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The Economics of Horizontal 
 Government Cooperation
                     Matt DalSanto
   Berkeley Center for Law, Business and the Economy

             Law and Economics Workshop
                    April 11, 2011
Outline of Today’s Presentation
• Introduction
    – Brief History
    – Overview of Enacted Compacts
•   Relevant Case Law
•   Policy Commitment
•   Negative Externality
•   Positive Externality
•   Intrastate Analog: Joint Powers Agreements
•   Policy Conclusions
•   Further Research
•   Questions/Comments
What is an Interstate Compact?

• Interstate Compact – An interstate compact is 
  an agreement in which states commit 
  themselves to a legally binding (contractual) 
  agreement.
History
• Use predates the American Revolution
  – Colonies had poorly defined borders
  – Boundary Disputes Settled in One of Two Ways
     • Joint Commission would attempt to negotiate a 
       settlement
        – If successful, submit to Crown for approval
     • If unsuccessful, then appealed to Crown in process 
       similar to litigation
History
• Articles of Confederation (Article VI, Section 2)
   – “No two or more States shall enter into any treaty, 
     confederation or alliance whatever between them, 
     without the consent of the United States in Congress 
     assembled, specifying accurately the purposes for 
     which the same is to be entered into, and how long it 
     shall continue.”
      • Mere agreements between states
         – Congressional Consent not typically required
      • Consent required 
         – if the general authority of Congress would be “weaken[ed]” or 
           “encroach[ed] upon.”
History
• US Constitution
  – “[n]o State shall enter into any Treaty, Alliance, or 
    Confederation....”

  – Compact Clause  (Art. I, Sect. 10, Cl. 3)
     • “No State shall, without the Consent of Congress, ... , 
       enter into any Agreement or Compact with another 
       State, or with a foreign Power....”
History
• Articles of Confederation v. US Constitution
   – “Treaty, Alliance, or Confederation”
      • Permitted with Congressional Consent under Articles
      • Prohibited under Constitution
   – “Compact” or “Agreement”
      • Permitted with Congressional Consent under Constitution
   – Attempting to Avoid Problems Under Articles
      • No real distinction
      • Preserve economic and political power of federal government
          – “In other cases the Fedl authy was violated by Treaties & wars .... By 
            compacts witht. the consent of Congress as between Pena. and N. Jersey, 
            and between Virga. & Maryd. From the Legisl: Journals of Virga. it 
            appears, that a vote to apply for a sanction of Congs. Was followed by a 
            vote agst. a communication of the Compact to Congs.”
               » Personal journal entry by James Madison at Convention.
History
• 1783 to 1920
  – 36 compacts


• 1920 to present
  – over 150 compacts
Compact Statistics
Mean = 29.4 Compacts/State, Max = 54 (VA), Min = 16 (HI)
Types of Interstate Compacts
Types of Interstate Compacts
•   AGRICULTURE (2)
•   BOUNDARY COMPACTS (26)
•   BRIDGES, NAVIGATION, AND PORT AUTHORITIES (13)
•   BUILDING CONSTRUCTION AND SAFETY (1)
•   CHILD WELFARE (3)
•   CONSERVATION AND ENVIRONMENT (24)
•   CORRECTIONS AND CRIME CONTROL (17)
•   EDUCATION (8)
•   ENERGY (16)
•   GAMBLING AND LOTTERIES (3)
•   HEALTH (4)
•   INSURANCE (1)
•   MOTOR VEHICLES (15)
•   PARKS AND RECREATION (4)
•   PEST CONTROL (1)
•   PLANNING AND DEVELOPMENT (10)
•   PROPERTY (2)
•   PUBLIC SAFETY (11)
•   TAXATION (2)
•   TRANSPORTATION (12)
•   WATER (37)
Interstate Compacts Case Law

• Two Legal Mechanisms to Resolve Interstate Disputes
    – Interstate Compact
    – Supreme Court
        • “[t]he judicial power [of the Supreme Court] shall extend to ...controversies 
          between two or more states...” Art. III, Sect. 2, Cl. 1


• “We cannot withhold the suggestion, inspired by the consideration
  of this case, that [this] grave problem ... is one more likely to be 
  wisely solved by co‐operative study and by conference and mutual 
  concession on the part of representatives of the states so vitally 
  interested in it than by proceedings in any court however 
  constituted.”
    – People of State of New York v. State of New Jersey, 256 U.S. 296, 313 
      (1921).
Interstate Compacts Case Law

• Compact Ratification and Cong. Consent
  – All state legislatures must pass identical implementing 
    legislation, governor signs into law
  – Congressional Consent
     • “[n]o State shall, without the Consent of Congress,..., enter 
       into any Agreement or Compact with another State...” Art. 
       I, Sect. 10, Cl. 1
     • Com. of Va. v. State of Tenn., 148 U.S. 503, 519 (1893),
         – Congressional consent for a compact is necessary: when the 
           compact’s enactment would “[tend] to the increase of political 
           power in the states, which may encroach upon or interfere with 
           the just supremacy of the United States.”
Compacts that Create Admin Agencies


• State ex rel. Dyer v. Sims, 341 U.S. 22 (1951)
  – Upheld legality of the relatively recent inception 
    of states entering into a compact that delegates 
    administrative authority to an interstate agency.
Compacts As Contracts

• “[A] Compact is, after all, a contract.”
   – Texas v. New Mexico, 482 U.S. 124, 128 (1987) (quoting Petty v. 
     Tennessee‐Missouri Bridge Comm’n, 359 U.S. 275, 285 (1959) 
     (Frankfurter, J., dissenting))

• “It remains a legal document that must be construed and 
  applied in accordance with its terms.”
   – Texas v. New Mexico, 482 U.S. 124, 128 (1987).

• Offer & Acceptance 
   – All signatory states adopt the exact language of the compact 
     agreement as a statute.
Breach of Compact
• Supreme Court sometimes analogizes a compact to a treaty 
  between sovereign nations, but....

• Signatory states are held to their compactual obligations
   – Old Legal Theory: “a State has no more power to impair an obligation 
     into which she herself has entered, than she can the contracts of 
     individuals....”
       • Green v. Biddle, 21 U.S. 1, 39 (1823).

   – New Legal Theory: “[W]here Congress has authorized the States to 
     enter into a cooperative agreement, and where the subject matter of 
     that agreement is an appropriate subject for congressional legislation, 
     the consent of Congress transforms the States’ agreement into federal 
     law under the Compact Clause.”
       • Cuyler v. Adams, 449 U.S. 433, 440 (1981).
Remedies for Breach of Compact
• Prospective Relief & Damages
   – “We find no merit in its submission that we may order only 
     prospective relief, that is, requiring future performance of 
     compact obligations without a remedy for past breaches. 
     If that were the case, New Mexico's defaults could never 
     be remedied.”
      • Texas v. New Mexico,  482 U.S. 124, 128 (1987).


• Damage Measure
   – Presumably Expectation Damages
      • A monetary amount that would put the breached against states in 
        as good of a position as they would have been had the breach not
        occurred.
Policy Commitment
• Tying Hands of Future Legislatures

• IC for Mississippi River Flood Plain Control
  – The Great Flood of 1993
     • $20 billion
     • 50,000 homes either destroyed or severely damaged
Negative Externality: Great Lakes
• Legislators only represent interests of state’s 
  citizenry not those of other states.
  – Do not internalize costs to other states.
• Lake Michigan (late 19th Century)
  – Chicago residents ill from dumping sewage into 
    Chicago River which flowed into Lake.
     • Chicagoans drank from the Lake
Negative Externality: Great Lakes
Repeated Prisoners’ Dilemma
• States repeatedly make decisions that affect 
  other states year after year.
  – Play a period Prisoner’s Dilemma game.
• No foreseeable end in sight.
  – Repeated
  – Assume states want to maximize their payoffs 
    today plus the net discounted value of future 
    payoffs.
Repeated Prisoners’ Dilemma
• In this environment cooperation can arise 
  endogenously.
  – But incentives to cooperate and incentives to 
    defect are both influenced by
     • The response to the defection by the other states
        – Are they punished?
     • The rate at which future payoffs are discounted
  – If discount rate too high, or if unable to commit to 
    punishing defecting state, then cooperation may 
    not be possible.
Repeated Prisoners’ Dilemma

• Solution
  – Interstate Compact
     • Compact requires cooperation
     • If defect, then liable to other states for expectation 
       damages award.
“Even before the Constitution we find that the 
common interest in natural resources, of a 
region embracing two States, was furthered 
by an agreement between such States. . . . An 
exploration of the possibilities of the compact 
idea furnishes a partial answer to one of the 
most intricate and comprehensive of all 
American problems.”
 – Frankfurter and Landis (1925).
The Great Lakes‐St. Lawrence River 
   Basin Water Resources Compact

• Requires the GL states to adhere to minimum 
  regulatory standards to which all signatory 
  states have agreed.

• No new transfers of water outside of GL Basin.
Compact Solution

• Problem
  – State may want to breach even though know 
    forced into compliance in the future.
    • Secondary Problem
       – Is efficient breach possible?  Should it be?
    • Solution
       – Let states determine how to calculate damages in event of 
         breach.
       – Sophisticated government actors; not unsophisticated private 
         parties.
Pos. Externality: Productivity Spillovers

• Most studies agree that there is an increase in TFP 
  from an increase in public infrastructure (capital).
   – Bridges, Ports, Railroads, Highways, Airports, Public 
     Transit, etc.

• When a jurisdiction undertakes investment in such 
  capital, it cannot confine the investment’s effects to 
  just its jurisdiction.
   – Spillovers between jurisdictions
   – Too little capital investment
States

Group of states, P = {1, 2, . . . , P }, that experience increases in
TFP from other states’ investment in public capital.
State Environment

Each state

has a representative household
  −preferences over consumption: uj (·)
  −discounts next period utility at the same rate β
  −endowed with an amount of private capital kj,0

has a representative firm that rents capital from the household
and sells its output in a national market

government has a sales tax τc (equivalent to the lump-sum tax
instrument Tj,t)
Representative Household’s Problem for State j



                                        ∞
                       max                    β tuj (ch )
                                                      j,t
               (ch ,xh ,kj,t+1 ,lj,t )∞ t=0
                 j,t j,t
                         h       h
                                      t=0

s. to   (1 + τj )ptch + ptxh ≤ rj,tkj,t + wj,tlj,t + πj,t
                    j,t     j,t
                                      h         h

                  kj,t+1 ≤ (1 − δk )kj,t + xh
                    h                h
                                            j,t
                               h
                              lj,t ≤ lj
                     ch , xh , kj,t+1, lj,t ≥ 0
                      j,t j,t
                                 h      h

                               lj = 1
                             h
                            kj,0 given.
Representative Firm’s Problem for State j



                                                   f            f    f
                       max           πj,t ≡ ptyj,t − rj,tkj,t − wj,tlj,t
                   f     f    f
                  yj,t ,kj,t ,lj,t
                                     f                     f    f
          s. to                   yj,t = F j (hj,t, kj,t, lj,t)
                                          f    f       f
                                         yj,t, kj,t, lj,t ≥ 0

where hj,t =   P
               i=1 ωj,i hj,t.
State Governments Run Balanced Budgets




         ptij,t = τj ptcj,t
        hj,t+1 = (1 − δh)hj,t + ij,t.
Market Clearing



       f
      yj,t =          ch +
                       j,t         xh +
                                    j,t         ij,t
j∈P            j∈P           j∈P          j∈P
       f         h
      kj,t =   kj,t    ∀j ∈ P
       f        h
      lj,t =   lj,t   ∀j ∈ P.
Characterization of Equilibrium

Letting f j (h, k) = F j (h, k, 1) and given ((Ti,t)∞ )i∈P , each re-
                                                    t=0
gion’s, for j ∈ P, equilibrium allocation is characterized by
            j
           uc (cj,t)         j
            j            = fk (hj,t+1, kj,t+1) + (1 − δk )
         βuc (cj,t+1 )
                cj,t + xj,t + Tj,t = f j (hj,t, kj,t)
                   kj,t+1 = (1 − δk )kj,t + xj,t
                  hq,t+1 = (1 − δh)hq,t + Tq,t               ∀q ∈ P
                                 kj,0 given
                                 hj,0 given.
where hj,t =     P
                 i=1 ωj,i hj,t.
Non-Cooperative Equilibrium

State j’s Government’s Problem
Each government j ∈ P takes as given the investments of the
other P − 1 governments, ((Ti,t)∞ )i∈P−{j} and thus the value
                                   t=0
of their public capital stocks ((hi,t)∞ )i∈P−{j}. In each period
                                      t=0
t, state government j chooses its optimal value of public capital
in period t + 1, hj,t+1, so as to satisfy
                                              ∞
                          max                        β tuj (cj,t)
           (Tj,t ,hj,t+1 ,cj,t,xj,t ,kj,t+1 )∞ t=0
                                             t=0
            j
           uc (cj.t )        j
s. to       j            = fk (hj,t+1, kj,t+1) + (1 − δk )
         βuc (cj,t+1 )
                cj,t + xj,t + Tj,t = f j (hj,t, kj,t)
                    kj,t+1 = (1 − δk )kj,t + xj,t
hq,t+1 = (1 − δh)hq,t + Tq,t   ∀q ∈ P
                      cj,t, kj,t+1, xj,t ≥ 0
                           kj,0 given
                           Tq,t given          ∀q ∈ P − {j}
                           hq,0 given          ∀q ∈ P.
where hj,t =   P
               i=1 ωj,i hj,t.
Compact Equilibrium

Given the terms of the compact, U, the compact authority’s
problem is to choose taxes ((Tj,t)∞ )j∈S and thus
                                         t=0
                             ∞ )
((hj,t+1, cj,t, xj,t, kj,t+1)t=0 j∈S , so as to solve,



                                                              ∞
                            max                        U ((       β tuj (cj,t))j∈S )
          ((Tj,t ,hj,t+1 ,cj,t ,xj,t ,kj,t+1 )∞ )j∈S
                                              t=0         t=0
                     j
                    uc (cj.t )        j
  s. to             j            = fk (hj,t+1, kj,t+1) + (1 − δk )
                 βuc (cj,t+1 )
                         cj,t + xj,t + Tj,t = f j (hj,t, kj,t)
                             kj,t+1 = (1 − δk )kj,t + xj,t
                             hj,t+1 ≤ (1 − δh)hj,t + Tj,t
cj,t, kj,t+1, xj,t ≥ 0
                                     kj,0 given
                                    hj,0 given.
where hj,t =   P
               i=1 ωj,i hj,t.
Results

Assume: Symmetric Environmnet

Proposition 1: The growth rate of state governments in a Sym-
metric Compact Equilibrium, where S ⊂ P with S > 1, is greater
along a balanced growth path than any state in a Symmetric
Non-Cooperative Equilibrium.

Corollary: As the number of signatory states, S, increases all
states grow at a faster rate.

Proposition 2: If S = P, the states are strictly better off by
entering into a compact than if they had not.
Intrastate Analog
• California
   – Joint Powers Agreements
   – Special Districts

   – Additional Uses
      • Insurance
         – Spread Risk
      • Achieve economies of scale
         – Police, Fire, etc.
Conclusions
• Compact
  – Internalization Principle (Cooter)
     • Assign power to the smallest unit of government that 
       internalizes the effects of its exercise.


  – Can be used to internalize interstate externalities
     • An option between 
        – single state independent action, and
        – federal action
             » takes into account preferences of other unaffected states
Further Research
• How are compacts negotiated?

• Intrastate Analogs.

• When is competition or non‐cooperation 
  preferable?
  – Antitrust of intergovernmental agreements.
Thanks!


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UC Berkeley, Law And Economics Workshop Presentation, April 11, 2011

  • 1. The Economics of Horizontal  Government Cooperation Matt DalSanto Berkeley Center for Law, Business and the Economy Law and Economics Workshop April 11, 2011
  • 2. Outline of Today’s Presentation • Introduction – Brief History – Overview of Enacted Compacts • Relevant Case Law • Policy Commitment • Negative Externality • Positive Externality • Intrastate Analog: Joint Powers Agreements • Policy Conclusions • Further Research • Questions/Comments
  • 3. What is an Interstate Compact? • Interstate Compact – An interstate compact is  an agreement in which states commit  themselves to a legally binding (contractual)  agreement.
  • 4. History • Use predates the American Revolution – Colonies had poorly defined borders – Boundary Disputes Settled in One of Two Ways • Joint Commission would attempt to negotiate a  settlement – If successful, submit to Crown for approval • If unsuccessful, then appealed to Crown in process  similar to litigation
  • 5. History • Articles of Confederation (Article VI, Section 2) – “No two or more States shall enter into any treaty,  confederation or alliance whatever between them,  without the consent of the United States in Congress  assembled, specifying accurately the purposes for  which the same is to be entered into, and how long it  shall continue.” • Mere agreements between states – Congressional Consent not typically required • Consent required  – if the general authority of Congress would be “weaken[ed]” or  “encroach[ed] upon.”
  • 6. History • US Constitution – “[n]o State shall enter into any Treaty, Alliance, or  Confederation....” – Compact Clause  (Art. I, Sect. 10, Cl. 3) • “No State shall, without the Consent of Congress, ... ,  enter into any Agreement or Compact with another  State, or with a foreign Power....”
  • 7. History • Articles of Confederation v. US Constitution – “Treaty, Alliance, or Confederation” • Permitted with Congressional Consent under Articles • Prohibited under Constitution – “Compact” or “Agreement” • Permitted with Congressional Consent under Constitution – Attempting to Avoid Problems Under Articles • No real distinction • Preserve economic and political power of federal government – “In other cases the Fedl authy was violated by Treaties & wars .... By  compacts witht. the consent of Congress as between Pena. and N. Jersey,  and between Virga. & Maryd. From the Legisl: Journals of Virga. it  appears, that a vote to apply for a sanction of Congs. Was followed by a  vote agst. a communication of the Compact to Congs.” » Personal journal entry by James Madison at Convention.
  • 8. History • 1783 to 1920 – 36 compacts • 1920 to present – over 150 compacts
  • 11. Types of Interstate Compacts • AGRICULTURE (2) • BOUNDARY COMPACTS (26) • BRIDGES, NAVIGATION, AND PORT AUTHORITIES (13) • BUILDING CONSTRUCTION AND SAFETY (1) • CHILD WELFARE (3) • CONSERVATION AND ENVIRONMENT (24) • CORRECTIONS AND CRIME CONTROL (17) • EDUCATION (8) • ENERGY (16) • GAMBLING AND LOTTERIES (3) • HEALTH (4) • INSURANCE (1) • MOTOR VEHICLES (15) • PARKS AND RECREATION (4) • PEST CONTROL (1) • PLANNING AND DEVELOPMENT (10) • PROPERTY (2) • PUBLIC SAFETY (11) • TAXATION (2) • TRANSPORTATION (12) • WATER (37)
  • 12. Interstate Compacts Case Law • Two Legal Mechanisms to Resolve Interstate Disputes – Interstate Compact – Supreme Court • “[t]he judicial power [of the Supreme Court] shall extend to ...controversies  between two or more states...” Art. III, Sect. 2, Cl. 1 • “We cannot withhold the suggestion, inspired by the consideration of this case, that [this] grave problem ... is one more likely to be  wisely solved by co‐operative study and by conference and mutual  concession on the part of representatives of the states so vitally  interested in it than by proceedings in any court however  constituted.” – People of State of New York v. State of New Jersey, 256 U.S. 296, 313  (1921).
  • 13. Interstate Compacts Case Law • Compact Ratification and Cong. Consent – All state legislatures must pass identical implementing  legislation, governor signs into law – Congressional Consent • “[n]o State shall, without the Consent of Congress,..., enter  into any Agreement or Compact with another State...” Art.  I, Sect. 10, Cl. 1 • Com. of Va. v. State of Tenn., 148 U.S. 503, 519 (1893), – Congressional consent for a compact is necessary: when the  compact’s enactment would “[tend] to the increase of political  power in the states, which may encroach upon or interfere with  the just supremacy of the United States.”
  • 14. Compacts that Create Admin Agencies • State ex rel. Dyer v. Sims, 341 U.S. 22 (1951) – Upheld legality of the relatively recent inception  of states entering into a compact that delegates  administrative authority to an interstate agency.
  • 15. Compacts As Contracts • “[A] Compact is, after all, a contract.” – Texas v. New Mexico, 482 U.S. 124, 128 (1987) (quoting Petty v.  Tennessee‐Missouri Bridge Comm’n, 359 U.S. 275, 285 (1959)  (Frankfurter, J., dissenting)) • “It remains a legal document that must be construed and  applied in accordance with its terms.” – Texas v. New Mexico, 482 U.S. 124, 128 (1987). • Offer & Acceptance  – All signatory states adopt the exact language of the compact  agreement as a statute.
  • 16. Breach of Compact • Supreme Court sometimes analogizes a compact to a treaty  between sovereign nations, but.... • Signatory states are held to their compactual obligations – Old Legal Theory: “a State has no more power to impair an obligation  into which she herself has entered, than she can the contracts of  individuals....” • Green v. Biddle, 21 U.S. 1, 39 (1823). – New Legal Theory: “[W]here Congress has authorized the States to  enter into a cooperative agreement, and where the subject matter of  that agreement is an appropriate subject for congressional legislation,  the consent of Congress transforms the States’ agreement into federal  law under the Compact Clause.” • Cuyler v. Adams, 449 U.S. 433, 440 (1981).
  • 17. Remedies for Breach of Compact • Prospective Relief & Damages – “We find no merit in its submission that we may order only  prospective relief, that is, requiring future performance of  compact obligations without a remedy for past breaches.  If that were the case, New Mexico's defaults could never  be remedied.” • Texas v. New Mexico,  482 U.S. 124, 128 (1987). • Damage Measure – Presumably Expectation Damages • A monetary amount that would put the breached against states in  as good of a position as they would have been had the breach not occurred.
  • 18. Policy Commitment • Tying Hands of Future Legislatures • IC for Mississippi River Flood Plain Control – The Great Flood of 1993 • $20 billion • 50,000 homes either destroyed or severely damaged
  • 19. Negative Externality: Great Lakes • Legislators only represent interests of state’s  citizenry not those of other states. – Do not internalize costs to other states. • Lake Michigan (late 19th Century) – Chicago residents ill from dumping sewage into  Chicago River which flowed into Lake. • Chicagoans drank from the Lake
  • 21. Repeated Prisoners’ Dilemma • States repeatedly make decisions that affect  other states year after year. – Play a period Prisoner’s Dilemma game. • No foreseeable end in sight. – Repeated – Assume states want to maximize their payoffs  today plus the net discounted value of future  payoffs.
  • 22. Repeated Prisoners’ Dilemma • In this environment cooperation can arise  endogenously. – But incentives to cooperate and incentives to  defect are both influenced by • The response to the defection by the other states – Are they punished? • The rate at which future payoffs are discounted – If discount rate too high, or if unable to commit to  punishing defecting state, then cooperation may  not be possible.
  • 23. Repeated Prisoners’ Dilemma • Solution – Interstate Compact • Compact requires cooperation • If defect, then liable to other states for expectation  damages award.
  • 25. The Great Lakes‐St. Lawrence River  Basin Water Resources Compact • Requires the GL states to adhere to minimum  regulatory standards to which all signatory  states have agreed. • No new transfers of water outside of GL Basin.
  • 26. Compact Solution • Problem – State may want to breach even though know  forced into compliance in the future. • Secondary Problem – Is efficient breach possible?  Should it be? • Solution – Let states determine how to calculate damages in event of  breach. – Sophisticated government actors; not unsophisticated private  parties.
  • 27. Pos. Externality: Productivity Spillovers • Most studies agree that there is an increase in TFP  from an increase in public infrastructure (capital). – Bridges, Ports, Railroads, Highways, Airports, Public  Transit, etc. • When a jurisdiction undertakes investment in such  capital, it cannot confine the investment’s effects to  just its jurisdiction. – Spillovers between jurisdictions – Too little capital investment
  • 28. States Group of states, P = {1, 2, . . . , P }, that experience increases in TFP from other states’ investment in public capital.
  • 29. State Environment Each state has a representative household −preferences over consumption: uj (·) −discounts next period utility at the same rate β −endowed with an amount of private capital kj,0 has a representative firm that rents capital from the household and sells its output in a national market government has a sales tax τc (equivalent to the lump-sum tax instrument Tj,t)
  • 30. Representative Household’s Problem for State j ∞ max β tuj (ch ) j,t (ch ,xh ,kj,t+1 ,lj,t )∞ t=0 j,t j,t h h t=0 s. to (1 + τj )ptch + ptxh ≤ rj,tkj,t + wj,tlj,t + πj,t j,t j,t h h kj,t+1 ≤ (1 − δk )kj,t + xh h h j,t h lj,t ≤ lj ch , xh , kj,t+1, lj,t ≥ 0 j,t j,t h h lj = 1 h kj,0 given.
  • 31. Representative Firm’s Problem for State j f f f max πj,t ≡ ptyj,t − rj,tkj,t − wj,tlj,t f f f yj,t ,kj,t ,lj,t f f f s. to yj,t = F j (hj,t, kj,t, lj,t) f f f yj,t, kj,t, lj,t ≥ 0 where hj,t = P i=1 ωj,i hj,t.
  • 32. State Governments Run Balanced Budgets ptij,t = τj ptcj,t hj,t+1 = (1 − δh)hj,t + ij,t.
  • 33. Market Clearing f yj,t = ch + j,t xh + j,t ij,t j∈P j∈P j∈P j∈P f h kj,t = kj,t ∀j ∈ P f h lj,t = lj,t ∀j ∈ P.
  • 34. Characterization of Equilibrium Letting f j (h, k) = F j (h, k, 1) and given ((Ti,t)∞ )i∈P , each re- t=0 gion’s, for j ∈ P, equilibrium allocation is characterized by j uc (cj,t) j j = fk (hj,t+1, kj,t+1) + (1 − δk ) βuc (cj,t+1 ) cj,t + xj,t + Tj,t = f j (hj,t, kj,t) kj,t+1 = (1 − δk )kj,t + xj,t hq,t+1 = (1 − δh)hq,t + Tq,t ∀q ∈ P kj,0 given hj,0 given. where hj,t = P i=1 ωj,i hj,t.
  • 35. Non-Cooperative Equilibrium State j’s Government’s Problem Each government j ∈ P takes as given the investments of the other P − 1 governments, ((Ti,t)∞ )i∈P−{j} and thus the value t=0 of their public capital stocks ((hi,t)∞ )i∈P−{j}. In each period t=0 t, state government j chooses its optimal value of public capital in period t + 1, hj,t+1, so as to satisfy ∞ max β tuj (cj,t) (Tj,t ,hj,t+1 ,cj,t,xj,t ,kj,t+1 )∞ t=0 t=0 j uc (cj.t ) j s. to j = fk (hj,t+1, kj,t+1) + (1 − δk ) βuc (cj,t+1 ) cj,t + xj,t + Tj,t = f j (hj,t, kj,t) kj,t+1 = (1 − δk )kj,t + xj,t
  • 36. hq,t+1 = (1 − δh)hq,t + Tq,t ∀q ∈ P cj,t, kj,t+1, xj,t ≥ 0 kj,0 given Tq,t given ∀q ∈ P − {j} hq,0 given ∀q ∈ P. where hj,t = P i=1 ωj,i hj,t.
  • 37. Compact Equilibrium Given the terms of the compact, U, the compact authority’s problem is to choose taxes ((Tj,t)∞ )j∈S and thus t=0 ∞ ) ((hj,t+1, cj,t, xj,t, kj,t+1)t=0 j∈S , so as to solve, ∞ max U (( β tuj (cj,t))j∈S ) ((Tj,t ,hj,t+1 ,cj,t ,xj,t ,kj,t+1 )∞ )j∈S t=0 t=0 j uc (cj.t ) j s. to j = fk (hj,t+1, kj,t+1) + (1 − δk ) βuc (cj,t+1 ) cj,t + xj,t + Tj,t = f j (hj,t, kj,t) kj,t+1 = (1 − δk )kj,t + xj,t hj,t+1 ≤ (1 − δh)hj,t + Tj,t
  • 38. cj,t, kj,t+1, xj,t ≥ 0 kj,0 given hj,0 given. where hj,t = P i=1 ωj,i hj,t.
  • 39. Results Assume: Symmetric Environmnet Proposition 1: The growth rate of state governments in a Sym- metric Compact Equilibrium, where S ⊂ P with S > 1, is greater along a balanced growth path than any state in a Symmetric Non-Cooperative Equilibrium. Corollary: As the number of signatory states, S, increases all states grow at a faster rate. Proposition 2: If S = P, the states are strictly better off by entering into a compact than if they had not.
  • 40. Intrastate Analog • California – Joint Powers Agreements – Special Districts – Additional Uses • Insurance – Spread Risk • Achieve economies of scale – Police, Fire, etc.
  • 41. Conclusions • Compact – Internalization Principle (Cooter) • Assign power to the smallest unit of government that  internalizes the effects of its exercise. – Can be used to internalize interstate externalities • An option between  – single state independent action, and – federal action » takes into account preferences of other unaffected states
  • 42. Further Research • How are compacts negotiated? • Intrastate Analogs. • When is competition or non‐cooperation  preferable? – Antitrust of intergovernmental agreements.