Fiscal dominance: |αβ| <1 and |β–1– γ | >1

In this region, monetary policy responds weakly to inflation (|αβ|<1) while fiscal policy does not respond

strongly to debt (|β-1—γ |>1). This regime also generates a single equilibrium. This is equivalent to the

situation described by Sargent and Wallace (1981) when they coined the expression “unpleasant

monetarist arithmetic”. In this case, monetary policy is passive and fiscal policy active. Now, the monetary

authority obeys the constraints imposed by fiscal policy.

There are two possible cases. The first arises when the two roots have modulus less than 1, i.e.

each authority is acting passively. Without an additional constraint imposed by one of the authorities to

take an active stance, there are many equilibrium-compatible money supply increase processes that

lead to price level indeterminacy, an outcome remarked by Sargent and Wallace (1975). In the second

case, the two roots have modulus greater than 1, so that both authorities are acting actively. Unless

shocks ψt

and μt

are supposed to be correlated, there is no process of increase in the money supply

that ensures that agents will finance government securities.

In light of the foregoing, some brief remarks are warranted on coordination between monetary,

fiscal and indeed exchange-rate policies, although the Leeper model (1991) does not address the

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Tito Belchior S. Moreira, Mario Jorge Mendonça and Adolfo Sachsida

last of these. Bearing in mind the trade-off between inflation and unemployment and the fact that in

1999 Brazil adopted an inflation-targeting system that implicitly admitted the prevalence of a monetary

dominance regime, a number of conjectures may be made.

If the central bank pursues lower inflation, even at the cost of higher unemployment, and the

Ministry of Finance pursues long-term public debt sustainability, the central bank will respond by raising

the Selic rate if inflation expectations rise. Similarly, fiscal policy will always seek to maintain a large

enough primary surplus to maintain public debt sustainability. This is an indication of coordination

between fiscal and monetary policymakers.

In other words, this is the policy that can ensure monetary dominance. Any other case must

correspond to a lack of coordination or, worse, a conflict of interest between policies. For example, if

the central bank tries to raise the base rate in order to keep inflation close to the target and fiscal policy

prioritizes increasing employment (a smaller surplus to boost aggregate demand) even at the expense

of inflation, the policy aims are contradictory. The opposite case, and cases in which both policies are

active or both passive, speak to policy conflicts, suggesting a lack of coordination between policymakers.

It may also be said that a deliberate policy of excessive build-up of foreign reserves can

generate adverse effects: on the one hand, it increases the monetization of the economy as a result of

foreign-exchange buying by the central bank, which pushes up inflation. On the other hand, to maintain

price stability, the central bank will be forced to issue repurchase agreements, which increases public

debt. The pass-through effect must also be borne in mind, whereby part of the exchange-rate variation

—whether rise or fall— is passed on to the rate of inflation.

III. Response function modelling

with regime-switching

The previous section presented the Leeper model (1991), which may be used to obtain the conditions to

determine whether policy is active or passive. From a practical point of view, it is necessary to ascertain

the fiscal and monetary policy rules, and on that basis to verify the stability of the model. On the basis

of the Leeper model (1991), Moreira, Souza and Almeida (2007) found evidence that Brazil underwent

a regime of fiscal dominance from 1995 to 2006.

The present study takes that literature further, taking as a basis the hypothesis that monetary and

fiscal policies may have undergone different regimes during the sample period analysed. The existence

of different regimes makes the conventional econometric techniques unsuitable to address the problem,

even working with different subsamples. A specific model is therefore used to treat supposed structural

breaks. That model allows the different stages undergone by monetary and fiscal policies since 2003

to be determined more clearly and accurately (Davig and Leeper, 2011). The model used to estimate

fiscal and monetary policy rules is discussed briefly below.

1. Markov-switching model

When a linear relationship undergoes a structural break —which can occur in the coefficients of the

variables, in the intercept and also in the variance of this relationship— the relevant parameters of the

regression model vary over time, producing non-linearities and, usually, violations of the stationarity and

normality hypotheses of the errors of conventional models. An alternative approach in this case is to

treat structural breaks (and, thus, “regime switches”) as exogenous, by introducing dummy variables

into the conventional linear models. However, this procedure requires advanced knowledge of the

86 CEPAL Review N° 135 • December 2021

Fiscal and monetary policy rules in Brazil: empirical evidence of monetary and fiscal dominance

precise moment at which breaks occurred, which in practice is rarely known. Even in the unlikely case

that the researcher “correctly guessed” the exact date of the relevant break or break, as well as their

respective durations, by itself the introduction of dummy variables does not resolve the problems

related to regime changes in the variance of the model errors. As Sims (2001) stated, it is a serious

error to disregard these or any other cause of residual non-normality when considering changes in the

parameters of the variables.

Markov-switching models explicitly assume that at any time there may be a finite (and generally

small) number of “regimes” or “states”, without knowing with certainty which obtains at that time. To cite

an intuitive example, it appears reasonable to suppose that an economy in recession will behave differently

(or have different parameters) to an economy that is growing rapidly. In this case, two “regimes” with

quite different characteristics —one “recessionary” and the other “fast-growing”— could be considered

to exist and to alternate every so often, without certainty as to which is occurring at each specific period.

Accordingly, Markov-switching models do not presume that “state switches”

—for example, the

passage from the “fast-growing” to the “recessionary” regime— are deterministic events. The hypothesis

is rather one of “probabilities of transition” from one regime to another, which are endogenous estimated

using Markov-switching models.3 There is nothing to prevent regime switches from being “once and

for all”, in other words after a switch a given regime may remain indefinitely.

Non-linear time series modelling has been gaining increasing importance for some time now

(Hamilton, 1989 and 1994; Krolzig, 1997; Kim and Nelson, 1999; Sims, 1999 and 2001; Franses and

Van Dijk, 2000; Lütkepohl and Kratzig, 2004). In the present study we use the Markov-switching model

to estimate fiscal and monetary response functions. We thus propose to specify each of these models

as follows:

y b S b S S t t m m t

P

0 mt t t 1

= + | v+ f = R R W W / R W (7)

with N S 0, t t 2 f v + S R WX;

where St

is an unobserved stochastic variable which determines the state k that the model assumes

in each period t.

Note that, ex hypothesis, the “latent variable” St

is governed by a stochastic process known as

the ergodic Markov chain and defined by matrix of transition probabilities whose elements are given by:

p S Pr j S i p 1 1 i j, , , k ij t t ij j

k

1 1 = = + ;

= = 0 d = R W,/ F ... I

pij ≥ 0 for i,j = 1, 2, ..., K (7.1)

Here, pij represents the probability that, in t + 1, the chain will switch from regime i to regime j.

The idea is thus that the probability of any regime St

occurring in the present depends solely on the

regime existing in the previous period, i.e. St–1. With k existing regimes, the probabilities of transition

between states may be represented by the matrix of transition probability P, with the dimension (k x k).

The parameters of this model are estimated via maximization of the model’s likelihood function

by means of the expectation–maximization (EM) algorithm (Dempster, Laird and Rubin, 1977), an

iterative technique for models with omitted or unobserved variables. It may be shown that the relevant

likelihood function increases with each iteration of this process, which ensures that the final result will be

3 More technically speaking, Markov-switching models fall within what Chib (1996) denominates “hidden Markov models”. For a

broad variety of these models, see Kim and Nelson (1999).

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Tito Belchior S. Moreira, Mario Jorge Mendonça and Adolfo Sachsida

close enough to the maximum likelihood in the relevant vicinity.4 However, it must be recalled that the

likelihood function of a Markov-switching models has no global maximum (Hamilton, 1991 and 1994;

Koop, 2003). Fortunately, the EM algorithm often yields a “reasonable” local maximum and pathological

cases are relatively rare (Hamilton, 1994).