  consumption).  

   

Equilibrium  government  spending  and  public  spending  provision  

 

Now   if   we   consider   a   modified   samuelson   rule   for   optimal   public   good   provision   t,   (Samuelson,   1955)   than   the   function   of   size   of   countries   satisfying  the  first  order  condition  becomes;  

    dW dg =g-­‐Θ λ-­‐ a 4s -­‐ g s2     ⇒  g1+Θ  =  s2 λ-­‐a 4s          ⇒g*=  s1+Θ2 .   λ-­‐a 4s 1 1+Θ        

The  optimal  provision  g∗  is  an  inverted  function  of  s.  

So,  the  second  relationship  between  g∗  and  scan  be  written  as  following;  

Given,    

   

(26)

     g*=  s1+Θ2 .   λ-­‐a 4s 1 1+Θ          ⇒g * s* =  s1+Θ2 s .   λ-­‐ a 4s 1 1+Θ          ⇒ t*=  s1+Θ1-­‐Θ.   λ-­‐a 4s 1 1+Θ*(s)       Comparative  statics:        

• The   cost   of   benefitting   from   the   public   spending12  is   higher   if   there  

exists  less  taxation  hence  less  public  spending  in  the  economy.      

• 𝑡∗  is  first  increasing  in  s  and  then  decreasing, with  a  peak  !!! !!!!!! .  

 

Henceforth  it  is  clear  that,  tradeoff  between  heterogeneity  costs  and  scale   of  economies  both  increase  in  the  size  of  a  country.  And  given  intermediate   size  of  country,  the  net  benefit  from  public  good  provision  is  the  higher  at   the  costs  of  heterogeneity.  

   

PROPOSITION   2:   The   optimal   per   capita   provision   of   public   good   is   non-­‐ monotonic   function   of   size,   which   means   that,   large   and   small   countries   should   impose   lower   taxes   and   countries   of   intermediate   size   should   impose  higher  taxes.    

   

                                                                                                                 

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