# Brazil

The number of states chosen for Brazil has, like Sargent et al. (2009), a configuration for the process that follows the deficit of 3 states for the mean (low, intermediate, and high), and 2 for the variance (low and high). The estimates use as input the month-by-month, seasonally adjusted inflation in the period from April 1979 to October 2022.

#### Inflation and Seasonally Adjusted Inflation

Between 1980 and the end of the sample, Brazil's inflation history could be broadly divided into two periods. The first extends from 1980 to 1994. This period was characterized by high inflation; there were even two episodes of hyperinflation. The second period began in 1994 and was characterized by significantly lower inflation. This change could be associated with a series of structural reforms.

**Notes:**

Month-to-month percentage changes of the Consumer Price Index. (SE), refers to seasonally adjusted data

**Sample:**
April 1979 to October 2022.
**Source:**
With data from the Central Bank of Brazil.

##### Recent Inflation Data

#### Estimated parameters for the model

The following table shows the parameters resulting from the
numerical solution of the optimization problem for the
likelihood function associated with the SWZ model. Refer to
the model description for
a
discussion on the intuition behind the model. In addition, the
interested reader is referred to Sargent, Williams and Zha
(2009), and Ramos-Francia, García-Verdú and Sánchez-Martínez
(2018) for further details.

Below is a brief description of the model parameters.

The model assumes an adaptive inflation expectation mechanism with constant gain. This means that agents form their inflation expectation for the next period based on their expectation of the present period and the observed inflation. The parameter ν determines the weight that the agents give to the observed inflation to generate their expectation. Thus, a parameter ν close to 0 indicates that the agents take into account only their past inflation expectation. In contrast, a parameter ν close to 1 indicates that the agents only take into account the observed inflation. It is called constant because the ν parameter is fixed.

The parameter λ measures the sensitivity of the demand for money to changes in expected inflation and can take values between 0 and 1. In this model, such demand for money (in real terms) depends linearly and with a negative sign on the expected price level. In this model, such demand for money (in real terms) depends linearly and negatively on the expected price level.

It is assumed that the parameters of the deficit distribution follow two independent Markov processes. In these processes each state has an associated set of values that indicate the probability of remaining in the same state or of moving to a neighboring state in the next period. In the table, the probability of remaining in the same state is presented. If there is only one possible neighbor state, the probability of transiting to it is the unit minus the probability of remaining in the original state. On the other hand, if you are in a state with two possible neighboring states, it is assumed that there is the same probability of transiting to any of them.

The parameter σ(π) measures the standard deviation of the process that determines the adjustment of inflation and inflation expectations in the case of a cosmetic reform. In such a case, inflation and its expectations are readjusted to the value of the balance for the state of the average associated with the low level (which is stable) plus some noise.

**Notes:**
The standard errors of the parameters
are estimated using the Crámer-Rao bound. The point in the
case of the deficit parameter represents that it is not
possible to obtain a proper estimate for the standard error
because the parameter value is a corner solution of the
problem.

#### Discussion

At the beginning of the sample, estimates of the probabilities of states with an intermediate or high mean, as well as the variance, are dominant. Thus, there seems to be no indication that in the 1980s and until the mid-1990s, estimates of the probabilities of the state with a low mean are very different from zero.

From the mid-1990s, this situation was reversed. Estimates of the state's probabilities with a low average have predominated. The estimates of the probabilities only vary in terms of the weight they give to a low or a high variance.

Remarkably, over the past five years, the probability of the state with low average and low volatility has been gradually falling, with an increase in early 2019. Thus, in recent periods, the estimate of the probability of the state with low average and high volatility has increased.

This dynamic has two main aspects. On one hand, the fact that the estimate of the probability of being in the state of a low mean has remained at a high level, which could be considered favorable for the economy. On the other hand, the fact that the estimate of the probability of the state with high volatility has increased could be unfavorable.

Considering now the estimates of the probability of escape, we have two clear peaks, one in the late 1980s and the other in the early 1990s. Consider that the estimate of the probability of a cosmetic reform for Brazil does not seem to exceed levels beyond 0.3. This suggests that, if there had been any reform, it would have been fundamental in the sense of SWZ. Indeed, as mentioned in the description of the model, reforms can be either cosmetic or fundamental.

Since 1996, the estimate of the probability of escape has remained essentially at zero. On a positive note, this property was maintained during several years of crisis, including those associated with the global financial crisis, and also at the end of the sample.

Not only do the estimates seem sensible from an econometric point of view, they also largely coincide with the narrative of economic events in, for example, Ayres, Garcia, Guillén and Kehoe (2019).

##### Estimation of the probability of being in one of the states of the model (mean, variance)

**Note:**
To consider any state for the
**mean**
of the deficit, it is necessary to add the probabilities of the low and high states for the variance. For example, to consider the probability of being in the
**low**
state for the mean of the deficit it is necessary to add the probabilities of the states
(
**low**
,
low) and (
**low**
, high).

To view a subset of the states in the model, please click on the legends in the graph to show or hide the corresponding state.

**Sample:**
April 1979 to October 2022.
**Source:**
With data from the Central Bank of Brazil

##### Self-Confirmed Equilibrium (SCE) and Expected Inflation

The solutions of the differential equation that determine
the equilibrium levels for expected inflation are shown.
When the probabilities of remaining in each of the states of
the mean are close to one, these equilibrium levels are
considered to be good approximations.

Specifically, the crosses of each curve with the vertical axis, represented by horizontal lines, determine the stable (those with lower levels) and unstable (those with higher levels) levels of equilibrium.

**Source:**
With data from the Central Bank of
Brazil.

The closer inflation expectations are to the unstable equilibrium level associated with the state in which they are most likely to be, the greater the probability of escape. An escape event would trigger the need for reform to bring the level of inflation and its expectations back to stable levels.

**Sample:**
April 1979 to October 2022.
**Source:**
With data from the Central Bank of Brazil.

##### Estimation of the probability of escape

**Sample:**
April 1979 to October 2022.
**Source:**
With data from the Central Bank of Brazil.

#### References

**Ayres, J., Garcia, M., Guillén, D. A., & Kehoe, P. J. (2019).**"The monetary and fiscal history of Brazil: 1960-2016". NBER Working Paper No. w25421, National Bureau of Economic Research.