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The interaction between fiscal and monetary policy is analyzed by means of a game theory approach. The coordination between these two policies is essential, since decisions taken by one institution may have disastrous effects on the other one, resulting in welfare loss for the society. We derived optimal monetary and fiscal policies in context of three coordination schemes: when each institution independently minimizes its welfare loss as a Nash equilibrium of a normal form game; when an institution moves first and the other follows, in a mechanism known as the Stackelberg solution; and, when institutions behave cooperatively, seeking common goals. In the Brazilian case, a numerical exercise shows that the smallest welfare loss is obtained under a Stackelberg solution which has the monetary policy as leader and the fiscal policy as follower. Under the optimal policy, there is evidence of a strong distaste for inflation by the Brazilian society.
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Ann Oper Res (2013) 206:341–366
DOI 10.1007/s10479-013-1379-3
Fiscal and monetary policy interactions: a game theory
Helton Saulo ·Leandro C. Rêgo ·Jose A. Divino
Published online: 23 April 2013
© Springer Science+Business Media New York 2013
Abstract The interaction between fiscal and monetary policy is analyzed by means of a
game theory approach. The coordination between these two policies is essential, since de-
cisions taken by one institution may have disastrous effects on the other one, resulting in
welfare loss for the society. We derived optimal monetary and fiscal policies in context of
three coordination schemes: when each institution independently minimizes its welfare loss
as a Nash equilibrium of a normal form game; when an institution moves first and the other
follows, in a mechanism known as the Stackelberg solution; and, when institutions behave
cooperatively, seeking common goals. In the Brazilian case, a numerical exercise shows that
the smallest welfare loss is obtained under a Stackelberg solution which has the monetary
policy as leader and the fiscal policy as follower. Under the optimal policy, there is evidence
of a strong distaste for inflation by the Brazilian society.
Keywords Fiscal policy ·Monetary policy ·Nash equilibrium ·Stackelberg equilibrium ·
Cooperative solution
1 Introduction
The macroeconomic analysis has experienced wide changes in recent years. The rule-based
policymaking approach has taken the scene in both fiscal and monetary policies all over the
H. Saulo ()
Department of Economics, Federal University of Rio Grande do Sul, 90040-000, Porto Alegre, RS,
L.C. Rêgo
Department of Statistics, Federal University of Pernambuco, 50740-540, Recife, PE, Brazil
J.A. Divino
Department of Economics, Catholic University of Brasilia, 70790-160, Brasilia, DF, Brazil
342 Ann Oper Res (2013) 206:341–366
world. Woodford (2003), for instance, calls our attention to the adoption of interest rate rules
by the monetary policy aiming at inflation stabilization. The relevance of commitment with
explicit rules is strengthened by the adoption of inflation targeting regimes by many central
banks worldwide, including Central Bank of Brazil, Bank of England, Reserve Bank of
New Zealand, Swedish Riksbank, among others. However, independent movements by the
monetary authority might result in conflicting interests with the fiscal authority. To resolve
this dispute, one might make use of the game theory framework.
Our goal is to analyze the interaction between fiscal and monetary policy, taking into
account different policy regimes, resulting from alternative forms of interactions between
the policy authorities in a game theory environment. We allow for the policymakers to si-
multaneously set their instruments without cooperation as in a normal form game, engage in
a Stackelberg leadership scheme, and simultaneously set their instruments in a cooperative
game to pursue common objectives. Whenever possible, the models are solved analytically.
Otherwise, we provide numerical approximation for the solutions using the Brazilian econ-
omy as a reference.
Backus and Driffill (1985) and Tabellini (1985), for instance, used the theory of repeated
games to demonstrate that, under certain conditions, equilibria with low inflation could also
appear under discretionary policymaking.1The argument is that when the monetary author-
ity fights against inflation by relying on good reputation, it influences private-sector expecta-
tions on future inflation. Thus, even under discretion, the policymakers need to demonstrate
a certain amount of credibility. In this scenario there appeared, for instance, the Taylor rule
(Taylor 1993), establishing a reaction function for the nominal interest rate in response to
variations in inflation and the output gap. Later on, Taylor’s empirical rule was rationalized
by optimizing behavior of individuals and firms in a New Keynesian framework.
Coordination between fiscal and monetary policies has to take care of conflicting inter-
ests, since each policymaker is primarily concerned with his own objectives. In this scenario,
the induced economic spillovers and externalities become very important. This issue is ad-
dressed by Engwerda (1998), Engwerda et al. (1999,2002), who modeled dynamic games
among monetary and fiscal policymakers.
Dixit (2001) built several models of the EMU (European Monetary Union) and the Euro-
pean Central Bank (ECB) in order to analyze the interactions of some countries’ monetary
and fiscal policies. He found that the voting mechanism2achieved moderate and stable in-
flation. In case of a repeated game, the ECM should foresee eventual member drawback and
overcome this perturbation. Dixit (2001) emphasizes the dangerous role played by uncon-
strained national fiscal policies, which can undermine the ECB’s monetary policy commit-
Van Aarle et al. (2002) implemented a monetary and fiscal policy framework in the EMU
area according to the Engwerda et al. (2002) model. The idea was to study various interac-
tions, spillovers, and externalities involving macroeconomic policies under alternative pol-
icy regimes. Numerical examples were provided for some types of coalitions. It is interesting
to highlight that, in the simulations, full cooperation did not induce a Pareto improvement
for the ECB.
The traditional three-equation Taylor-rule New Keynesian model was extended by Kir-
sanova et al. (2005) to include the fiscal policy and analyze policy coordination. The idea
was to amend the set-up to a five-equation system in order to describe the role of the fiscal
1Macroeconomic policy characterized by absence of commitment.
2This is a mechanism of decision-making in the European Central Bank (ECB).
Ann Oper Res (2013) 206:341–366 343
policy, which might give feed back on the level of debt and helps the monetary authority to
stabilize inflation. Policy interactions were considered in three scenarios: (i) non-cooperative
policies, (ii) partially cooperative policies, and (iii) benevolent policies. The results sug-
gested that, if the authorities are benevolent and cooperative, the monetary authority will
bear all the burden of the stabilization. In addition, the Nash equilibrium will produce large
welfare losses when the monetary authority is benevolent and the fiscal authority discounts
too much the future or aims for an excessive level of output.
Lambertini and Rovelli (2003) also studied monetary and fiscal policy coordination using
a game theory approach. Particularly, they argue that each policy maker prefers to be the
follower in a Stackelberg situation. Moreover, when compared to the Nash equilibrium,
both Stackelberg solutions are preferable. Due to implementation issues, they also claim
that fiscal authorities would naturally behave as leaders in a strategic game with monetary
authorities. Favero (2004), on the other hand, shows that the strategic complementarity or
substitutability between fiscal and monetary policy might depend on the type of shock hitting
the economy. In addition, countercyclical fiscal policy might be welfare-reducing if fiscal
and monetary policy rules are inertial and not coordinated.
Our major contribution states that, in the Brazilian case, the monetary leadership under
the Stackelberg solution yields the smallest welfare loss for the society. The monetary lead-
ership might be associated to the existence of a monetary dominance in the Brazilian econ-
omy during the recent period, as empirically suggested by Tanner and Ramos (2002), Fialho
and Portugal (2005), and Gadelha and Divino (2008). Under the optimal policy, a sensitivity
analysis performed by varying the relative weights placed by themonetary and fiscal author-
ities on their target variables revealed a strong distaste for inflation by the Brazilian society.
In addition, impulse response functions indicated strong reactions of the monetary author-
ity to inflationary pressures. There is also an inflationary effect coming from fiscal shocks,
which contributes to reinforce the key role played by the monetary authority to stabilize the
The remainder of the paper is organized as follows. The next section details the baseline
macroeconomic model and discusses some elements of game theory. The third section in-
troduces the fiscal and monetary policy games. The fourth section discusses the numerical
approach used to approximate some of the solutions. The numerical results are presented
and analyzed in the fifth section. Finally, the sixth section is dedicated to the concluding
2 The baseline model
The New Keynesian framework has been largely used to analyze optimal monetary and fis-
cal policy rules. The system of equations is a linear approximation, in logarithmic form, of
a dynamic stochastic general equilibrium (DSGE) model with sticky prices. The DSGE ap-
proach attempts to explain aggregate economic fluctuations, such as economic growth and
the effects of monetary and fiscal policies, on the basis of macroeconomic models derived
from microeconomic principles. The model is forward-looking and consists of an aggregate
supply equation, also known as the New Keynesian Phillips curve, an aggregate demand
equation, also called the IS curve. Additionally, there is an intertemporal budget constraint,
with which the government should comply, and the optimal monetary and fiscal policy rules.
These two policy rules will be derived later on. The aggregate demand function, represented
by the intertemporal IS curve, results from the first-order conditions of the individual’s op-
timization problem. The IS curve can be modeled taking into account the primary deficit,
344 Ann Oper Res (2013) 206:341–366
as in Nordhaus (1994), the public debt as in Kirsanova et al. (2005) and Bénassy (2007),
or even the level of government expenditures as in Muscatelli et al. (2004). In this paper,
we amend the IS curve proposed by Woodford (2003) in order to capture the effects of the
public debt on aggregate demand. Thus, the set-up considers the following closed economy
IS curve in log-linearized form3
where ˆxt=(
t)is the output gap (difference between actual and potential output), ˆ
is the nominal interest rate, ˆrn
tis a demand shock, Etrepresents the time texpected value
of the next period inflation rate πt+1and output gap ˆxt+1,btis the real stock of government
debt, σ>0 is the intertemporal elasticity of substitution in private spending, and αmeasures
the sensitivity of the output gap with respect to the debt. Notice that the aggregate demand
relationship depends also on future expected values and not just current ones.
On the aggregate supply curve (Phillips curve), firms face a decision to choose a price
that solves their profit maximization problem. The assumption of price rigidity (Calvo 1983),
according to which a fraction 0 <1 of prices remains fixed during each period, allows
the derivation of the following (log-linearized) aggregate supply:
where the current inflation rate t)depends on the expected Etinflation rate at t+1, and
the current output gap ˆx. We allow a supply shock νt, as in Woodford (2003), to have a
trade-off between inflation versus output gap stabilization. The parameter κ>0 measures
the sensitivity of inflation with respect to the output gap and β,where0<β<1isthe
intertemporal discount factor.
The debt in Eq. (1) also needs to be modeled. Here, the real stock of debt ˆ
btis treated
as in Kirsanova et al. (2005). Thus, the period treal stock of debt, ˆ
bt, depends on the stock
of debt in the previous period, ˆ
bt1, flows of interest payments, government spending, and
revenues, such that:
where iis the equilibrium interest rate, baccounts for the steady state value of the debt, ˆ
is the interest rate, ˆgtrepresents the government spending, is the tax rate, ˆxtdenotes the
output gap, and ηtstands for the debt shock.
The monetary policy and fiscal policy variables are interest rate and government spend-
ing, respectively. Through Eq. (1), one can see that the aggregate demand monetary policy
transmission takes place when an increase (decrease) in the interest rate is greater than the
expected increase (decrease) in the inflation rate at t+1. The reduction (rise) in the ag-
gregate demand of the economy lowers (increases) inflation via Eq. (2). On the other hand,
Eq. (3) establishes that an increase (decrease) in the government spending raises (lowers)
the level of debt, which in turn increases (decreases) the level of activity of the economy
through Eq. (1). Everything else constant, the ultimate result is an increase (decrease) in the
inflation rate by Eq. (2). Notice also that a high inflation rate has corrosive effects on the
income coming from public bonds, as argued by Kirsanova et al. (2005).
Equations (1), (3), and (2) define the basic equilibrium conditions of the model. The op-
timization problems of Sect. 3closes the model by deriving optimal rules for both monetary
policy (interest rate rule) and fiscal policy (government spending rule).
3The hat notation is used to denote deviations from the steady state in logarithm form.
Ann Oper Res (2013) 206:341–366 345
2.1 Game theoretic approach
Monetary and fiscal authorities interact with each other in order to minimize their respec-
tive loss functions. We use game theory models to analyze such interactions. The games
analyzed here have two individual players, namely monetary authority (central bank) and
fiscal authority (treasury). Each player has his own instrument, represented by the interest
rate (i) and government spending (g). If players act independently of each other, then we
have a non-cooperative game, while if they coordinate their actions, we have a cooperative
We consider three different scenarios where the interactions between fiscal and monetary
authorities take place.
2.1.1 Normal form game
When monetary and fiscal policymakers set their instruments simultaneously and non-
cooperatively, we model this situation using a normal form game. In general, a normal form
game is described by the set of players in the game, a set of actions for each player in the
game, and for each player a utility function that assigns a real value to every possible way the
game can be played; the higher the value of the utility function, the better the outcome of the
game for the player. In our case, there are two players: the fiscal and monetary authorities.
The fiscal authority chooses a level of government spending (g) and the monetary authority
chooses the level of interest rate (i). Both players try to minimize their loss function. We
consider the most well-known solution in game theory, the so-called Nash equilibrium of
the game. Intuitively, a pair of interest rate and government spending is a Nash equilibrium
if none of the players can unilaterally deviate from the equilibrium and obtain some gain.
2.1.2 Extensive form game
When the fiscal and monetary authorities move sequentially, we model this situation using an
extensive form game. In general, an extensive form game is described by a game tree where
in each node of the tree a player chooses one of the available actions which are described
by the branches of the tree. We consider only games with perfect information where each
player knows the history of the game each time he moves. A utility value for each player
is associated to each final node of the tree. In economics, if there are only two players and
each one of them moves only once, the player who moves first is known as the Stackelberg
leader and the player who moves last is known as the follower. We use the solution concept
which in game theory is known as subgame perfect equilibrium. Intuitively, in such solution
concept the game is solved from the end of the tree to the beginning. We consider that each
player (fiscal and monetary authorities) acts as the Stackelberg leader and anticipates the
response from the other player.
2.1.3 Cooperative game
When monetary and fiscal policymakers set their instruments simultaneously but in a coop-
erative way in order to pursue a common objective of maximizing social welfare, we model
the situation as a cooperative game.
The cooperation mechanism between the fiscal and monetary authorities occurs indi-
rectly when both authorities associate a positive weight on their instrumental variables. This
mechanism permits a direct adjustment to ongoing actions taken by the other authority. The
authorities face a common optimization problem, i.e. they try to minimize a common loss
346 Ann Oper Res (2013) 206:341–366
3 Fiscal and monetary policy games
In this section, we derive the optimal reaction functions for different regimes of coordina-
tion. The monetary and fiscal authorities minimize their loss functions subject to the equi-
librium conditions of the economy. The authorities solve each optimization problem and
commit themselves to the optimal policy rules, having no incentive to deviate from them.
The rules present relevant properties of time consistency and timelessness. The former char-
acteristic is due to commitment, and the latter hinges on the fact that the monetary and fiscal
authorities need only be committed to determine policies at the later dates by rules that are
optimal from a similar perspective. As stressed by Damjanovic et al. (2005), the timeless
optimal policy is the policy that these authorities would have decided upon for the current
period had such a decision been taking infinitely far in the past.
The technical tools considered throughout this paper follow the general linear-quadratic
policy approach introduced by Giannoni and Woodford (2002a), with applications in Gian-
noni and Woodford (2002b). This approach is widely used in the monetary policy literature.
Particularly, Giannoni and Woodford (2002a) justify the use of this approach since (a) the
policy rule should be consistent with the desired equilibrium, which is a determinate equi-
librium under commitment; (b) the policy rule should be time-invariant and refer only to the
evolution of target variables which represent the authority’s stabilization goals; and (c) the
derived policy rule should continue to be optimal no matter what the statistical properties of
the exogenous disturbances hitting the economy are. Appendix A provides more details on
this technique.
3.1 A normal form game between fiscal and monetary policymakers
The monetary authority, represented by the central bank, tries to minimize a current period
quadratic loss function, with positive weights γπ,γx,andγion deviations of inflation from
the target (zero), output gap, and deviations of the interest rate from the equilibrium rate
(i), such that:
subject to the equilibrium conditions of the economy.
Thus, the monetary authority’s problem can be written as:
subject to (4)
Notice that the equilibrium conditions can be represented by Eqs. (1), (2)and(3). However,
under the current solution, there is no interaction between fiscal and monetary policies,
and the monetary authority takes as given the fiscal variables, which are exogenous to his
choices. Therefore, Eq. (3) is excluded because it defines the dynamics of the debt and the
Ann Oper Res (2013) 206:341–366 347
fiscal side of the economy.4A similar reasoning can be applied to equivalent policy problems
discussed ahead. The Lagrangian for this problem is:5
+Λ1,t (ˆxt−ˆxt+1+σ(ˆ
+Λ2,t tκˆxtβπt+1νt)
where Λ1,t and Λ2,t are the Lagrange multipliers associated to the constraints in period t.
See Appendix Bfor an explanation on how to derive the results. The first order conditions
yield the following equations:
1,t1+Λ2,t Λ2,t 1=0,
ˆxt=γxˆxt+Λ1,t β1Λ1,t1κΛ2,t =0,
1,t =0.
Isolating and substituting the Lagrange multipliers we obtain the following optimal nom-
inal interest rate rule:6
where the coefficients are Γ0=σκ
and Γx,1=γxσ
The rule (7), which the central bank commits to follow, has contemporaneous and lagged
responses to the output gap. Additionally, it encompasses a history dependence since it de-
pends on past interest rates. The response is inversely related to the size of β. Therefore,
the more importance consumers attach to future variables, the stronger the monetary pol-
icy leverage is. Notice that the steeper the slope of the Phillips curve, measured by κ,the
stronger the interest rate response to inflation deviations from the target. On the other hand,
an increase in the weight placed on interest rate deviations, γi, diminishes the interest rate
reaction to inflation and output gap deviations. The elasticity of intertemporal substitution,
σ, also plays an important role in the monetary authority reaction function. For instance,
a higher value of σimplies stronger responses of the interest rate to deviations in both infla-
tion rate and output gap.
The fiscal side resembles the monetary one, with the difference being that the fiscal au-
thority (treasury) takes into account government spending. So, the period loss function as-
sumes the following form:7
4Equation (3) might bring on a multiplier effect into the other equations, which is neglected under the current
5Note that the dating of the expectations operator captures the idea of the policy maker choosing a rule ex-
ante which will be followed in the future. As we have a solution under commitment, the Lagrangian is solved
for expectations at time zero, which characterizes the time when the rule was defined, thereafter followed
without deviations. Thus, we removed the expectations operator on both inflation and output gap at t+1.
6This solution coincides with that proposed by Woodford (2003).
7Kirsanova et al. (2005) and Dixit and Lambertini (2000) use a similar loss function.
348 Ann Oper Res (2013) 206:341–366
where ρπ,ρx,andρgare positive weights placed on deviations of inflation rate, output
gap, and government spending, respectively. The debt does not enter the loss function. The
reason relies on the fact that if the fiscal policy feeds back on debt with a large coefficient,
then it tends to be welfare-reducing, since the economy will exhibit cycles and increase the
volatility of both inflation and output (Kirsanova et al. 2005).
The fiscal authority’s problem is to solve:
subject to (8)
(1), (2)and(3).
The fiscal authority’s Lagrangian is
+Λ1,t (ˆxt−ˆxt+1+σ(ˆ
+Λ2,t tκˆxtβπt+1νt)
+Λ3,t (ˆ
The associated first order conditions are:
1,t1+Λ2,t Λ2,t 1=0,
ˆxt=ρxˆxt+Λ1,t β1Λ1,t1κΛ2,t +Λ
3,t =0,
ˆgt=ρgˆgtΛ3,t =0,
bt=−αΛ1,t +Λ3,t 1+iβEt3,t+1)=0.
Isolating and substituting for the Lagrangian multipliers, we have the optimal nominal
government spending rule:
where the coefficients are: Θπ,0=ρπακ
βB ,Θg,+1=(1+i)β
ρgB. Additionally, A=1σκ +1
β+1+(1+i)),B=((1+i)(σ κ α +
1+β) +α+1).
According to Eq. (11), which the fiscal authority commits to follow, fiscal policy feeds
back on current inflation, current and past output gap, and lagged and expected government
spending. The rule encompasses a forward and backward history dependence since the gov-
ernment spending responds to past and future government spending. Notice that increases
in the weight placed on government spending ρgreduces the reaction to inflation and output
gap deviations.
3.2 Stackelberg leadership
We now address the equilibrium which emerges when the fiscal (monetary) authority moves
first, as a Stackelberg leader, anticipating the response from the monetary (fiscal) authority.
The leader takes into account the follower’s optimal policy, whereas the follower’s optimal
policy remains as a Nash equilibrium solution.
Ann Oper Res (2013) 206:341–366 349
Consider, first, the loss function for the fiscal authority acting as leader. We have the
following problem:
subject to (12)
(1), (2), (3)and(7).
The corresponding Lagrangian might be written as:
+Λ1,t (ˆxt−ˆxt+1+σ(ˆ
+Λ2,t tκˆxtβπt+1νt)
+Λ3,t (ˆ
+Λ4,t (ˆ
The associated first order conditions are:
1,t1+Λ2,t Λ2,t 1Γπ,0Λ4,t =0,
ˆxt=ρxˆxt+Λ1,t β1Λ1,t1κΛ2,t +Λ
3,t Γπ,0Λ4,t +βΓx,1Et4,t+1)=0,
ˆgt=ρgˆgtΛ3,t =0,
bt=−αΛ1,t +Λ3,t 1+iβEt3,t+1)=0.
This optimization problem cannot be solved analytically. Thus, we implement the numer-
ical solution proposed by Juillard and Pelgrin (2007), where a timeless-perspective solution
is derived according to Woodford (2003). The next section will provide further details on
such a problem.
On the other hand, when acting as a leader, the monetary authority aims to minimize:
subject to (15)
(1), (2)and(11).
The corresponding Lagrangian is given by:
+Λ1,t (ˆxt−ˆxt+1+σ(ˆ
+Λ2,t tκˆxtβπt+1νt)
+Λ3,t (ˆgt+Θπ,0πtΘg,1ˆgt1+Θg,2ˆgt2
The implied first order conditions are:
350 Ann Oper Res (2013) 206:341–366
1,t1+Λ2,t Λ2,t 1+Θπ,0Λ3,t =0,
ˆxt=γxˆxt+Λ1,t β1Λ1,t1κΛ2,t +Θx,0Λ3,t βΘx,1Et3,t+1)=0,
1,t =0.
Likewise, there is no analytical solution for this problem. The numerical solution, based
on Juillard and Pelgrin (2007), is discussed in the next section.
3.3 Cooperation between policymakers
Here we analyze the outcome which emerges when the fiscal and monetary policymakers
cooperate with each other in pursuing a common objective. This means that the fiscal (mone-
tary) authority takes into account the monetary (fiscal) reaction function. Under cooperation,
both fiscal and monetary authorities face a common optimization problem:
subject to (18)
(1), (2)and(3),
where ξπ=γπ+ρπ,ξx=γx+ρx,ξi=γiand ξg=ρg. That is, the positive weights placed
on the deviations of inflation and output gap are the sum of the weights placed by each
authority on those variables, while the weights on interest rate and government spending
deviations remain unchanged.
The Lagrangian for this problem is given by:
+Λ1,t (ˆxt−ˆxt+1+σ(ˆ
+Λ2,t tκˆxtβπt+1νt)
+Λ3,t (ˆ
with the following first order conditions:
1,t1+Λ2,t Λ2,t 1=0,
ˆxt=ξxˆxt+Λ1,t β1Λ1,t1κΛ2,t +Λ
3,t =0,
1,t 3,t =0,
ˆgt=ξgˆgtΛ3,t =0.
The resulting optimal nominal interest rate rule is:
Ann Oper Res (2013) 206:341–366 351
where the coefficients are: Γ0=σκ
and Γx,1=ξπσ
The resulting optimal government spending rule is given by:
where the coefficients are defined as: Θπ,0=κξπ
σC ,Θi,1=(κξi
βC +ξi
βσC +ξi
βσC ,Θx,0=Θx,1=ξx
βC +g
βσC +g
σC +ξ
βσC . Finally, C=
The above rules resemble the ones obtained in the normal form game. However, in both
equations, there are cross responses to the other authority policy instrument. That is, the
optimal nominal interest rule responds to current and lagged government spendings, while
the optimal government spending rule reacts to current and lagged interest rates. The coop-
eration occurs via those cross responses. One can also notice that, in the fiscal rule, there
is no response to future government spending, possibly because cooperation eliminated the
forward looking feature of that policy rule.
4 Numerical approach
4.1 Simulation of the Nash equilibrium
The model’s equilibrium is described by ten equations, being five endogenous and five ex-
ogenous processes. The endogenous variables are (ˆxt
it,ˆgt)while the exogenous
ones are (ˆrn
t). Following the definitions from previous sections, the set of
equations characterizing the equilibrium can be represented as:
IS curve: ˆxt=Etˆxt+1σ(ˆ
Phillips curve: πt=κˆxt+βEtπt+1+νt
Public debt: ˆ
Monetary rule: ˆ
Fiscal rule: ˆgt=−Θπ,0πt+Θg,1ˆgt1Θg,2ˆgt2+Θg,+1Etˆgt+1Θx,0ˆxt+Θx,1ˆxt1+Ot
Demand shock: ˆrn
Supply shock: νt=χννt1+εν
Debt shock: ηt=χηηt1+εη
Monetary policy shock: Ξt=χΞΞt1+εΞ
Fiscal policy shock: Ot=χOOt1+εO
As usual, the exogenous processes are assumed to follow AR(1)stationary processes.
The AR(1)process reflects, relatively well, the persistence that exists in many macroeco-
nomic time series. Moreover, each εjis independent and identically distributed with zero
mean and variance σ2
j. Based on Brazilian data, we set χj=0.9 in order to capture the high
persistence of those shocks and σ2
j=0.04, j. At this point, we do not allow for nonzero
correlations among the shocks. The DYNARE for MATLAB was used to solve for the ra-
tional expectations model.8
8See Laffargue (1990), Boucekkine (1995), Juillard (1996), Collard and Juillard (2001a,2001b) for details
on how the model can be solved.
352 Ann Oper Res (2013) 206:341–366
4.2 Simulation of the Stackelberg solution
The Stackelberg solution, as stressed earlier, is numerically solved under commitment fol-
lowing Juillard and Pelgrin (2007) and Woodford (2003). The structural equations, which
represent constraints on possible equilibrium outcomes under Stackelberg leadership, are
represented by a system of the form:
where ztis a nz×1 vector of non-predetermined (forward looking) variables, Ztis a nZ×1
vector of predetermined (backward looking) variables, utis a k×1 vector of policy in-
struments, and εt+1is a nZ×1 vector of zero-mean uncorrelated shocks. The number of
rows of each matrix is, then, n=nz+nZ. The matrices Aand Bare functions of structural
The above representation allows us to deal with all structural equations in matrix format.
The intertemporal loss function can be written as:
where, for the sake of simplicity, we can define the vector xt=(Zt,z
The matrix Wis Wxx Wxu
xu Wuu (25)
where the matrices Wxx and Wuu are, without loss of generality, assumed to be symmetric.
The Lagrangian that follows from (23)and(24) is given by:
where ξt+1=t+1,z
t+1Ezt+1)and ρt+1is a vector of multipliers. Subsequently, we
should take the first order conditions with respect to ρt+1,xt,andut, such that
In0nxk 0nx n
0nxn 0nx k βA
0kxn 0nxk B
βWxx βWxu In
xu Wuu 0kxn
where ρ0=0andx0given.
Klein (2000) shows how to solve the above via generalized Schur decomposition. How-
ever, the optimal Ramsey policy, as previously described, is time inconsistent. The time in-
consistency comes from the fact that, in the current period, the policymaker sets the optimal
policy after the private agents’ expectations realization, such that he might have an incentive
to re-optimize in the future. The method proposed by Woodford (2003) to overcome this
issue was numerically implemented by Juillard and Pelgrin (2007). They generalize Wood-
ford’s timeless perspective solution by computing initial values for the Lagrange multipliers.
A timeless perspective hinges on the fact that the equilibrium evolution from time t=t0on-
ward is optimal, subject to the constraint that the economy’s initial evolution be the one
Ann Oper Res (2013) 206:341–366 353
associated with the policy in case (Woodford 2003). That is, the policymaker renounces the
possibility of setting the Lagrange multipliers to zero if he reoptimizes later on (Juillard and
Pelgrin 2007).
Considering now a timeless perspective solution, the Lagrange multipliers can be defined
Further, inserting the above restriction and adopting a timeless perspective policy,
namely, that the choice of the Lagrange multipliers ρ0is governed by the same rule from
time t=t0onwards, we have the Lagrangian for the timeless perspective policy
where y0=(x
0,0). The first order conditions remain as before:
In0nxk 0nx n
0nxn 0nx k βA
0kxn 0nxk B
βWxx βWxu In
xu Wuu 0kxn
where ρ0=0andx0given.
The non-predetermined variables of y0are selected such that (i) the function of the prede-
termined variables exists in the initial period, and (ii) there is a solution for the optimization
problem under the following condition y0=y0,fort>0. The Stackelberg problem is, then,
solved with the help of MATLAB.
4.3 Simulation of the cooperative solution
The cooperative case is similar to the one obtained in the normal form game. The major
differences are in the optimal policy rules (fiscal and monetary). Additional variables enter
those equations modifying thus the optimal responses to other variables.
The equilibrium of the model is described by ten equations, where five are endoge-
nous and the other five are exogenous processes. The endogenous ones are represented by
it,ˆgt)while the exogenous ones are (ˆrn
t). Next, we describe each
one of those equations.
IS curve: ˆxt=Etˆxt+1σ(ˆ
Phillips curve: πt=κˆxt+βEtπt+1+νt
Public debt: ˆ
Monetary rule: ˆ
Fiscal rule: ˆgt=−Θπ,0πt+Θi,0(ˆ
Demand shock: ˆrn
Supply shock: νt=χννt1+εν
Debt shock: ηt=χηηt1+εη
Monetary policy shock: Ξt=χΞΞt1+εΞ
Fiscal policy shock: Ot=χOOt1+εO
354 Ann Oper Res (2013) 206:341–366
Tab le 1 Calibration of the parameters
Parameter Definition Value Reference
σIntertemporal elasticity of
substitution in private
5.00 Nunes and Portugal (2009)
αSensitivity of output gap to the
0.20 Pires (2008)
κSensitivity of inflation rate to
the output gap
0.50 Gouvea (2007), Walsh (2003)
βSensitivity of agents to the
inflation rate
0.99 Cavallari (2003), Pires (2008)
iNatural rate of interest 0.07 Barcelos Neto and Portugal (2009)
bSteady state debt value 0.20 Kirsanova et al. (2005), Nunes and
Portugal (2009)
Tax rate 0.26 Kirsanova et al. (2005), Nunes and
Portugal (2009)
In the cooperative solution, as in the Nash equilibrium one, the exogenous processes are
assumed to follow stationary AR(1)representations, where each εjis independent and iden-
tically distributed with zero mean and constant variance σ2
j. The same calibration described
in Table 1is applied here. The simulation was carried on in Dynare for MATLAB.
5 Numerical results
In order to evaluate the performance of the alternative regime of coordination, we simulate
the models encompassing the Phillips curve, IS curve, government budget constraint, and
optimal monetary and fiscal rules. Additionally, we provide an overview on the social losses
generated by the distinct monetary and fiscal policy arrangements, and compute impulse
response functions. The calibration exercise is meant for the Brazilian economy in the period
after the implementation of the Real Plan.9Following most of the literature, we assume that
each period corresponds to one quarter of a year. The calibrated parameters, along with the
respective sources, are reported in Table 1.
One of the major goals of the simulation is to obtain variances of the variables under
the optimal trajectories, allowing for the computation of the expected social loss associated
to each regime of coordination. As a robustness check, we calculate and plot social losses
generated by alternative monetary and fiscal policy decisions, i.e. by varying the weights
placed on the target variables. We also compute impulse response functions to analyze how
the dynamics of the model behave under shocks of demand, supply, debt, monetary policy,
and fiscal policy. Therefore, the analysis will focus on efficient aspects for macroeconomic
5.1 Social loss analysis
The social loss is defined as the sum of the authorities’ expected individual losses, which
can be easily obtained by computing the unconditional variance.10 Taking, for instance, the
9The Real Plan was edited in June 1994.
10See Woodford (2003) for details.
Ann Oper Res (2013) 206:341–366 355
Tab le 2 Loss values for different coefficients under the Nash solution
Variance of
0.50 0.10 12.7452 0.7057 19.1851 27.5664 3.4317 12.9905 4.2008 17.1913
0.50 5.2119 0.2723 7.9440 11.3445 1.4225 5.3084 1.7033 7.0117
0.90 2.7197 0.1369 4.1761 5.9437 0.7486 2.7688 0.8842 3.6500
2.50 0.10 9.6978 2.1892 211.2660 16.3928 11.3685 10.2861 5.6368 15.9229
0.50 2.3218 0.4530 52.7042 4.0432 2.6607 2.4452 1.2729 3.7181
0.90 0.9891 0.1819 22.8264 1.7428 1.1210 1.0389 0.5301 1.5690
5.00 0.10 8.1027 2.9793 414.0482 11.6572 18.6392 8.8767 6.6826 15.5593
0.50 1.5190 0.4980 81.3970 2.2583 3.4490 1.6492 1.1882 2.8374
0.90 0.6059 0.1908 33.0275 0.9111 1.3681 0.6559 0.4654 1.1213
monetary authority period loss function, LM
iti)2, it is easy to
calculate the expected loss for the monetary authority, given by:11
Thus, the social loss is given by LS=LM+LF.
The welfare criterion defines a function which depends upon both monetary and fiscal
social losses. We make use of that criterion to analyze the cooperative solution, which occurs
indirectly when both authorities associate a positive weight on their instrumental variables.
The mechanism permits a direct adjustment to ongoing actions taken by the other authority.
Basically, the problem is to maximize a social utility (welfare) or, on the other hand, to
minimize the social loss function LS, which is defined by LS=LM+LF,thatis,thesum
of the authorities’ individual losses.
The results reported in Tables 2,3,4and 5show the variance of each time series and
the losses of each authority for different values of σand κ. The former parameter is the
intertemporal elasticity of substitution in private consumption and the latter one measures
the sensitivity of the inflation rate to the output gap in the Phillips curve. These parameters
came from Eqs. (1)and(2). The reason for choosing these parameters is that they play a
crucial role in both structural equations and policy rules.
According to Table 2, keeping κunchanged, the increases in σtend to reduce the loss for
the monetary but not for the fiscal authority. A high intertemporal elasticity of substitution in
private spending means a preference for future consumption, namely, the agents are willing
to postpone consumption. Under a higher interest rate, aggregate demand experiences a
shrinkage, reducing the output gap and inflation. The monetary policy is more effective,
leading to smaller monetary loss under a higher σ. The fiscal policy also experiences a
similar decrease in loss, but not for all parameter combinations.
Turning now to the parameter κ, when it increases for a given σ, both fiscal and monetary
losses decrease. The idea behind a rise in parameter κis a steeper Phillips curve. Thus,
a higher value of κtends to increase the sensitivity of inflation to the output gap, yielding a
negative effect on the loss. It is interesting to notice that when σ=5.00 and κ=0.90, we
11In order to simplify the notation, we will not distinguish between social loss and expected social loss.
356 Ann Oper Res (2013) 206:341–366
Tab le 3 Loss values for different coefficients under the Stackelberg solution: Fiscal leadership
Variance of
0.50 0.10 0.0355 0.0077 0.0318 0.0612 0.0034 0.0376 0.0169 0.0545
0.50 0.0219 0.0066 0.0183 0.0365 0.0036 0.0236 0.0124 0.0360
0.90 0.0149 0.0052 0.0120 0.0241 0.0035 0.0163 0.0092 0.0255
2.50 0.10 0.0311 0.0677 0.1868 0.0213 0.0087 0.0481 0.0763 0.1244
0.50 0.0142 0.0311 0.0238 0.0086 0.0034 0.0220 0.0350 0.0570
0.90 0.0080 0.0173 0.0071 0.0047 0.0017 0.0123 0.0195 0.0318
5.00 0.10 0.0296 0.1147 0.1973 0.0095 0.0072 0.0583 0.1227 0.1810
0.50 0.0121 0.0427 0.0148 0.0038 0.0020 0.0228 0.0459 0.0687
0.90 0.0064 0.0217 0.0057 0.0021 0.0010 0.0118 0.0234 0.0352
Tab le 4 Loss values for different coefficients under the Stackelberg solution: Monetary leadership
Variance of
0.50 0.10 0.0325 0.0051 1.1690 0.0001 0.0486 0.0338 0.0176 0.0514
0.50 0.0143 0.0119 0.3080 0.0018 0.0337 0.0173 0.0185 0.0358
0.90 0.0073 0.0103 0.1555 0.0050 0.0196 0.0099 0.0139 0.0238
2.50 0.10 0.0325 0.0050 1.1446 0.0013 0.0491 0.0338 0.0175 0.0513
0.50 0.0132 0.0138 0.2759 0.0009 0.0353 0.0167 0.0203 0.0370
0.90 0.0055 0.0132 0.1352 0.0001 0.0212 0.0088 0.0165 0.0253
5.00 0.10 0.0326 0.0050 1.1389 0.0015 0.0490 0.0339 0.0176 0.0515
0.50 0.0133 0.0137 0.2690 0.0018 0.0353 0.0167 0.0202 0.0369
0.90 0.0055 0.0133 0.1305 0.0006 0.0213 0.0088 0.0166 0.0254
obtain the lowest loss (LS=1.1213), meaning that social welfare is maximized under that
parameter combination.
The results reported in Table 3resembles the Nash equilibrium case when we consider
variations in κ. On the other hand, variations in σdo not have clear effects, given that there
are decreases and increases in the monetary loss depending on the value of κ.Thecombi-
nation of σ=0.50 and κ=0.90 provides the lowest loss (LS=0.0255). In addition, the
losses for the fiscal leadership are lower than the losses for the Nash equilibrium, suggesting
that the former is more efficient.
Table 4shows losses similar to what was observed under the fiscal leadership. However,
increases in σhave lower impacts on the fiscal loss. Once again, the pair of values σ=0.50
and κ=0.90 provides the lowest loss (LS=0.0238). Comparing all tables, that value is the
global minimum, which was obtained under a monetary leadership solution.
The coordination scheme presented in Table 5has characteristics similar to the Nash
equilibrium outcome. Thereby, the same analysis can be employed here. The combination of
Ann Oper Res (2013) 206:341–366 357
Tab le 5 Loss values for different coefficients under the cooperative solution
Variance of
0.50 0.10 12.1107 0.7355 29.9229 30.4118 4.0704 12.3706 4.1296 16.5002
0.50 4.4734 0.2630 11.2059 11.3251 1.5229 4.5675 1.5184 6.0859
0.90 2.2562 0.1300 5.7000 5.7413 0.7742 2.3030 0.7637 3.0667
2.50 0.10 7.8141 1.6191 364.3679 15.3638 11.8087 8.2573 4.6354 12.8927
0.50 0.1146 0.1094 0.5639 0.1531 0.4110 0.1423 0.1750 0.3173
0.90 1.6526 0.3492 72.2684 3.1152 2.4879 1.7477 0.9862 2.7339
5.00 0.10 5.6878 1.9734 769.0163 9.0333 17.8931 6.2037 5.0057 11.2094
0.50 1.0476 0.3632 112.2076 1.4691 3.0751 1.1421 0.9019 2.0440
0.90 0.4451 0.1524 44.5084 0.6046 1.2813 0.4847 0.3790 0.8637
Fig. 1 Social losses for different weights under the Nash solution
σ=2.50 and κ=0.50 leads to the minimum value for the loss function (LS=0.3173). This
performance, however, is well above the smallest loss obtained under a monetary leadership
in the Stackelberg game.
According to the smallest social loss criterion, the policy regimes might be ordered as
(1) monetary leadership, (2) fiscal leadership, (3) cooperative solution, and (4) Nash equilib-
rium solution. Thus, when the monetary authority moves first as a Stackelberg leader we get
the best scheme of coordination between the authorities. In addition, both Stackelberg so-
lutions are superior to the remaining ones. Finally, comparing the cooperative and the Nash
equilibrium solutions, we can note that the former regime is more efficient in minimizing
the social loss.
5.2 Sensitivity analysis
As a robustness check, we evaluated social losses generated by the three mechanisms of
coordination discussed in the previous section. In each case, it is assumed that the economy
is hit by a supply shock and the weights placed in output gap, inflation, and government
spending vary from 0.10 to 1.50, and in interest rate from 0.05 to 1.00. The resulting losses
are shown in Figs. 1,2,3and 4.
358 Ann Oper Res (2013) 206:341–366
Fig. 2 Social losses for different weights under the fiscal leadership solution
Fig. 3 Social losses for different weights under the monetary leadership solution
Under the Nash equilibrium solution, Fig. 1shows that the monetary loss increases pro-
portionately to the relative weights placed by the central bank on output gap and interest rate.
This is due to the fact that the society dislikes inflation more than the other two variables.
Notice that the distaste for interest rate fluctuations is the smallest, given that its impact on
the social loss is the strongest. Differently, the fiscal loss directly increases with the size
of the relative weights placed by the fiscal authority on government spending and inflation
stabilization. The reason is because the output gap is an important variable for the fiscal
policy. So, the society would prefer that the fiscal authority give more relative importance
to output gap stabilization. Here, changing the relative weight on the government spending
stabilization has the greater impact on the fiscal loss.
Furthermore, Fig. 2reveals that under a fiscal leadership in the Stackelberg solution, the
monetary loss is very sensitive to the relative weight attached by the central bank to output
gap stabilization. On the other hand, the fiscal loss presents a high sensitivity to the weight
on inflation stabilization. Note that Figs. 1and 2strengthen the different consequences on
the loss under the Nash and Stackelberg (fiscal leadership) solutions.
Subsequently, Fig. 3demonstrates that, under a monetary leadership in the Stackelberg
solution, the monetary loss behaves similarly to the case under fiscal leadership when the
central bank changes the relative weights on the output gap and interest rate. The fiscal loss
under a monetary leadership is more sensitive to the relative weight placed on government
Ann Oper Res (2013) 206:341–366 359
Fig. 4 Social losses for different weights under the cooperative solution
Fig. 5 Impulse responses to a supply shock under the monetary leadership solution
Finally, the losses shown in Fig. 4under the full cooperative solution are quite similar to
the Nash equilibrium case, but to a lower degree. In general, the Nash equilibrium and fully
cooperative solutions display closer responses when the relative weights placed on target
variables are changed.
5.3 Impulse response analysis
We limit our attention to the monetary leadership solution since it is the best scheme of
coordination according to the loss analysis. The impulse responses to alternative exogenous
shocks are presented in Figs. 5,6and 7. The responses of the variables are for one standard
deviation supply, demand or fiscal shock under the monetary leadership solution.
Figure 5shows the effects of a supply shock under monetary leadership. The immediate
effect of the shock is a rise in inflation, which leads the monetary authority to increase the
interest rate. A peak of that policy is reached in the ninth quarter, when the interest rate
360 Ann Oper Res (2013) 206:341–366
Fig. 6 Impulse responses to a demand shock under the monetary leadership solution
Fig. 7 Impulse responses to a fiscal shock under the monetary leadership solution
starts going back to the equilibrium. Due to the strong response of the monetary policy, the
output gap falls and pushes the government expenditure to a lower level. The debt response
is hump-shaped because it follows movements in the interest rate, reaching a peak after six
Ann Oper Res (2013) 206:341–366 361
The effects of a demand shock under monetary leadership are shown in Fig. 6. On impact,
the shock pushes the output gap upwards, which in turn increases inflation and leads the
monetary authority to raise the interest rate. The peak in the interest rate is reached in the
fourth quarter and convergence to the equilibrium is faster than under a supply shock. The
debt and government spending are less volatile when compared to the supply shock.
A positive fiscal shock, displayed in Fig. 7, increases government spending, debt, and the
output gap. In addition, that shock is inflationary, given that there is a rise in inflation on
impact. The response of the monetary policy is delayed, but the increase in the interest rate
is sufficient to bring the economy back to equilibrium. Also, the debt converges slower than
the government spending due to the effects of high interest rates.
6 Concluding remarks
This paper has applied the game theory approach to a conventional macroeconomic opti-
mization problem to analyze the performance of alternative coordination schemes, repre-
sented by the Nash equilibrium solution, Stackelberg leadership, and the cooperative solu-
tion, in the interaction between fiscal and monetary policies. The comparisons among the
distinct regimes were made in terms of social loss, sensitivity to selected parameters, and
impulse response functions. Whenever possible, analytical solutions were derived for opti-
mal monetary and fiscal rules. In the Stackelberg case, however, due to the complexity of
the solution, only a numerical simulation was obtained.
The numerical approach provided evidence of relative superiority for the monetary lead-
ership in the Stackelberg solution. Thus, when the monetary authority moves first, as a
Stackelberg leader, taking into account the optimal fiscal policy obtained under the Nash
equilibrium solution, one reaches the smallest social loss. This monetary leadership might
be associated to the existence of a monetary dominance in the Brazilian economy during
the recent period. This evidence is supported by empirical findings provided by Tanner and
Ramos (2002), Fialho and Portugal (2005), Gadelha and Divino (2008), among others.
In particular, according to our results, the monetary leadership led to the lowest social
loss. A sensitivity analysis executed by varying the relative weights placed by the monetary
and fiscal authorities on their target variables showed that the Nash equilibrium and cooper-
ative solutions yielded more uniform responses. On the other hand, the monetary leadership
revealed a strong distaste for inflation by the Brazilian society. The impulse response func-
tions, computed for the best coordination scheme, indicated strong reactions of the monetary
authority to inflationary pressures. In addition, there is a clear inflationary effect coming
from fiscal shocks. Under the Stackelberg solution, the time series presented low volatility
and faster convergence to the equilibrium after the alternative exogenous shocks.
For future works, it would be interesting to analyze the performance of coordination
regimes under commitment and discretion, to apply the framework to a bargain problem in
a more complex environment and to extend the model to a block of countries, particularly
in South America, involving a monetary integration with common fiscal targets.
Acknowledgements J.A. Divino and H. Saulo acknowledge CNPq for the financial support. L.C. Rêgo
acknowledges financial support from FACEPE under grants APQ-0150-1.02/06 and APQ-0219-3.08/08, and
from MCT/CNPq under grants 475634/2007-1 and 306358/2010-7.
Appendix A
In this appendix we describe the general linear-quadratic policy approach introduced by
Giannoni and Woodford (2002a) with applications by Giannoni and Woodford (2002a), to
362 Ann Oper Res (2013) 206:341–366
derive an optimal monetary policy rule. Note that this approach can easily be extended to
the fiscal optimization problems discussed in this paper.
Woodford (2003, pp. 23–24) argues that standard dynamic programming methods are
valid only for optimization problems that evolve in response to the current action of the
controller. Hence, they do not apply to problems of monetary stabilization policy since the
central bank’s actions depend on both the sequence of instrument settings in the present
time and the private-sector’s expectations regarding future policies. A direct implementa-
tion of the maximum principle is not indicated, since we have discrete-time problems with
conditional expectations on some variables which affect the solution under commitment.
A.1 General linear-quadratic policy problem
Giannoni and Woodford (2002a) deal with policy problems in which the constraints for the
various state variables can be represented by a system of linear (or log-linear) equations, and
in which a quadratic function of these variables can be used to represent the policymaker’s
objectives. In general, the optimal policy rules considered by the authors take the form
φ, (31)
where itis the policy instrument, ¯ztand ¯
Ztare the vectors of nonpredetermined and prede-
termined endogenous variables (e.g., the output gap forecast Etxt+kmay be an element of
¯zt), ¯stis a vector of exogenous state variables, and φi,φz,φZ,andφs, are vectors of coeffi-
cients and ¯
φis a constant. As pointed out by Buiter (1982), a variable is nonpredetermined
if and only if its current value is a function of current anticipations of future values of en-
dogenous and/or exogenous variables. It is predetermined if its current value depends only
on past values of endogenous and/or exogenous variables.
The discounted quadratic loss function is assumed to have the form
where t0stands for the initial date at which a policy rule is adopted, 0 <β<1 denotes the
discount factor, and Ltspecifies the period loss, that is,
where τtis a vector of target variables, τis its corresponding vector of target values, and
Wis a symmetric, positive-definite matrix. The target variables are assumed to be linear
where yt≡[Ztztit],Ztis a subset of the predetermined variables ¯
Zt,ztis a subset of the
vector of nonpredetermined endogenous variables ¯zt,andTis a matrix of coefficients. It is
assumed that Ztencompasses all of the predetermined endogenous variables that constrain
the possible equilibrium evolution of the variables ZTand zTfor Tt.Also,st, i.e. the sub-
set of exogenous states, encompasses all of the exogenous states which possess information
on the possible future evolution of the variables ZTand zTfor Tt.
The endogenous variables ztand Zttake the form
Ann Oper Res (2013) 206:341–366 363
where each matrix has n=nz+nZrows, nzand nZdenotes the number of nonpredeter-
mined and predetermined endogenous variables, respectively. Note that we may partition
the matrices as
E,A=A11 A12
A21 A22 ,B=0
where the upper and lower blocks have nZand nzrows, respectively. The zero restrictions
in the upper blocks refer to the fact that the first nZequations define the elements of Ztas
elements of ztjfor some j1. It is assumed that A22 is non-singular in order to let the
last nzequations be solved for ztas a function of Zt,st,it,andEtzt+1. In addition, B2is not
zero in all elements, resulting in an instrument with some effect.
Definition (Giannoni and Woodford 2002a) A policy rule that determines a unique non-
explosive rational expectations equilibrium is optimal from a timeless perspective if the
equilibrium determined by the rule is such that (a) the nonpredetermined endogenous
variables ztcan be expressed as a time-invariant function of a vector of predetermined
variables ¯
Ztand a vector of exogenous variables ¯st; that is, a relation of the form zt=
Zt+fs¯st, applies for all dates tt0; and (b) the equilibrium evolution of the en-
dogenous variables {yt}for all dates tt0minimizes (32) among the set of all bounded
processes, subject to the constraints implied by the economy’s initial state Zt0, the require-
ments for rational expectations equilibrium (i.e., the structural equations (35)), and a set of
additional constraints of the form
on the initial behavior of the nonpredetermined endogenous variables.
According to Woodford (1999), the Lagrangian for the minimization problem can be
written as
where ˜
A≡[AB]and ˜
I0].NotethatL(yt)denotes the period loss Ltexpressed as a
quadratic function of ytand ϕt+1denotes the vector of Lagrange multipliers related to the
constraints (35). Applying the law of iterated expectations, the conditional expectation can
be eliminated from the term Etzt+1in these constraints. Set
and insert the term
into (37), where ξ
t0Zt0represents the constraints imposed by the given initial values Zt0,and
Ezt0represents the constraints (36). Finally, differentiating the Lagrangian (37) with
respect to the endogenous variables yt, we yield the first-order conditions
for each tt0. Solving (39) under some assumptions (Giannoni and Woodford 2002a), it is
possible to obtain a policy rule of the form expressed in (31).
364 Ann Oper Res (2013) 206:341–366
Appendix B
This appendix explains the solution method used to derive the optimal nominal interest rate
rulegivenby(7). Note that a similar procedure can be used to derive the other optimal rules.
The monetary authority minimizes the constrained loss function given by:
+Λ1,t (ˆxtEtˆxt+1+σ(ˆ
+Λ2,t tκˆxtβEtπt+1νt)
where the constraints include Eqs. (1)and(2), and Λ1,t and Λ2,t are the Lagrange multipli-
In order to write the first-order conditions, we need to differentiate this equation with
respect to the instrument (ˆ
iti)and the state variables πtand ˆxt.Beforemovingforward
we need to consider how to deal with the expectation terms within the constraint. Since this
is a policy under commitment, the dating of the expectations operator captures the idea of
the policymaker choosing an ex-ante rule which will be followed in the future. Hence, the
expectations operator on inflation and the output gap at t+1 are removed. For example, if
the inflation rate which the policymaker sets influences both actual and expected inflation,
then he may directly optimize over the two. The first-order conditions are:
1,t1+βtΛ2,t βt1Λ2,t 1(β) =0,(41)
ˆxt=βtγxˆxt+βtΛ1,t βt1Λ1,t 1βtκΛ2,t =0,(42)
1,t =0.(43)
Isolating Λ1,t in (43) and inserting into (42), we obtain
βσ ˆ
it1iκΛ2,t =0,(44)
where Λ1,t =−γi
iti)and Λ1,t1=−γi
it1i). Repeating the procedure for Λ2,t ,
we can eliminate all the Lagrange multipliers in (41). Then, isolating ˆ
itwe have
where Γ0=σκ
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... We analyse this interaction using the game theory 1 approach, which has already been employed in previous research devoted to the co-dependencies between monetary and fiscal policy (e.g., Saulo et al., 2013). The aim of the article is to investigate how the level of cooperation influences the decision making process in a specific policy mix model. ...
... Thirdly, we consider and analyse a few special cases of the different attitudes of both players to cooperation. We do not make additional assumptions that put the central bank in a privileged position, as is the case in the Stackelberg model, 3 where the central bank is often considered a leader (Fialho & Portugal, 2005;Saulo et al., 2013;Tanner & Ramos, 2003). Despite the lack of these assumptions, we obtain an original result, indicating that it is only up to the central bank whether any elements of cooperation in the interaction of these two players can occur at all and affect the equilibrium levels of the decision variables. ...
... Further, Franta et al. (2011) showed that fiscal policy outcomes improve shortly after the adoption of an inflation-targeting regime, one of the main pillars of which is relatively high central bank independence. Saulo et al. (2013) believe that coordinated monetary and fiscal policies play an important role in improving the welfare of society. Many studies show that in noncooperative models of the monetary and fiscal game, solutions are not optimal and lead to the choice of a non-optimal policy mix. ...
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The objective of this paper is to consider the cooperative game between the central bank and the government in the case of a non-euro country in the European Union or another country in the world that conducts an independent monetary policy and where statutory deficit restrictions were imposed on its budget. The study takes into account two independent players – the government and the central bank – that make autonomous decisions and are responsible for fiscal and monetary policy, respectively. Our mathematical policy mix model is based on the assumption that there exists some level of coordination between these policies. The article aims to analyse how the level of cooperation influences the behaviour of decision-makers in a specific policy mix model. As a result, the government taking into account the central bank’s goals has no impact on the equilibrium of the budget deficit and interest rates. The conclusion about the central bank’s privileged position emerged as a mathematical consequence of the proposed model. This is confirmed by another case where the government does not consider the central bank’s target in its decisions; then, it does not prevent the monetary authorities from influencing the Nash equilibrium level of either decision variable.
... It is concluded that, according to micro-founded social preferences, fiscal leadership policy is the most appropriate model for the UK and Sweden, while for the United States Nash or non-cooperative regime is the most appropriate model. Saulo et al. (2013) analyzed the interaction between a monetary and fiscal policy with Brazilian data within the framework of game theory. In the model where they derived and analyzed the Nash and Stackelberg solutions for a small closed economy, it was found that the lowest social loss occurs when the monetary authority is the leader. ...
... In this framework, behaviors of policymakers are modeled according to alternative leader-follower scenarios. Giannoni and Woodford (2002a), Giannoni and Woodford (2002b) were consulted for the solution of models, and Saulo et al. (2013) for game-theoretical setting. ...
... In this study, the representative economy needed to derive policy rules based on the strategic interaction of monetary and fiscal policymakers is formed based on small-scale open economy models described in Gali and Monacelli, (2005) and (2015) and Çebi (2012). Our intuition for choosing this model is that it contains an open economy setup, unlike Saulo et al. (2013), which inspired us. Besides, the model's factoring of Calvo style nominal price rigidities, distortionary taxation, rule of thumb price-setters, and perfect exchange rate pass-through properties was also effective. ...
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The problem of coordination between policymakers seems to have created fundamental problems related to economic and social costs, targeted inflation, potential growth, and a high budget deficit. To resolve these problems in this framework, it is important to see the results of the interaction between policymakers and to propose an optimal policy strategy. In this study, the interactions between monetary and fiscal policymakers are examined game theoretically within the framework of the New Keynesian model. The strategic interaction between these policymakers is assessed using the DSGE (Dynamic Stochastic General Equilibrium) model for a small open economy. From this point of view, the interaction between policymakers is assessed within the framework of hypothetical scenarios. The optimal monetary and fiscal policies for a small open economy are derived from the leader-follower mechanism solution known as the Stackelberg solution. Optimal Stackelberg policy rules derived for a small open economy contribute to the literature of economics. The performance of the game theoretically derived optimal policy rules is evaluated through dynamic simulation within the framework of counterfactual experiments. The parameters developed for the model are calibrated for the Turkish economy. Dynamic simulation of the models, the impulse response functions, and the social loss analysis shows that the optimal policy mix for the Turkish economy is when the monetary policymaker is the leader, and the fiscal policymaker is the follower.
... This approach is used since it ensures consistency with the desired equilibrium and time. The Lagrangian technique used by Gioanni and Woodford (2002a), Gioanni and Woodford (2002b) and Saulo et al. (2013) is used in this study to solve the optimization problem. This approach is widely used in the literature on monetary policy. ...
... Because of this, the expectation operators on inflation, output gap, and government expenditure are removed. To illustrate, policy authority can optimize both at the same time, when the inflation rate determined by the policymaker can affect both the nominal and expected inflation rate (Saulo et al. 2013). A similar process is followed to derive the other optimal rules. ...
... Then, ω and λ the coefficients are obtained and σ a = 1 is determined as in Çebi (2012). In the monetary and financial loss functions, the parameters of inflation, output, optimal interest and deviation from government spending according to the equilibrium condition of the economy are determined according to the studies of Fragetta and Kirsanova (2010), Çebi (2012), Flotho (2012) and Saulo et al. (2013). In the monetary loss function, the parameter of the deviation of inflation from the target is 1, the parameter of deviation of output from the potential level of is 0.4, and the parameter of the deviation from the equilibrium interest rate is 0.5, according to the equilibrium condition of the economy. ...
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Interactions between the monetary and fiscal policy are analyzed in a game-theoretical framework on the base of the new-Keynesian model. The interactions between policymakers are modeled by using a dynamic stochastic equilibrium model (DSGE) for a small-scale open economy. From this point of view, the interactions between policymakers are evaluated in two different hypothetical scenarios. Optimal policy rules for a small-scale open economy are derived by using Nash Solution (a non-cooperative solution) and cooperative equilibrium. The performances of the derived policy rules are evaluated by comparing counter-factual experiments via dynamic simulation. The model parameters are calibrated for the Turkish economy. Then, the policy mix providing the minimum social loss is obtained. The main finding of dynamic simulations is that cooperative interaction shows better performance in the Turkish economy than non-cooperative interaction.
... Coordination of monetary and fiscal policy contributes to the improvement of stability of the country's financial system too. For example, Badarau and Levieuge (2011), Saulo, Rego, and Divino (2013) and Cui (2016) consider the coordination of monetary and fiscal policy beneficial for the economy. In turn, Stawska, Malaczewski, and Szymańska (2019, 3554-3556), while looking for an equilibrium in the game between the central banks and the government in the EU countries, noticed that in the policy-mix equilibrium model the budget deficit and the interest rate depend on exogenous data such as: core inflation, inflation target or Maastricht deficit limits. ...
ABSTRACT The importance of the decisions made by central banks and governments has been increasing recently, especially in the EU countries. The relationships between short-term interest rates, inflation rates, and public deficits have not been thoroughly described in the literature concerning the recent European cases. It is worth observing how the relationships between the key variables in the field of monetary and fiscal policy behave in various groups of countries, e.g. in countries with low/high General Government deficits or in countries with low high public debt. The aim of the article is to empirically analyse the relationship between interest rates, inflation rates, and public deficits in European countries in the years between 1996–2019. We studied the relationships between interest rates, inflation rates, and public deficits. We turned to dynamic panel data methods (two-step system GMM). First, interest rates and inflation rates have been related following the Taylor-rule direction across the European economies. Second, we have also found a positive relationship between inflation rates and public deficits, but reverting the postulated Sargent and Wallace (1981) hypothesis of seigniorage. Third, deficit and inflation rates have positive relations across European observations but more significantly in the cases of high deficits or with highly indebted economies.
... Within the traditional Tinbergen macroeconomic models, gaming approaches were originally introduced to examine policy outcomes under three basic monetary and fiscal interaction setups: 1) cooperative or fully-coordinated policies pursuing common objectives; 2) simultaneous normal form game or non-cooperative behavior under a Nash equilibrium; and 3) other noncooperative Stackelberg leader-follower model (Barro & Gordon, 1983;Blinder, 1982;Nordhaus, Schultze, & Fischer, 1994). Emergent literature extended the game analysis and complexities to include aspects such as credibility, political cycles, institutional setups, and rules governing the monetary and fiscal policymaking (Backus & Driffill, 1985;Kirsanova, Stehn, & Vines, 2005;Saulo, Rêgo, & Divino, 2013). However, what has received less attention is the information content of such rules, their analysis is limited to an investment decision or institutional design that shapes the outcomes of the game. ...
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This paper examines how rules and institutions and monetary-fiscal coordination setup impact welfare outcomes during political instability. Our theoretical model extends the analysis of Alesina and Tabellini (1987), Alesina and Gatti (1995), and Ferre and Manzano (2014) to examine the signaling content of the fiscal authority’s decision to engage in a fiscal reform when the policymaker’s preferences are private information. In a two-stage signaling game featuring a central banker, a government, and private agents, we examine the fiscal authority’s decision to engage in a fiscal reform under a Nash game, a cooperative setup, and a model of Stackelberg leadership. Three main results: 1) rules and commitments contribute to decreasing time inconsistency; 2) the more control the fiscal authority has over monetary policy, the more undesirable welfare outcomes, especially during political instability; 3) central bank independence signals fiscal discipline and produces relatively more desired outcomes during times of political uncertainty. Nevertheless, even with low degrees of central bank independence, proper fiscal “rules” produce close outcomes of an independent central bank even under the dominance of a centralized political authority and can secure close welfare gains in terms of inflation and fiscal outcomes. We propose these theoretical findings for empirical examination in emerging countries with prevailing schemes of fiscal dominance and more dependence on discretionary interventions to secure growth rates and financing gaps. Such setups are argued to contribute to lowering welfare outcomes that could be reduced if proper fiscal rules were used as a substitute for low monetary independence.
... The use of these models allows to observe the problems also arising from the conflict of monetary and fiscal authorities (Payer 1974). A lack of such coordination was criticised, e.g., by Nordhaus (1994) and Saulo et al. (2013). ...
Our aim is to identify periods of restrictive versus expansionary economic policy in the euro area in the last two decades. We firstly conducted the study for identifying the dominant trend in fiscal policies and then in monetary policies. We studied several fiscal outputs, focusing on the cyclical adjusted primary balance. We also analysed the European long-term and short-term interest rates. The study was conducted for several windows, namely for 3-, 4- and 5-year periods. Additional procedures were conducted for robustness checks, namely the study of structural breaks in the analysed time series as well as a study of them recurring to Markov-Switching Regimes models. For most of the analysed periods and subperiods of the series, we concluded for the presence of expansionary policies either in the fiscal or in monetary European domains. Finally, the results and the analysis of dependencies in the euro area economy favour the evidence that economic authorities in the euro area have sought to coordinate monetary and fiscal policy to stabilise the economy.
... Another study by Santos (2010) using the game theoretic approach and categorizing the policy interaction from perfect coordination to complete lack of coordination, found that policy mix outcome is sub-optimal in the case of lack of coordination. Utilizing the leader-follower model, he emphasized that both monetary and fiscal policy makers should first consider each other's policy reaction functions before setting the desire targets, for in so doing, policy mix strategy would gain more promising results. ...
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1. Background to the Study This study is carried out to assess the impact of the interaction of monetary and fiscal policy coordination on the economic performance in Nigeria. Monetary and fiscal policies play a crucial role in providing sustainable and credible economic stability in the country, thus creating the environment for rapid economic growth and development. But the precondition for a successful functioning of any economy is the existence of effectively coordinated activities of policies. The economy will suffer from poor overall economic performance if these policies are not well articulated. Both monetary and fiscal policies in Nigeria are, by all intent, mutually dependent though conducted by two separate authorities-the fiscal and monetary authorities. Therefore, it is expedient to accomplish a consistent and sustainable policy-mix framework within which monetary and fiscal policies can be harmonized to avoid possible inconsistencies (Rakia and Radenovic, 2013). The dramatic economic fluctuations after the great depression of the 1930s puts pressure on policy makers all over the world to direct their attention to the accountability of monetary and fiscal policies in the supply and demand management to a greater extent. Their focus was on selecting the most suitable policy option for low inflation with a near full-employment level of output. This was pioneered by Friedman (1948) who emphasized self-sustaining policies for long-term economic prosperity and stressed that increasing the quantity of money in circulation will prevent sluggish economic condition. This view of the monetarist became popular and monetary policy became a leading policy choice to curb inflation and raise output level. Although inflationary rate declined, but the expected results were marginal because unemployment rate went up. This made policy makers to believe that there is a trade-off between unemployment and inflation in the long-term and therefore, policy focus turned to the short-term and priorities were given to fiscal policy during the 1960s. This thought process was stimulated by the Keynesian ideology which demonstrates that short-term macroeconomic forecasting is an essential part of stabilization and capable of speedily achieving full employment level. This, they argued, can be fulfilled through an effective management of aggregate demand which should be done through effective implementation of monetary and fiscal policy. As a result, tight monetary policies were adopted during the 1960s while allowing fiscal stimulus packages. This too, was short-lived and began to disappear in the 1970s following the dramatic rise in the prices of crude oil and food exports. During this period, neither increase in government spending nor tax cut impacted positively to reduce rising inflation and unemployment in general. Although the situation improves Abstract: Fiscal and monetary policies have been adjudged by scholars to have strong implications for economic performance of countries across the globe. This paper assesses the impact of the interaction of monetary and fiscal policy coordination on the economic performance of Nigeria. The study adopted an econometric method in analyzing data which were obtained mainly from secondary sources, especially the CBN statistical bulletins. The estimation techniques used in the study are the Auto-Regressive Distributed Lag (ARDL) model, the Granger Causality and Vector Auto-regression. The data were tested for stationarity using ADF (1979) methods. The results obtained shows that all monetary variables react strongly to changes in fiscal variables except interest rate. Inflation and external debt are negatively signed in both long run and short run, implying that an increase in both variables will have a negative effect on economic performance. Also, the coefficient of INTR and FGRRg has positive impact in the long run, meaning that an increase in both will have a positive impact on economic performance. Also, the elasticity status of our model shows that while INTR, RGDPg and INF rate and their lags had coefficient of elasticity less than one, EXDBT and FGRRg and their lags had coefficients greater than one. Thus, it could be concluded from the findings that fiscal policy measures exert greater impact on the level of economic performance in Nigeria, than monetary policy. The study made some policy recommendations, which if implemented, could increase the level of interaction between fiscal and monetary policies and enhance their coordination for improved economic performance in the country.
This study investigates whether monetary and fiscal policies are consistent in reaction to the demand pressure and inflationary conditions. To answer this question, the coordination between monetary and fiscal policies was examined for the period 1988:1-2021:4, based on Demid’s approach (2018) and using a model with time-varying parameters (TVP). Following the study of Kuttner (2016) in the framework of game theory, Nash equilibrium, scenarios for the interaction of these two policies were extracted in the policy matrix. The results confirm that two periods, from the first quarter of 1992 to the second quarter of 1992 (two seasons) and also from the second quarter of 2011 to the third quarter of 2011 (two seasons), were the only ones in which monetary and fiscal policymakers simultaneously and consistently tried to reduce the inflation gap. Also, in the first three seasons of 2006 and the second quarter of 2008 to the end of 2009 (7 seasons), the monetary and fiscal authorities reacted positively to the negative output gap simultaneously and had a counter-cyclical reaction to reduce the output gap in a coordinated manner. Based on these results and in the framework of the policy matrix, the Central Bank of Iran has been submissive to fiscal policies for most of the years. Therefore, it is suggested that to strengthen coordination between fiscal and monetary policymakers, establishment of some institutional arrangements and legal frameworks should be on the agenda, including the implementation of both fiscal rules and inflation targeting, and setting a legal framework for strengthening the central bank independence.
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Purpose Since the first moment of the pandemic, national and international travel restrictions are in place to reduce human mobility. This actual situation makes the tourism industry one of the areas most affected by the pandemic. Many microeconomic factors (households and firms) were adversely affected by the pandemic, and this situation brought about macroeconomic contraction. Naturally, governments seek to sustain production and employment by offering financial packages to reduce the negative economic effects of the pandemic. Given such information, the study aims to examine the financial policies implemented by countries to support the tourism industry during the pandemic period. Design/methodology/approach Content analysis, which is a technique of qualitative research method, was applied in the analysis process of the data. Assessments were made based on data published by the United Nations World Tourism Organization (UNWTO) on the financial and monetary policies implemented by countries to support the tourism industry. The data were analyzed using the MAXQDA qualitative analysis program. Findings According to the results of the study, countries support the tourism industry financially in terms of credit and liquidity. Also, tourism investments are encouraged by tax breaks and low interest rates. Originality/value It is aimed to determine what issues the financial and monetary policies published by the UNWTO focus on to solve the problems in the tourism sector. In this way, it is thought that the study will reveal the problems experienced by tourism enterprises during the pandemic period with a holistic perspective.
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The aim of this study is to verify whether there is fiscal or monetary dominance in the Brazilian economy in the period of the post-Real pl an. We investigate the long run equilibrium relationship and bivariate and multivar iate Granger causality among the variables nominal interest rate, debt to GDP ratio, primary s urplus to GDP ratio, real exchange rate and risk premium. The results have shown Brazil as a co untry under monetary dominance regime, according to Sargent and Wallace (1981) definition. In addition, the model proposed by Blanchard (2004) does not find empirical support in the Brazilian economy.
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The aim of the present paper is to verify the predominance of a monetary or fiscal dominance regime in Brazil in the post-Real period. The analysis is based on a model proposed by Canzoneri, Cumby and Diba (2000). This model proposes that there is a relationship between the public debt/GDP and primary surplus/GDP series by using the vector autoregression (VAR) framework and analyzing the impulse response functions. Another aim is the extension of the article written by Muscatelli et al. (2002) about the interactions between monetary and fiscal policies using the Markov-switching vector autoregressive model (MS-VAR) introduced by Krolzig (1997), since the relationship between these policies may not be constant over time. In conclusion, the macroeconomic coordination between monetary and fiscal policies in Brazil was virtually a substitute policy throughout the study period, with a predominantly monetary regime, in opposition to the non-Ricardian policies of the Fiscal Theory of The Price Level.
With the collapse of the Bretton Woods system, any pretense of a connection of the world's currencies to any real commodity has been abandoned. Yet since the 1980s, most central banks have abandoned money-growth targets as practical guidelines for monetary policy as well. How then can pure "fiat" currencies be managed so as to create confidence in the stability of national units of account. Interest and Prices seeks to provide theoretical foundations for a rule-based approach to monetary policy suitable for a world of instant communications and ever more efficient financial markets. In such a world, effective monetary policy requires that central banks construct a conscious and articulate account of what they are doing. Michael Woodford reexamines the foundations of monetary economics, and shows how interest-rate policy can be used to achieve an inflation target in the absence of either commodity backing or control of a monetary aggregate.The book further shows how the tools of modern macroeconomic theory can be used to design an optimal inflation-targeting regime--one that balances stabilization goals with the pursuit of price stability in a way that is grounded in an explicit welfare analysis, and that takes account of the "New Classical" critique of traditional policy evaluation exercises. It thus argues that rule-based policymaking need not mean adherence to a rigid framework unrelated to stabilization objectives for the sake of credibility, while at the same time showing the advantages of rule-based over purely discretionary policymaking.
This paper studies the interactions of fiscal policy and monetary policy when they stabilize a single economy against shocks in a dynamic setting. If both policy-makers are benevolent, then, in our model, the best outcome is achieved when monetary policy does nearly all of the stabilization. If the monetary authorities are benevolent, but the fiscal authority discounts the future, or aims for an excessive level of output, then a Nash equilibrium will result in large welfare losses: after an inflation shock there will be excessively tight monetary policy, excessive fiscal expansion, and a rapid accumulation of public debt. However, if, in these circumstances, there is a regime of fiscal leadership, then the outcome will be very nearly as good as when both policy-makers are benevolent.
In this paper, we study macroeconomic stabilization in the Economic and Monetary Union(EMU) using a dynamic games approach. In modeling this problem, it turns out that theplayers include the time derivative of the state variable of the game in their performancecriterion. As far as the authors know, this kind of problem has not before been dealt withrigorously in dynamic games theoretic literature. Therefore, we first consider a generalizationof the linear-quadratic differential game, in which we allow for cross terms in theperformance criteria. Following the analysis of Engwerda [10,12], we present formulas tocalculate open-loop Nash equilibria for both the finite-planning horizon and the infinite-planninghorizon. Particular attention is paid to computational aspects. In the second part ofthis paper, we use the obtained theoretical results to study macroeconomic stabilization inthe Economic and Monetary Union (EMU).
RESUMO: Este trabalho busca identificar se a condução das políticas macroeconômicas, fiscal e monetária, no Brasil para o período pós-metas de inflação ocorreu de maneira ativa e/ou passiva. Para isso, foi estimado, pelo método Bayesiano, um modelo DSGE com rigidez de preços e concorrência monopolística, em que o superávit primário e a taxa de juros nominal são os instrumentos de política econômica disponíveis. A falta de coordenação dessas políticas no Brasil, freqüentemente, tem sido apontada como motivo para os desequilíbrios macroeconômicos, de modo que diversos autores apontaram a política fiscal ativa como fator restritivo ao desempenho eficiente da política monetária. Contudo, a análise dessas relações dentro do arcabouço dos modelos DSGE ainda é restrita, principalmente em aplicações para a economia brasileira. As estimações do modelo apontaram para um regime em que ambas as políticas foram ativas durante o período de 2000I a 2002IV, enquanto que para o período posterior, 2003I a 2008IV, a política fiscal comportou-se de maneira passiva e a política monetária foi ativa. ABSTRACT: This paper seeks to identify whether fiscal and monetary macroeconomic policies in Brazil were active and/or passive after the inflation targeting regime. To achieve that, we used the Bayesian method to estimate a