Time Consistency Problem in a Monetary Union

Transcription

1 Time Consistency Problem in a Monetary Union University of Alicante 10th International Meeting Society for Social Choice and Welfare July 21-24, 2010

2 Research Questions Monetary theorists should start paying attention to the nature of decision making by committee, which is rarely mentioned in the academic literature. Alan Blinder In a monetary union with the monetary authority that lacks commitment 1 How important are collective monetary decisions? 2 How desirable are borrowing constraints?

3 Collective Decisions in Monetary Unions European Central Bank Governing Council: 22 members, 16 are governors of participating central banks majority rule West African Monetary Union Council of Ministries: 8 votes, one per state unanimity Monetary Community of Central Africa Council of Ministries: 6 votes, one per state unanimity or qualified majority of 5 votes Federal Reserve Bank Federal Open Market Committee: 12 members, with 5 representing regional FRBs majority rule

4 Borrowing Constraints in European Union Maastricht criteria government deficit must not exceed 3% of GDP government debt must not exceed 60% of GDP

5 Borrowing Constraints in European Union

6 Preview of Results 1 Multiplicity of noncooperative majority equilibria under the majority voting rule. Nonsymmetric noncooperative majority equilibria consists of a majority and a minority group; the minority free-rides on the majority and obtains higher welfare than the majority. The best noncooperative majority equilibrium is nonsymmetric 2 Fiscal constrains, if binding, shrink the set of the noncooperative equilibria, precluding the best noncooperative equilibrium.

7 Basic Model A monetary union with an odd number N of identical counties A representative agent in each country with preferences U ( c i ) ( ) 1 + βu c i 2 U > 0, U < 0, 0 < β 1; endowments ω in the first period; endowments y (π) in the second period, where π is the rate of inflation between the two periods y < 0, y < 0.

8 Basic Model Each country ia allowed to issue nominal debt b i, which has to be repaid the next period in the nominal amount x i Budget constraints c i 1 ω + b i c i 2 y (π) x i /π All countries are negligibly small relative to the rest of the world, which is populated by risk-neutral lenders with the discount factor β βx i /π b i 0

9 Monetary Policy Lack of commitment: Monetary authority chooses its policy collectively in the second period after fiscal policies have been decided Majority rule Condorcet winner in the voting over inflation Median voter theorem applies the voting problem is one-dimensional agents preferences over inflation are single-peaked π m ( x 1,..., x n) { [ ( = median arg max U y (π) x i /π )]} π 1,...,π n π

10 Monetary Policy Utilitarian rule π u ( x 1,..., x n) = arg max π [ 1 N N U ( y (π) x i /π )] i=1 Unionwide rule Consensus rule

11 Fiscal Policy Noncooperative fiscal policy: A representative agent in each country solves utility maximization problem given monetary policy π (x) π ( x 1,..., x n) max x i [ U ( ω + βx i /π (x) ) + βu ( y (π (x)) x i /π (x) )]

12 Noncooperative Equilibrium Definition A noncooperative equilibrium is an allocation c i 1, ci 2, bi, and x i for each country i and an inflation rate π such that 1 given debt allocation for all countries x i the inflation rate π solves the respective monetary problem; 2 for each country i given the monetary rule π ( x 1,..., x n) and choices x j for all countries j i the allocation c i 1, ci 2, bi, and x i maximizes the utility of the representative agent of country i subject to the budget constraints and the lender constraint.

13 Symmetric Noncooperative Equilibrium The symmetric equilibrium under majority rule is unique. The symmetric equilibrium under utilitarian rule is unique under additional conditions (Lemma 1). Debt repayment in the symmetric equilibrium under utilitarian rule is increasing in the number of monetary union countries (Lemma 2). The symmetric equilibrium debt allocation under majority rule is the upper limit of the equilibrium debt under utilitarian rule as the number of monetary union countries goes to infinity.

14 Nonsymmetric Noncooperative Equilibrium Definition A group symmetric allocation is an allocation in which the majority group of (N + 1) /2 countries chooses the same debt within the group, and the minority group of (N 1) /2 countries also chooses the same debt within the group. Proposition There are multiple noncooperative equilibria under the majority rule. All the equilibria are group symmetric.

15 Numerical Example The best nonsymmetric noncooperative majority equilibrium U x 1 x 2,x x 2 x x 1

16 Numerical Example Another nonsymmetric noncooperative majority equilibrium U x 1 x 2,x x 2 x x

17 Welfare Among noncooperative majority equilibria Welfare is the lowest at the symmetric equilibrium the welfare is lower than at a symmetric noncooperative equilibrium under utilitarian rule Welfare is the highest at the group symmetric equilibrium in which the majority of countries chooses the cooperative equilibrium allocation the majority group obtain the same welfare as in the cooperative equilibrium the minority free rides on the majority obtaining higher welfare

18 Fiscal Constraints Noncooperative majority equilibria with fiscal constraints x i x c (Proposition 3) U 1 U 2 U x c

19 Asymmetric countries Countries are different in the the first period endowment ω i ϖ C D 0.4 B D 0.2 A ϖ1 ( Example: endowments ω 1, ω 2, ω 3) ( ) = ω 1, ω 2, 0 C

20 Asymmetric countries Case A: ω 1 ω 2 ω 3 (Proposition 4) Continuum of equilibria All equilibria are group-symmetric Among equilibria any country can be in majority or minority U x2 x1,x3 U x3 x1,x x x ( Example: endowments ω 1, ω 2, ω 3) ( = (.05,.05, 0); equilibrium x 1, x 2, x 3) = (.67,.56,.56)

21 Asymmetric countries Case B: ω 1 ω 2 ω 3 and similar Continuum of equilibria All equilibria are group-symmetric Poor country is always in minority U x2 x1,x3 U x3 x1,x x ( Example: endowments ω 1, ω 2, ω 3) ( = (.50,.50, 0); equilibrium x 1, x 2, x 3) = (.21,.21,.59)) x3

22 Asymmetric countries Case B: ω 1 ω 2 ω 3 and similar Majority equilibria vs. utilitarian equilibrium under fiscal constraints x i x c U1 U2 U xc ( Example: endowments ω 1, ω 2, ω 3) ( = (.50,.50, 0); equilibrium x 1, x 2, x 3) = (.21,.21,.59))

23 Asymmetric countries Case C: ω 1 ω 2 ω 3 and similar Two equilibria Rich country always chooses the lowest debt One poor country is a median voter, the other free-rides U x1 x2,x U x2 x1,x x x ( Example: endowments ω 1, ω 2, ω 3) ( = (.50, 0, 0); equilibrium x 1, x 2, x 3) = (.32,.56,.71) 0.38

24 Asymmetric countries Case D: ω 1 ω 2 ω 3 and similar One equilibrium Rich country always chooses the lowest debt Poor country always chooses the highest debt U x1 x2,x U x2 x1,x x x2 ( Example: endowments ω 1, ω 2, ω 3) ( = (.80,.40, 0); equilibrium x 1, x 2, x 3) = (.11,.26,.61)

25 Conclusions 1 Under majority rule there are multiple noncooperative equilibria. In all of the equilibria only the majority of the union countries takes directly into account the actions of the noncommitted monetary authority. The minority free-rides on the majority and obtains higher welfare. 2 Fiscal constraints, if binding, shrink the set of the noncooperative equilibria, which calls into question the desirability of the fiscal constraints as a tool to combat the lack of commitment.