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Fiscal-monetary policy coordination and debt management: a two-stage analysis

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Abstract

We study interactions between two policymakers, central bank and government, in managing public debt as the result of a two-stage game. In the first stage, the institutional regime is established. This determines the equilibrium solution for the second stage, in which a differential game is played between the two policymakers. It is shown that, if the policymakers can communicate before the game is played (multiple-equilibrium), coordination problems can be solved by using the concept of correlated equilibrium.

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Notes

  1. A number of empirical studies support the proposition that central bank independence and low rates of inflation are correlated (see, e.g., Berger et al. 2001). However, it has also been argued (see, e.g., Hayo and Hefeker 2002) that this correlation does not indicate causality and that the reasons why central banks are made independent are related to legal, cultural, political and economic factors.

  2. Seminal studies are those of Sargent and Wallace (1981), Tabellini (1986), Alesina and Tabellini (1987) and Turnovsky et al. (1988). More recent contributions are, among others, Levine and Brociner (1994), Neck and Dockner (1995), Pappa (2004). Particular emphasis has been recently placed on the problem of macroeconomic policy coordination in a monetary union (see, e.g., Cooper and Kempf 2000; Beetsma et al. 2001; Buti et al. 2001; Beetsma and Jensen 2004; van Aarle et al. 2002, 2004; Engwerda et al. 2002; Dixit and Lambertini 2003; Plasmans et al. 2005).

  3. See North (1990) for a discussion of institutions as rules of the game.

  4. Two-stage games have recently been used in order to establish the institutional arrangements (first stage) separately from the “main” game that is played in such arrangements (second stage). An example is provided by non-cooperative endogenous coalition theory: in the first stage coalitions are formed, whereas in the second stage coalitions play the game (Ray and Vohra 1999). van Aarle et al. (2002) provide an economic application of this approach to the coordination of fiscal and monetary policies in the EMU.

  5. See the discussion in Debrun (2000) and Dixit and Lambertini (2000).

  6. A formal definition of correlated equilibrium is given in Sect. 5. The references for correlated equilibrium are Aumann (1974, 1987).

  7. See also van Aarle et al. (1995, 1997). As they point out, the main advantage of the two-step procedure lies in its practicability, notwithstanding its limits.

  8. The private sector consists of small agents. They do not act strategically and therefore, their joint decisions on consumption and savings affect only the parameters of the model.

  9. It can be a legislative device or an external authority which prevents the players from reneging on the announcements made, a reputation mechanism so that the player who deviates will not be believed in the future, or an institution which enhances the players’ credibility.

  10. Notice that the central bank and the government have the same rate of time preference ρ (assumed to be constant over time) and the same time horizon, which is infinite.

  11. Tabellini (1987) justifies the inclusion of public debt in the policymakers’ loss function by appealing to the fact that, in the absence of lump-sum taxes, a larger stock of public debt implies larger tax distortions in order to pay interest on the debt. Another reason for including the level of public debt among the central bank’s objectives is offered by the fiscal theory of the price level. According to this theory, if fiscal policy does not ensure satisfaction of the government’s inter-temporal budget constraint, then the price level must do so and the central bank cannot control inflation (see Woodford 2001, and literature cited therein). If doubts exist as to the independence of the central bank, further reasons for including public debt among monetary policy targets are the preoccupation with an inflation bail-out, were the central bank forced to give in to government pressure for monetizing the debt, or for an ex-post bail-out, in the case of a financial crisis stemming from the government defaulting on its debt.

  12. The assumption that a is constant over time is introduced to limit the analytical complexity. An endogenous real interest rate would imply a non-linear dynamic constraint in the differential game. Similar assumptions are very common in the literature (see, among others, Tabellini 1986; Jensen 1994; van Aarle et al. 1995, 1997; Beetsma and Bovenberg 1997; Muscatelli et al. 2003).

  13. As suggested by Darby (1984), if the growth rate of real income is larger than the real interest rate, then, contrary to Sargent and Wallace (1981), the economy is not on an explosive path and the “arithmetic is not so unpleasant”.

  14. Without loss of generality, we only consider the case in which F > M so that \( \bar d > 0 \).

  15. The same results are found by Tabellini (1986) and van Aarle et al. (1995), who have also, as previously pointed out, investigated the transition dynamics of the model.

  16. Formally, this is due to the fact that, in all the regimes, deviations from instrumental variable targets equal the shadow prices of the fiscal debt for the policymakers (see Eqs. (6) and (7)).

  17. “One can imagine a monetary authority sufficiently powerful vis-à-vis the fiscal authority that by the imposition of slower rates of growth of base money […] it can successfully constrain fiscal policy by telling the fiscal authority how much seigniorage it can expect. […] On the other hand, one can imagine that the monetary authority is not in a position to influence the government’s deficit path but is limited simply to managing the debt that is implied by the deficit path chosen by the fiscal authority. Under this second scheme the monetary authority is much less powerful than under the first scheme” (Sargent and Wallace 1981, p. 158).

  18. The following results can be easily verified with standard calculus. Proofs are, however, available upon request.

  19. The six rankings are obtained by combining the inequalities \( \bar V_{V} < \bar V_{W} \) and \( \bar V_{N} < \bar V_{G} \).

  20. These are, together with their homologues for G, (recall that we have assumed the same ordering of the losses between the two policymakers): (1) \( \bar V_{N} < \bar V_{V} < \bar V_{G} < \bar V_{W} \), (2)\( \bar V_{N} < \bar V_{G} < \bar V_{V} < \bar V_{W} \), (3)\( \bar V_{V} < \bar V_{W} < \bar V_{N} < \bar V_{G} \), (4) \( \bar V_{V} < \bar V_{N} < \bar V_{G} < \bar V_{W} .\)

  21. In our context the ranking \( \bar V_{N} < \bar V_{V} < \bar V_{W} < \bar V_{G} \) (together with its homologous ranking for G) describes a coordination game with common interest.

  22. Since binding agreements in a non-cooperative game are ruled out by definition, only self-enforcing agreements have to be considered.

  23. The Nash equilibrium in mixed strategies is \( \left[ {\begin{array}{*{20}c} {p^{\prime}} & {1 - p^{\prime}} \\ p & {1 - p} \\ \end{array} } \right] \). In this equilibrium the central bank must be indifferent between being leader or follower. This requires that the probability with which the government chooses to follow the leader, denoted by p, should be such that: \( V(f, \cdot ) = p\bar V_{N} + (1 - p)\bar V_{G} = p\bar V_{V} + (1 - p)\bar V_{W} = V(l, \cdot ) \) Analogously, the probability with which the central bank chooses to follow the leader, denoted by \( p^{\prime} \), should be such that: \( G( \cdot ,f) = p^{\prime}\bar G_{N} + (1 - p^{\prime})\bar G_{V} = \) \( p^{\prime}\bar G_{G} + (1 - p^{\prime})\bar G_{W} = G( \cdot ,l) \).

  24. See, e.g., the discussion in Dixit (2000).

  25. Which is of major importance to ensure the accountability of individual policy-makers.

References

  • van Aarle B, Bovenberg AL, Raith MG (1995) Monetary and fiscal policy interaction and government debt stabilization. J Econ 2:111–140

    Google Scholar 

  • van Aarle B, Bovenberg AL, Raith MG (1997) Is there a tragedy for a common Central Bank? A dynamic analysis. J Econ Dyn Control 21:417–447

    Article  Google Scholar 

  • van Aarle B, Di Bartolomeo G, Engwerda J, Plasmans J (2002) Monetary and fiscal policy design in the EMU using a dynamic game approach: an overview. Open Econ Rev 13:321–340

    Article  Google Scholar 

  • van Aarle B, Di Bartolomeo G, Engwerda J, Plasmans J (2004) Policymakers’ coalitions and the stabilization policy in the EMU. J Econ 82:1–24

    Article  Google Scholar 

  • Alesina A, Tabellini G (1987) Rules and discretion with noncoordinated monetary and fiscal policy. Econ Inq 25:619–630

    Article  Google Scholar 

  • Aumann R (1974) Subjectivity and correlation in randomized strategies. J Math Econ 1:67–96

    Article  Google Scholar 

  • Aumann R (1987) Correlated equilibria as an expression of Bayesian rationality. Econometrica 55:1–18

    Article  Google Scholar 

  • Ben Porath E (1998) Correlation without mediation: expanding the set of equilibrium outcomes by ‘Cheap’ pre-play procedures. J Econ Theory 80:108–122

    Article  Google Scholar 

  • Beetsma RMWJ, Bovenberg AL (1997) Public debt policy and Central Bank independence. J Econ Dyn Control 21:873–894

    Article  Google Scholar 

  • Beetsma RMWJ, Bovenberg AL (1998) Monetary union without fiscal coordination may discipline policymakers? J Int Econ 45:239–258

    Article  Google Scholar 

  • Beetsma RMWJ, Jensen H (2004) Monetary and fiscal policy interactions in a microfounded model of a monetary union. University of Copenhagen, Mimeo

    Google Scholar 

  • Beetsma RMWJ, Debrun X, Klaassen F (2001) Is fiscal policy coordination in EMU desirable? Swed Econ Policy Rev 8:57–98

    Google Scholar 

  • Berger H, de Haan J, Eijffinger SCW (2001) Central Bank independence: an update of theory and evidence. J Econ Surveys 15:3–40

    Article  Google Scholar 

  • Buti M, Roeger W, in’t Veld J (2001) Stabilising output and inflation: policy conflicts and coordination under a stability pact. J Common Market Stud 39:801–828

    Article  Google Scholar 

  • Cooper R, Kempf H (2000) Designing stabilization policy in a monetary union. NBER Working Paper No. 7607. Forthcoming in Rev Econ Stud

  • Darby MR (1984) Some pleasant monetarist arithmetic. Federal Minneap Q Rev 8:15–20

    Google Scholar 

  • Debrun X (2000) Fiscal rules in a monetary union: a short-run analysis. Open Econ Rev 11:323–358

    Article  Google Scholar 

  • Dixit A (2000) A repeated game model of monetary union. Econ J 110:769–780

    Article  Google Scholar 

  • Dixit A, Lambertini L (2000) Monetary-fiscal policy interactions and commitment versus discretion in a monetary union. Eur Econ Rev 4–6:987–997

    Google Scholar 

  • Dixit A, Lambertini L (2003) Interactions of commitment and discretion in monetary and fiscal policies. Am Econ Rev 93:1522–1542

    Article  Google Scholar 

  • Ecchia G, Mariotti M (1998) Coalition formation in international environmental agreements and the role of institutions. Eur Econ Rev 42:573–582

    Article  Google Scholar 

  • Engwerda JC, van Aarle B, Plasmans J (2002) Cooperative and non-cooperative fiscal stabilisation policies in the EMU. J Econ Dyn Control 26:451–481

    Article  Google Scholar 

  • Forges F (1990) Equilibria with communication in a job market example. Q J Econ 105:375–398

    Article  Google Scholar 

  • Foster D, Vohra R (1997) Calibrated learning and correlated equilibrium. Games Econ Behav 21:40–55

    Article  Google Scholar 

  • Hart S, Mas Colell A (2000) A simple adaptive procedure leading to correlated equilibrium. Econometrica 68:1127–1150

    Article  Google Scholar 

  • Hart S, Mas Colell A (2001) A general class of adaptive strategies. J Econ Theory 98:26–54

    Article  Google Scholar 

  • Hayo B, Hefeker C (2002) Reconsidering Central Bank independence. Eur J Polit Econ 18:653–674

    Article  Google Scholar 

  • Jensen H (1994) Loss of monetary discretion in a simple dynamic policy game. J Econ Dyn Control 18:764–779

    Article  Google Scholar 

  • Lehrer E (1996) Mediated talk. Int J Game Theory 25:177–188

    Article  Google Scholar 

  • Levine P, Brociner A (1994) Fiscal Coordination & EMU: a dynamic game approach. J Econ Dyn Control 18:699–729

    Article  Google Scholar 

  • Moreno D, Wooders J (1998) An experimental study of communication and coordination in noncooperative games. Games Econ Behav 24:47–76

    Article  Google Scholar 

  • Muscatelli VA, Natale P, Tirelli P (2003) A simple and flexible alternative to the stability and growth pact deficit ceilings. CESIFO Working Paper No. 1060

  • Neck R, Dockner E (1995) Commitment and coordination in a dynamic game model of international economic policy making. Open Econ Rev 6:5–28

    Article  Google Scholar 

  • North D (1990) Institutions, institutional change and economic performance. Cambridge University Press, Cambridge

    Google Scholar 

  • Pappa E (2004) Do the ECB and the FED really need to cooperate? Optimal monetary policy in a two-Country World. J Monet Econ 51:753–779

    Article  Google Scholar 

  • Plasmans J, Engwerda JC, van Aarle B, Di Bartolomeo G, Michalak T (2005) Dynamic modeling of monetary and fiscal cooperation among nations. Springer, Berlin

    Google Scholar 

  • Ray D, Vohra R (1999) A theory of endogenous coalition structures. Games Econ Behav 26:286–336

    Article  Google Scholar 

  • Sargent T, Wallace N (1981) Some unpleasant monetarist arithmetic. In: Sargent T (ed) Rational expectations and inflation. Harper & Row, New York

    Google Scholar 

  • Tabellini G (1986) Money, debt and deficits in a dynamic game. J Econ Dyn Control 8:472–442

    Google Scholar 

  • Tabellini G (1987) Central Bank reputation and the monetization of deficits: the 1981 Italian monetary reform. Econ Inq 25:185–201

    Article  Google Scholar 

  • Turnovsky S, Basar T, d’Orey V (1988) Dynamic strategic monetary policies and coordination in interdependent economies. Am Econ Rev 78:341–361

    Google Scholar 

  • Woodford M (2001) Fiscal requirements for price stability. J Money Credit Bank 33:669–728

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank N. Acocella, F. Ambrosio, V. Di Simone, A. Hughes Hallett, P. Krusell, S. Papa and participants at the workshop on “Sustainability of Public Debt” in Klagenfurt for their comments. The usual disclaimer applies. This research project has been supported by MIUR (PRIN 2005) and a Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Program under contract number MTKD-CT-014288. Giovanni Di Bartolomeo would also like to acknowledge the hospitality of the University of Crete.

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  1. University of Teramo, Coste S.Agostino, 64100, Teramo, Italy

    Giovanni Di Bartolomeo

  2. University of Rome La Sapienza, 00161, Rome, Italy

    Debora Di Gioacchino

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  1. Giovanni Di Bartolomeo
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Correspondence to Giovanni Di Bartolomeo.

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Di Bartolomeo, G., Di Gioacchino, D. Fiscal-monetary policy coordination and debt management: a two-stage analysis. Empirica 35, 433–448 (2008). https://doi.org/10.1007/s10663-008-9077-0

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